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\begin{flushright}
PM--02--39\\
CERN TH/2002--325\\
November 2002
\end{flushright}

\vspace{1.5cm}

\begin{center}

{\large\sc {\bf {\Large \tt  SuSpect}: a Fortran Code for the Supersymmetric}} 

\vspace*{3mm}

{\large\sc {\bf and Higgs Particle Spectrum in the MSSM\footnote{The program
with all relevant information can be downloaded from the web at the http site: 
{\tt www.lpm.univ-montp2.fr:6714/\~\,kneur/Suspect} or  obtained by sending an
E--mail to one of the authors, {\tt djouadi@lpm.univ-montp2.fr, 
kneur@lpm.univ-montp2.fr, moultaka@lpm.univ-montp2.fr}.}} }

\vspace*{9mm}
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\mbox{{\sc Abdelhak DJOUADI}$^{1,2}$, {\sc Jean--Lo\"{\i}c KNEUR}$^1$ 
and {\sc Gilbert MOULTAKA}$^1$}

\vspace*{0.9cm}

{\it $^1$ Laboratoire de Physique Math\'ematique et Th\'eorique, UMR5825--CNRS,
\\ Universit\'e de Montpellier II, F--34095 Montpellier Cedex 5, France.} \s

{\it $^2$ Theory  Division, CERN, CH--1211 Gen\`eve 23, Switzerland.}

\end{center}

\vspace{1cm}

\begin{abstract}

\nn We present the {\sc Fortran} code {\tt SuSpect} version 2.1, which calculates the
Supersymmetric and Higgs particle spectrum in the Minimal Supersymmetric
Standard Model (MSSM). The calculation can be performed in constrained models 
with universal boundary conditions at high scales such as the gravity (mSUGRA),
anomaly (AMSB) or gauge (GMSB) mediated breaking models, but also in the 
non--universal MSSM case with R--parity and CP conservation. Care
has been taken to treat important features such as the renormalization group
evolution of parameters between low and high energy scales, the consistent
implementation of radiative electroweak symmetry breaking and the calculation
of the physical masses of the Higgs  bosons and supersymmetric particles taking
into account the dominant radiative corrections. Some checks of important
theoretical and experimental features,  such as the absence of non desired
minima, large fine-tuning in the electroweak symmetry breaking condition, as
well as agreement with precision measurements can be performed.  The program is
user friendly, simple to use, self--contained and can  easily be linked
with other codes; it is rather fast and flexible, thus allowing scans of  
the parameter space with several possible options and choices  for model
assumptions and approximations.
\end{abstract}

\newpage

\begin{center}
{\bf CONTENTS} 
\end{center} 

{\bf 1. Introduction} \hfill 4\sx

{\bf 2. The constrained and unconstrained MSSMs} \hfill 7\s

\hspace*{0.20cm} 2.1 The unconstrained MSSM \hfill 7\s

\hspace*{0.20cm} 2.2 The ``phenomenological" MSSM \hfill 9\s

\hspace*{0.20cm} 2.3 The mSUGRA model \hfill 10\s

\hspace*{0.20cm} 2.4 The AMSB model  \hfill 11\s

\hspace*{0.20cm} 2.5 The GMSB model  \hfill 13\s

\hspace*{0.20cm} 2.6 Non--universal models  \hfill 15\sx

{\bf 3. The Particle Spectrum Calculation with {\tt Suspect}}  \hfill 17\sx

\hspace*{0.2cm} 3.1 General algorithm\s  \hfill 17\s

\hspace*{0.2cm} 3.2 Calculation of the soft SUSY--breaking terms  \hfill 19\\
 \hspace*{1.5cm} 3.2.1 Choice and treatment of the SM input  \hfill 19\\
 \hspace*{1.5cm} 3.2.2 Renormalization Group Evolution  \hfill 20\\
 \hspace*{1.5cm} 3.2.3 Electroweak Symmetry Breaking \hfill 22\s

 \hspace*{0.2cm} 3.3 Calculation of the physical particle masses  \hfill 23\\
 \hspace*{1.5cm} 3.3.1 The sfermion sector  \hfill 24\\
 \hspace*{1.5cm} 3.3.2 The gaugino sector  \hfill 24\\
 \hspace*{1.5cm} 3.3.3 The Higgs sector  \hfill 25\s

 \hspace*{0.2cm} 3.4 Theoretical and Experimental Constraints on the spectra
 \hfill  27 \\
 \hspace*{1.5cm} 3.4.1 CCB and UFB  \hfill 27\\
 \hspace*{1.5cm} 3.4.2 Fine--Tuning  \hfill 28\\
 \hspace*{1.5cm} 3.4.3 Electroweak precision measurements \hfill 28\\
 \hspace*{1.5cm} 3.4.4 The muon $(g-2)$  \hfill 29\\
 \hspace*{1.5cm} 3.4.5 The radiative decay $b \to s\gamma$  \hfill 30\s

 \hspace*{0.2cm} 3.5 Scanning the parameter space  \hfill 31\sx


{\bf 4. Running {\tt SuSpect}}  \hfill 34\sx

 \hspace*{0.2cm} 4.1 Basic facts about \sus\  \hfill 34\s

 \hspace*{0.2cm} 4.2 The input file  \hfill 35\s
 
 \hspace*{0.2cm} 4.3 The output files \hfill 38\\
  \hspace*{1.5cm} 4.3.1 The output in the pMSSM case  \hfill 38\\
  \hspace*{1.5cm} 4.3.2 The output in the mSUGRA case  \hfill 40\\
  \hspace*{1.5cm} 4.3.3 The output in the  GMSB case  \hfill 42 \\
  \hspace*{1.5cm} 4.3.4 The output in the AMSB case  \hfill 44\newpage
 

{\bf 5. Calculations with {\tt SuSpect} } \hfill 46\sx

 \hspace*{0.2cm} 5.1 Comparison with other codes  \hfill 46\s
 
 \hspace*{0.2cm} 5.2 Interface with other programs  \hfill 47\s

 \hspace*{0.2cm} 5.3 Future upgrades  \hfill 48\sx 

 \hspace*{0.2cm} 5.4 Web information and maintenance  \hfill 50\sx
 

{\bf 6. Summary of changes compared to previous versions}  \hfill 52\sx

\hspace*{0.2cm}  6.1 The version \sus\ 1.0 \hfill 52\s

\hspace*{0.2cm}  6.2 The version \sus\ 2.0 \hfill 52\s
 
\hspace*{0.2cm}  6.3 The version \sus\ 2.1 \hfill 53\sx

{\bf 7. Conclusion}  \hfill 54\sx

{\bf Appendix A: Some analytic expressions used in \sus } \hfill 56\s

 \hspace*{0.2cm} A.1 Renormalization Group Evolution \hfill 56\s
 
 \hspace*{0.2cm} A.2 The one-loop scalar potential and EWSB \hfill 60\s
 
 \hspace*{0.2cm} A.3 The particle spectrum \hfill 62\\
 \hspace*{1.6cm} A.3.1 Diagonalization of the mass matrices \hfill 62\\
 \hspace*{1.6cm} A.3.2 Radiative corrections to the fermion masses \hfill 63\\  
 \hspace*{1.6cm} A.3.3 Radiative corrections to the sparticle masses \hfill 64\\
 \hspace*{1.6cm} A.3.4 Radiative corrections to the Higgs boson masses \hfill 
66\sx

{\bf Appendix B: Contents of the Fortran Code} \hfill 67\sx

\hspace*{0.2cm} B.1 The subroutines and their main purpose \hfill 67\\
\hspace*{1.6cm} B.1.1 The main routine\hfill 67\\
\hspace*{1.6cm} B.1.2 Routines for the models \hfill 68\\
\hspace*{1.6cm} B.1.3 Routines for the fermion masses and $\alpha_s$ \hfill 70\\
\hspace*{1.6cm} B.1.4 Routines for SUSY and Higgs particle masses\hfill 71\\
\hspace*{1.6cm} B.1.5 Routine for the EWSB \hfill 74\\
\hspace*{1.6cm} B.1.6 Routines for the RGEs \hfill 74\\
\hspace*{1.6cm} B.1.7 Routines for the checks of the spectrum \hfill 76\s


\hspace*{0.2cm} B.2 List of the various Commons \hfill 78\\
\hspace*{1.6cm} B.2.1 Commons for input parameters \hfill 78\\
\hspace*{1.6cm} B.2.2 Commons for output masses and mixing angles \hfill 79\\
\hspace*{1.6cm} B.2.3 Internal Commons \hfill 79\s

\hspace*{0.2cm} B.3 Example of a calling routine \hfill 81\sx

{\bf References} \hfill 88


\newpage

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\section*{1. Introduction} 

Supersymmetric theories (SUSY) \cite{SUSY}, which provide an elegant way to
stabilize the large hierarchy between the Grand Unification (GUT) and the
electroweak scales and to cancel the quadratic divergences of the radiative
corrections to the Higgs boson masses, are by far the most studied extensions 
of the Standard Model (SM). The most economical low--energy SUSY extension of
the SM, the Minimal Supersymmetric Standard Model (MSSM), which allows for a
consistent unification of the SM gauge couplings  and provides a natural
solution of the Dark Matter problem, has been widely investigated; for reviews
see Refs.~[2-5]. As a corollary, the search for  Supersymmetric particles and
for the extended Higgs spectrum  has become the main goal of present and future
high--energy colliders  \cite{searches}.  \s

It is well--known that in the unconstrained MSSM, it is a rather tedious task
to deal with the basic parameters of the Lagrangian and to derive in an exhaustive 
manner their relationship with the physical parameters, i.e. the particle masses 
and couplings. This is mainly due to the fact that in  the
MSSM, despite of the  minimal gauge group, minimal particle content, minimal
couplings imposed by R--parity conservation and the minimal set of soft
SUSY-breaking parameters, there are more than hundred new parameters 
\cite{parameters}. Even if one constrains the model to have a viable
phenomenology [we will call later such a model the phenomenological MSSM],
assuming for instance no intergenerational mixing to avoid flavor changing
neutral currents, no  new source of CP violation, universality of first
and second generation  sfermions to cope with constraints from kaon physics,
etc.., there are still more than 20 free parameters left.  This large number of
input enters in the evaluation of the masses of ${\cal O}(30)$ SUSY particles
and Higgs bosons as well as their complicated couplings, which involve several
non--trivial aspects, such as the mixing between different states, the Majorana
nature of some particles, etc.  The situation becomes particularly difficult if
one aims at rather precise calculations and hence, attempts to include some
refinements such as higher order corrections, which for the calculation of a
single parameter need the knowledge of a large part of, if not the whole,
spectrum. \s

Thus, the large number of free parameters in the unconstrained or even
phenomenological MSSM, makes a detailed phenomenological analysis of the
spectra and the comparison with the outcome or expectation from experiment, a
daunting task, if possible at all. Fortunately, there are well motivated
theoretical models where the soft SUSY--breaking parameters obey a number of
universal boundary conditions at the high (GUT) scale, leading to only a handful set
of basic parameters. This is the case for instance of the minimal Supergravity
model (mSUGRA) \cite{mSUGRA}, where it is assumed that SUSY--breaking occurs in
a hidden sector which communicates with the visible sector only through
``flavor--blind'' gravitational interactions. This leads to the simpler
situation where the entire spectrum of superparticles and Higgs bosons is
determined by the values of only five free parameters and makes comprehensive
scans of the parameter space and detailed studies of the spectrum feasible.\s

However, there are also similarly constrained and highly predictive 
alternative SUSY--breaking models in the literature, such as anomaly mediated
\cite{AMSB,AMSBp} or gauge mediated \cite{GMSB,GMSBp} SUSY--breaking models for
instance, which should be investigated as well. We then have to trade a
complicated situation where we have one model with many input parameters, with
a not less complicated situation where we have many models with a small number
of basic parameters. In addition, in these unified models, the low--energy
parameters are derived from the high--energy (GUT and/or possibly some
intermediate scales) input parameters through Renormalization Group Equations
(RGE) and they should also necessarily involve radiative electroweak symmetry
breaking (EWSB), which sets additional constraints on the model.  The
implementation of the RG evolution and the EWSB mechanism poses numerous
non--trivial technical problems if they have to be done in an accurate way,
i.e. including higher order effects. This complication has to be added to the
one from the calculation of the particle masses and couplings with radiative
corrections (RC) which is still present.\s

Therefore, to deal with the supersymmetric spectrum in all possible cases, one
needs very sophisticated programs to encode all the information and,
eventually, to pass it to other programs or Monte Carlo generators to simulate
the physical properties of the new particles, decay branching ratios,
production cross sections at various colliders, etc... These programs should
have a high degree of flexibility in the choice of the model and/or the input
parameters and an adequate level of approximation at different stages, for
instance in the incorporation of the RGEs, the handling of the EWSB  and the
inclusion of radiative corrections to (super)particle masses, which in many cases
can be very important. They should also be reliable, quite fast to allow for
rapid comprehensive scans of the parameter space and simple enough to be linked
with  other programs.  There are several public codes, in particular {\tt
ISASUGRA} \cite{ISASUGRA}, {\tt SOFTSUSY} \cite{SOFTSUSY} and {\tt SPHENO}
\cite{SPHENO}, as well as a number of private codes, which deal with this
problem.  In this paper we present our program \sus. \s

{\tt SuSpect}, in the version 2.1 that we present here, is a {\sc Fortran} 
code which calculates the supersymmetric and Higgs particle spectrum in the
constrained  and unconstrained MSSMs. The acronym is an abbreviation of SUsy
SPECTrum and a  preliminary version of the program is available since some time
and has been  described in Ref.~\cite{SUSPECT}. At the present stage, it deals
with the ``phenomenological  MSSM" with 22 free parameters defined  either at a
low or high energy scale, with the  possibility of RG evolution to arbitrary
scales, and the most studied  constrained models, namely mSUGRA, AMSB and GMSB.
Many ``intermediate" models  [e.g. constrained models but without unification
of gaugino or scalar masses,  etc..] are also easily  handled.  The program
includes the three major ingredients  which should be incorporated in any
algorithm for the constrained MSSMs:  
%
$i)$ renormalization group evolution of parameters between the low
energy scale [$M_Z$ and/or the electroweak symmetry breaking scale] and the
high--energy scale [17--19]; 
%
$ii)$ consistent implementation of radiative electroweak symmetry
breaking [loop corrections to the effective potential are included using the 
tadpole method] [20--23];  
%
$iii)$ calculation of the physical (pole) masses of the superparticles and 
Higgs bosons, including all relevant features such as the mixing between  
various states [diagonalization of mass matrices] and the radiative corrections
when important [24--31]. \s


The code contains two source files: the main subroutine {\tt suspect2.f} and  a
separate calling routine file {\tt suspect2$\_$call.f}, plus one input file,
{\tt suspect2.in}. Any choice and option is driven either from the input file
[which is sufficient and convenient when dealing with a few model points]  or
from the {\tt suspect2$\_$call.f} file, which also provides examples of call
for different model choices with all the necessary features [this option is
useful to interface with other routines or to perform scans of the parameter
space].  The program has several flags which allow to select the model to be
studied and its input parameters, the level of accuracy of the algorithm [e.g.
the iterations for the RGEs and the convergence of the EWSB], the level of
approximation in the calculation of the various (s)particle masses [e.g. 
inclusion or not of RC].   Besides the fact that it is  flexible, the code is
self--contained [the default version includes all routines needed for the
calculation], rather fast [thus allowing large scans of the parameter space]
and can be easily linked to other routines or Monte--Carlo generators [e.g.\,to
calculate branching ratios, cross sections, relic densities]. All results,
including comments when useful and some theoretical and experimental
constraints, are found in the output file {\tt suspect2.out} which is
created at any run of the program. It is hoped that  the code may be readily 
usable even without much prior knowledge on the MSSM.\s

This ``users' manual" for the program, is organized as follows. In section 2,
we briefly discuss the main ingredients of the unconstrained and
phenomenological  MSSMs as well as the constrained models mSUGRA, AMSB and
GMSB, to set the  notations and conventions used in the program. In section 3,
we summarize the procedure for the calculation of the (s)particle spectrum: 
the soft SUSY--breaking terms [including the treatment of the input, the RG
evolution and the implementation of EWSB], the physical particle masses
[summarizing our conventions for the sfermion, gaugino and Higgs sectors] as
well as the theoretical [CCB, UFB, fine-tuning] and experimental [electroweak
precision measurements, the muon $g-2$, $b \to s \gamma$] constraints that we 
impose on the spectra, and  give an example on how it can be used for scans. In
section 4, we summarize the basic  practical  facts about the program  and  
discuss the content of the input and  output files with all possible choices.
In section 5, we make a brief comparison with other similar existing codes, 
discuss the interface with other programs, the maintenance on the web  and some
future improvements. In section 6, we list the main changes from the  previous
versions of the code. A conclusion will be given in section 7. In Appendix A,
we list some of the analytical formulae used in the program and in Appendix B,
the various subroutines and functions used in the program  are  explicited.

\newpage


\section*{2. The constrained and unconstrained MSSMs}

In this section, we will summarize the basic assumptions which define the MSSM
and the various constraints which can be imposed on it. This will also set the
notations and conventions used in the program. We will mainly focus on the
unconstrained MSSM, what we will call the phenomenological MSSM with 22 free
parameters,  and constrained models such as the minimal Supergravity (mSUGRA),
anomaly mediated  (AMSB) and gauge mediated (GMSB) supersymmetry breaking
models.  


\subsection*{2.1 The unconstrained MSSM} 

The unconstrained MSSM is defined usually by the following four basic assumptions
\cite{MSSMdef,mSUGRA}:\s

\nn {\it (a) Minimal gauge group:}  the MSSM is based on the group  ${\rm
SU(3)_C \times  SU(2)_L \times  U(1)_Y}$, i.e. the SM symmetry. SUSY implies
then that the spin--1 gauge bosons and their spin--1/2 partners, the gauginos
[bino $\tilde{B}$, winos $\tilde{W}_{1-3}$ and gluinos $\tilde{G}_{1-8}$], are
in vector  supermultiplets.\s

\nn {\it (b) Minimal particle content:} there are only three generations of
spin--1/2 quarks and leptons [no right--handed neutrino] as in the SM. The
left-- and right--handed chiral fields belong to chiral superfields together
with their spin--0 SUSY partners, the squarks and sleptons: ${\hat{ Q}}, {\hat{
u}}_{R}, {\hat{ d}}_{R}, {\hat{ L}},  {\hat{ l}}_{R}$. In addition, two chiral
superfields $\hat{H}_d$, $\hat{H}_u$ with respective hypercharges $-1$ and $+1$
for the cancellation of chiral anomalies, are needed. Their scalar components,
$H_d$ and $H_u$, give separately masses to the isospin +1/2 and $-$1/2 fermions
and lead to five Higgs particles: two CP--even $h,H$ bosons, a pseudoscalar $A$
boson  and two charged $H^\pm$ bosons. Their spin--1/2 superpartners, the
higgsinos, will mix with the winos and the bino, to give the ``ino" mass 
eigenstates: the two charginos $\chi_{1,2}^\pm$ and the four neutralinos
$\chi^0_{1,2,3,4}$. \s

\nn {\it (c) Minimal Yukawa interactions and R--parity conservation:} to
enforce lepton  and baryon  number conservation, a discrete and multiplicative
symmetry called R--parity is imposed.  It is defined by $R_p= (-1)^{2s+3B+L}$,
where L and B are the lepton and baryon numbers and $s$ is the spin quantum
number. The R--parity quantum numbers are then $R_p=+1$ for the ordinary
particles [fermions, gauge and Higgs bosons], and $R_p=-1$ for their
supersymmetric partners. In practice, the conservation of $R$--parity has
important consequences: the SUSY particles are always produced in pairs, in
their decay products there is always an odd number of SUSY particles, and the
lightest SUSY particle (LSP) is absolutely stable.  \s

The three conditions listed above are sufficient to completely determine  a
globally supersymmetric Lagrangian. The kinetic part of the Lagrangian is
obtained by generalizing the notion of covariant derivative to the SUSY case.
The most general superpotential, compatible with gauge invariance, 
renormalizability and R--parity conservation is written as: 
\begin{equation}
W=\sum_{i,j=gen} - Y^u_{ij} \, {\hat {u}}_{Ri} \hat{H_u}.{\hat{ Q}}_j+
     Y^d_{ij} 
\, {\hat{ d}}_{Ri} \hat{H}_d.{\hat{ Q}}_j+
       Y^l_{ij} \,{\hat{ l}}_{Ri} \hat{H}_u.{\hat{ L}}_j+
     \mu \hat{H}_u.\hat{H}_d
\label{defW}
\end{equation}
The product between SU(2)$_{\rm L}$ doublets reads $H.Q \equiv \epsilon_{a b}
H^a Q^b$ where $a, b$ are SU(2)$_{\rm L}$ indices and $ \epsilon_{12}=1 = -
\epsilon_{21}$, and $Y^{u,d,l}_{ij}$ denote the Yukawa couplings among
generations. The first three terms in the previous expression are nothing else
but a superspace generalization of the Yukawa interaction in the SM, while the 
last term is a globally supersymmetric Higgs mass term.  The supersymmetric 
part of the tree--level potential $V_{\rm tree}$ is the sum of the  so--called
F-- and D--terms \cite{DF}, where the F--terms come from the superpotential  through
derivatives with respect to all scalar fields  $\phi_{a}$, $V_{F}={\sum_{a} 
|W^{a}|^2}$ with $W^{a} = \partial{W}/\partial{ \phi_a}$, and the D--terms 
corresponding to the ${\rm U(1)_Y}$, ${\rm SU(2)_L}$, and ${\rm  SU(3)_C}$
gauge symmetries  are given by $V_{D}= \frac{1}{2}  \sum_{i=1}^{3}  (\sum_{a}
g_i \phi_a^* T^i \phi_a)^2$ with $T^i$ and $g_i$ being the generators  and the
coupling constants of the corresponding gauge groups. \bigskip

\nn {\it (d) Minimal set of soft SUSY--breaking terms:} 
to break Supersymmetry, while preventing the reappearance of the quadratic
divergences [soft breaking], one adds to the supersymmetric Lagrangian a set
of terms which explicitly but softly break SUSY \cite{mSUGRA}: 
\begin{itemize} 
\item[$\bullet$] Mass terms for the gluinos, winos and binos:
\beq
- {\cal L}_{\rm gaugino}=\frac{1}{2} \left[ M_1 \tilde{B}  
\tilde{B}+M_2 \sum_{a=1}^3 \tilde{W}^a \tilde{W}_a +
M_3 \sum_{a=1}^8 \tilde{G}^a \tilde{G}_a  \ + \ {\rm h.c.} 
\right]
\eeq
\item[$\bullet$] Mass terms for the scalar fermions: 
\beq
-{\cal L}_{\rm sfermions} = 
{\sum_{i=gen} m^2_{{\tilde {Q}}i} {\tilde{Q}}_i^{\dagger}{\tilde{Q}}_i+
m^2_{{\tilde{ L}}i} {\tilde{L}}_i^{\dagger} {\tilde{L}}_i +
         m^2_{ {\tilde{u}}i} |{\tilde{u}}_{R_i}|^2+m^2_{ {\tilde{d}}i} 
|{\tilde{d}}_{R_i}|^2+  m^2_{{\tilde{l}}i} | {\tilde{l}}_{R_i}|^2}   
\eeq
\item[$\bullet$] Mass and bilinear terms for the Higgs bosons: 
\beq
-{\cal L}_{\rm Higgs} = m^2_{H_u} H_u^{\dagger} H_u+m^2_{H_d}  H_d^{\dagger} 
H_d + B \mu (H_u.H_d + {\rm h.c.} ) 
\eeq
\item[$\bullet$] Trilinear couplings between sfermions and Higgs bosons 
\beq
-{\cal L}_{\rm tril.}= 
{\sum_{i,j=gen} { \left[ A^u_{ij} Y^u_{ij}  {\tilde{u}}_{R_i} H_u. 
{\tilde{Q}}_j+
A^d_{ij} Y^d_{ij}  {\tilde{d}}_{R_i} H_d.{\tilde{Q}}_j
+A^l_{ij} Y^l_{ij} {\tilde{l}}_{R_i} H_u.{\tilde{L}}_j\ + \ {\rm h.c.} 
\right] }}
\eeq
\end{itemize} 
The soft SUSY--breaking scalar potential is the sum of the three last terms:
\beq
V_{\rm soft} = -{\cal L}_{\rm sfermions} -{\cal L}_{\rm Higgs}-
{\cal L}_{\rm tril.}
\eeq
Up to now, no constraint is applied to this Lagrangian, although for generic
values of the parameters, it might lead to severe phenomenological problems, 
such as flavor changing neutral currents [FCNC] and unacceptable amount 
of additional CP--violation \cite{flavorev} color and charge breaking minima 
\cite{CCBold} an incorrect value of the $Z$ boson mass, etc... The MSSM 
defined by the four hypotheses $(a)$--$(d)$ above, will be called the 
unconstrained MSSM. 

\subsection*{2.2 The ``phenomenological" MSSM}

In the unconstrained MSSM, and in the general case where one allows for
intergenerational mixing and complex phases, the soft SUSY breaking terms will
introduce a huge number (105) of unknown parameters, in addition to the 19
parameters of the SM \cite{parameters}. This large number of free parameters makes any
phenomenological analysis in the general MSSM very complicated as mentioned
previously. In addition, many ``generic'' sets of these parameters are excluded by the
severe phenomenological constraints discussed above. A phenomenologically
viable MSSM can be defined by making the following three assumptions: 
$(i)$ All the soft SUSY--breaking parameters are real and therefore there is no
new source of CP--violation generated, in addition to the one from the CKM 
matrix.
$(ii)$ The matrices for the sfermion masses and for the trilinear couplings 
are all diagonal,  implying the absence of FCNCs at the tree--level.  $(iii)$
First and second sfermion generation universality at low energy to  cope with
the severe constraints from $K^0$--$\bar{K}^0$ mixing, etc [this is also 
motivated by the fact that one can neglect for simplicity all the masses of 
the first and second generation fermions which are small enough to have any 
effect on the running of the SUSY--breaking parameters].\s 

Making these three assumptions will lead to 22 input parameters only: \s

\nn \hspace*{2cm} $\tan \beta$: the ratio of the vevs of the two--Higgs doublet
fields.\\
 \hspace*{2cm} $m^2_{H_u}, m^2_{H_d}$: the Higgs mass parameters squared. \\
 \hspace*{2cm} $M_1, M_2, M_3$: the bino, wino and gluino mass parameters. \\
 \hspace*{2cm} $m_{\tilde{q}}, m_{\tilde{u}_R}, m_{\tilde{d}_R}, 
               m_{\tilde{l}}, m_{\tilde{e}_R}$: the first/second generation
 sfermion mass parameters.\\ 
  \hspace*{2cm} $m_{\tilde{Q}}, m_{\tilde{t}_R}, m_{\tilde{b}_R}, 
               m_{\tilde{L}}, m_{\tilde{\tau}_R}$: the third generation
 sfermion mass parameters.\\
  \hspace*{2cm} $A_u, A_d, A_e$: the first/second generation trilinear 
  couplings. \\
  \hspace*{2cm} $A_t, A_b, A_\tau$: the third generation trilinear couplings. \s

Two remarks can be made at this stage: \s
\vspace*{-1mm}

$(i)$ The Higgs--higgsino (supersymmetric) mass parameter $|\mu|$ (up to a
sign) and the soft SUSY--breaking  bilinear Higgs term $B$ are determined,
given the above parameters,  
through the electroweak symmetry  breaking conditions as will be discussed
later. Alternatively, one can trade  the values of $m^2_{H_u}$ and $m^2_{H_d}$
with the ``more physical" pseudoscalar Higgs boson  mass $M_A$ and parameter
$\mu$ [such an alternative choice is explicitly possible in \sus\ by
appropriate setting of the input parameters; see section 4]. \s 
\vspace*{-1mm}

$(ii)$ Since the trilinear sfermion couplings will be always multiplied by the
fermion masses, they are important only in the case of the third generation.
However, there are a few (low scale) situations, such as the  muon $(g-2)$ and
the neutralino--nucleon scattering for direct Dark Matter  searches, where they
will play a role. We therefore add them as input. \s

Such a model, with this relatively moderate number of parameters [especially
that, in general, only a small subset appears when one looks at a given sector
of the model] has much more predictability and is much easier to investigate
phenomenologically, compared to the unconstrained MSSM. We will refer to this 
22 free input parameters model as the  ``phenomenological" MSSM or pMSSM
\cite{GDR}. 

\subsection*{2.3 The mSUGRA model}

Almost all problems of the general or unconstrained MSSM are solved at once if
the soft SUSY--breaking parameters obey a set of universal boundary conditions
at the GUT scale. If one takes these parameters to be real, this solves all
potential problems with CP violation as well. The underlying assumption is that
SUSY--breaking occurs in a hidden sector which communicates with the visible
sector only through gravitational--strength interactions, as specified by
Supergravity.  Universal soft breaking terms then emerge if these Supergravity
interactions are ``flavor--blind'' [like ordinary gravitational interactions]. 
This is assumed to be the case in the constrained MSSM or minimal Supergravity
(mSUGRA) model \cite{mSUGRA}. \s

Besides the unification of the gauge coupling constants $g_{1,2,3}$ of the
U(1), SU(2) and SU(3) groups, which is verified given the experimental results
from LEP1 \cite{PDG} and which can be viewed as fixing the Grand Unification
scale $M_{\rm GUT} \sim 2 \cdot 10^{16}$ GeV \cite{LEPunif}, the unification
conditions in mSUGRA, are as  follows: \s

-- Unification of the gaugino [bino, wino and gluino] masses: 
\beq
M_1 (M_{\rm GUT})=M_2(M_{\rm GUT})=M_3(M_{\rm GUT}) \equiv m_{1/2}
\eeq

-- Universal scalar [i.e. sfermion and Higgs boson] masses [$i$ is the 
generation index]: 
\beq
M_{\tilde{Q}_i} (M_{\rm GUT}) &=& M_{\tilde{u}_{Ri}} (M_{\rm GUT}) =
M_{\tilde{d}_{Ri}}(M_{\rm GUT})  =M_{\tilde{L}_i} (M_{\rm GUT}) 
= M_{\tilde{l}_{Ri}} (M_{\rm GUT}) \non \\
&=& M_{H_u}(M_{\rm GUT}) =M_{H_d} (M_{\rm GUT}) \equiv  m_0
\eeq

-- Universal trilinear couplings: 
\beq
A^u_{ij} (M_{\rm GUT}) = A^d_{ij} (M_{\rm GUT}) = A^l_{ij} (M_{\rm
GUT}) \equiv  A_0 \, \delta_{ij}
\eeq

Besides the three parameters $m_{1/2}, m_0$ and $A_0$, the supersymmetric
sector is described at the GUT scale by the bilinear coupling $B$ and the
supersymmetric Higgs(ino) mass parameter $\mu$. However, one has to require
that EWSB takes place at some low energy scale. This results in two necessary
minimization conditions of the two--Higgs doublet scalar potential which, at
the tree--level, has the form [to have a more precise description, one--loop
corrections to the scalar potential have to be included, as will be discussed
later]: %
\begin{eqnarray} 
V_{\rm Higgs} &=& \overline{m}_1^2 H_d^{\dagger} H_d + \overline{m}_2^2 
H_u^{\dagger} H_u + \overline{m}_3^2 (H_u \cdot H_d + {\rm h.c.}) \nonumber \\
 &+& \frac{g_1^2+g_2^2}{8}  (H_d^{\dagger} H_d - H_u^{\dagger} H_u)^2 + 
\frac{g_2^2}{2} (H_d^{\dagger}  H_u) (H_u^{\dagger}  H_d)
\label{vhiggs}, 
\end{eqnarray}
%
where we have used the usual short--hand notation: $\overline{m}_1^2= m^2_{H_d}
+\mu ^2 ,  \overline{m}_2^2= m^2_{H_u}+\mu ^2$, $\overline{m}_3^2= B\mu$ and
the SU(2) invariant product of the two doublets $\phi_1 \cdot \phi_2 = 
\phi_1^1 \phi_2^2 - \phi_1^2 \phi_2^1$. The two minimization equations
$\partial V_{\rm Higgs} / \partial H_d^0 = \partial V_{\rm Higgs} /
\partial H_u^0 = 0$ can be solved for $\mu^2$ and $B \mu$:
%
\begin{eqnarray} \label{eq:ewsb}
\mu^2 &=& \frac{1}{2} \bigg[ \tan 2\beta (m^2_{H_u} \tan \beta
- m^2_{H_d} \cot \beta) -M_Z^2 \bigg] \non \\
B\mu &=& \frac{1}{2} \sin 2\beta \Bigg[ m^2_{H_u} + m^2_{H_d} + 2
\mu^2 \Bigg] 
\end{eqnarray}
%
Here, $M_Z^2=(g_1^2+g_2^2) \cdot (v_u^2 + v_d^2) /4$ and $\tan \beta= v_u/v_d$
is defined in terms of the vacuum expectation values of the two neutral Higgs
fields. Consistent EWSB is only possible if eq.~(\ref{eq:ewsb}) gives a
positive value of $\mu^2$. The sign of $\mu$ is not determined. Therefore, in
this model, one is left with only four continuous free parameters, and an
unknown sign\footnote{Note  that the number of parameters can be further
reduced by introducing  an additional constraint which is based on the
assumption that the $b$ and $\tau$ Yukawa couplings unify at the GUT scale, as
predicted in minimal SU(5). This restricts $\tb$ to two narrow ranges around
$\tb \sim 1.5$ and $\sim m_t/m_b$ \cite{Yunif}. The low $\tb$ solution is ruled
out since it leads to a too light an $h$ boson, in conflict with searches at
LEP2 \cite{LEPH}. However, Yukawa unification is not particularly natural in
the context of Superstring theories, and minimal SU(5) predictions are known to
fail badly for the lighter generations. We therefore treat all three third 
generation  Yukawa couplings as independent parameters.}:
%
\beq 
\tan \beta \ , \ m_{1/2} \ , \ m_0 \ , \ A_0 \ , \ \ {\rm sign}(\mu). 
\eeq 
%
All the soft SUSY breaking parameters at the weak scale are then
obtained through Renormalization Group Equations.

\subsection*{2.4 The AMSB model}

In mSUGRA, Supersymmetry is broken in a hidden sector and the breaking is
transmitted to the visible sector by gravitational interactions. In Anomaly
Mediated Supersymmetry Breaking models, the SUSY--breaking occurs also in a
hidden sector, but it is transmitted to the visible sector by the super--Weyl
anomaly \cite{AMSB}. The gaugino, scalar masses and trilinear couplings are then simply
related to the scale dependence of the gauge and matter kinetic functions. 
This leads to soft SUSY--breaking scalar masses for the first two generation
sfermions that are almost diagonal [when the small Yukawa couplings  are
neglected] which solves the SUSY flavor problem which affects mSUGRA for
instance. \s
 
In terms of the gravitino mass $m_{3/2}$ [which is much larger than the 
gaugino and squark masses, a cosmologically appealing feature], the  $\beta$
functions for the gauge and Yukawa couplings $g_a$ and $Y_i$, and  the
anomalous dimensions $\gamma_i$ of the chiral superfields, the soft SUSY 
breaking terms are given by:
\beq
M_a &=& \frac{\beta_{g_a}}{g_a} m_{3/2} \ , \  % \non \\
A_i = \frac{\beta_{Y_i}}{Y_i}  m_{3/2} \non \\  
m_i^2 &=& -\frac{1}{4} \left( \Sigma_a \frac{\partial \gamma_i}{\partial g_a} \beta_{g_a} +
\Sigma_k \frac{\partial \gamma_i}{\partial Y_k} \beta_{Y_k} \right) m_{3/2}^2 
\eeq
These equations are RG invariant and thus valid at any scale and make the model
highly predictive.  The additional parameters, $\mu^2$ and $B$ are obtained as
usual by requiring the correct breaking of the electroweak symmetry. One then
has, in principle, only three input parameters $m_{3/2}, \tan\beta$ and
sign$(\mu)$. However, this rather simple picture is spoiled by the fact that
the anomaly mediated contribution to the slepton scalar masses squared is
negative and the sleptons are in general tachyonic. This problem can be cured
by adding a positive non--anomaly mediated contribution to the soft masses. The
simplest phenomenological way of parameterizing the non--anomaly contribution
is to add a common mass parameter $m_0$ at the GUT scale, which would be then
an additional input parameter to all the (squared) scalar masses. However in
the general case, the non--anomaly mediated contribution might be different for
different scalar masses and depend on the specific model which has been chosen.
One should then write a general non--anomalous contribution at the GUT scale for
each scalar mass squared:
\beq
m_{\tilde{S}_i}^2 = c_{S_i}m_0^2 -\frac{1}{4} \left( \Sigma_a \frac{\partial 
\gamma_i} {\partial g_a} \beta_{g_a} + \Sigma_k \frac{\partial \gamma_i}
{\partial Y_k} \beta_{Y_k}  \right)  m_{3/2}^2 +{\rm D\, terms.} 
\eeq
where the coefficients $c_{S_i}$ depend on the considered model. \s

A few examples of models with different non--anomalous contributions are: \s

\nn -- The minimal anomaly mediated supersymmetry breaking model with a universal 
$m_0$ \cite{AM1}:
\beq
c_{Q}=c_{u_R}=c_{d_R}=c_{L}=c_{e_R}=c_{H_u}=c_{H_d}=1
\eeq
-- The gaugino assisted AMSB model where one assumes that gauge and gaugino 
fields reside in the bulk of an extra dimension \cite{AM2}:
\beq
c_{Q}=21/10,c_{u_R}=8/5,c_{d_R}=7/5,c_{L}=9/10,c_{e}=3/5,c_{H_u}=9/10=
c_{H_d} 
\eeq
-- Models where an extra U(1) factor is added; a  particular scenario is interesting 
phenomenologically since   it leads to a light top squark \cite{AM3}: 
\beq
c_{Q}=3,c_{u_R}=c_{d_R}=-1,c_{L}=c_{e}=1,c_{H_u}=c_{H_d}=-2
\eeq 

A simple way to account for all the different models is to add to the three
continuous and one discrete original basic parameters, the set of coefficients
$c_{S_i}$ as input to specify, and therefore one would have the set of  input 
parameters:
\beq
m_0 \ , \ m_{3/2} \ , \ \tb \ , \ {\rm sign}(\mu) \ {\rm and} \ c_{S_i}
\eeq 
This is the approach that we will follow in the program. 

\subsection*{2.5 The GMSB model}

In Gauge Mediated Supersymmetry Breaking models, SUSY--breaking is
transmitted to the MSSM fields via the SM gauge interactions. In the original
scenario \cite{gmsb1}, the model consists of three distinct sectors: a secluded
sector where SUSY is broken, a ``messenger" sector containing a singlet field
and messenger fields with ${\rm SU(3)_c\times SU(2)_L\times U(1)_Y}$ quantum
numbers, and a sector containing the fields of the MSSM. Another possibility,
the so--called ``direct gauge mediation" \cite{gmsb2} has only two sectors: one
which is responsible for the SUSY breaking and contains the messenger fields,
and another sector consisting of the MSSM fields. In both cases, the soft 
SUSY--breaking masses for the gauginos and squared masses for the sfermions arise,
respectively, from one--loop and two--loop diagrams involving the exchange of
the messenger fields, while the trilinear Higgs--sfermion--sfermion couplings
can be taken to be negligibly small at the messenger scale since they are [and
not their square as for the sfermion masses] generated by two--loop gauge
interactions.  This allows an automatic and natural suppression of FCNC and
CP--violation; for a review see, Ref.~\cite{GMSB}. \s

In the GMSB models that we will consider, the source of SUSY breaking is
parameterized by an ${\rm SU(3)_C \times SU(2)_L \times U(1)_Y}$ gauge--singlet
chiral  superfield $\hat{S}$ whose scalar and auxiliary components acquire
vacuum  expectation values denoted by $S$ and $F_S$, respectively.  We assume
$n_{\hat{q}}$ pairs of $\hat{q}, \hat{\bar{q}}$ quark--like [resp.
$n_{\hat{l}}$ pairs of  $\hat{l}, \hat{\bar{l}}$ lepton--like]  messenger
superfields transforming as  $(3, 1, -\frac{1}{3}),  (\bar{3}, 1,
\frac{1}{3})$  [resp. $(1, 2, \frac{1}{2}), (1, 2, -\frac{1}{2})$] under ${\rm
SU(3)_C \times SU(2)_L \times U(1)_Y}$ and coupled to $\hat{S}$ through a
superpotential  of the form $\lambda \hat{S} \hat{q} \hat{ \bar{q}} + \lambda 
\hat{S} \hat{l} \hat{\bar{l}}$. Soft SUSY--breaking parameters are then
generated at the messenger scale  $M_{\rm mes} = \lambda S$,  
\begin{eqnarray}
M_G(M_{\rm mes}) &=& \frac{\alpha_G(M_{\rm mes})}{4 \pi} \Lambda \,
g \bigg(\frac{\Lambda}{M_{\rm mes}} \bigg) \defsum N^G_R(m)
  \label{gasoft} \\
m_s^2(M_{\rm mes}) & =& 2 \Lambda^{2} f\bigg(\frac{\Lambda}{M_{\rm mes}} 
\bigg)\defsumg  \bigg[ \frac{\alpha_G(M_{\rm mes})}{4 \pi} \bigg]^2  
N^G_R(m) C_R^G(s)
\label{scalsoft} \\
A_{f} (M_{\rm mes})  &\simeq & 0
\end{eqnarray}
where $\Lambda=F_S/S$, $G= {\rm U(1), SU(2), SU(3)}$, $m$ labels the 
messengers and $s$  runs over the Higgs doublets  as well as the left--handed 
doublets and right--handed singlets of squarks and sleptons. The 
one-- and two loop functions $g$ and $f$ are given by [Li$_2$ is the 
Spence function]:
\beq
g(x)&=&  \frac{1}{x^2} [(1+x)\log (1+x)+(1-x) \log (1-x)]  \non \\
f(x) &=& \frac{1+x}{x^2} \bigg[\log (1+x) -2 {\rm Li}_2 \bigg( \frac{x}{1+x} 
\bigg) + \frac{1}{2} {\rm Li}_2 \bigg( \frac{2x}{1+x} \bigg) \bigg] + 
(x \leftrightarrow -x)  
\eeq 
Defining the Dynkin index $N_R^G$ by
\begin{equation}
{\rm Tr}\, (T_R^a T_R^b) = \frac{N_R^G}{2} \delta^{a b}
\end{equation}
\noindent
for non--abelian groups, and $N^{U(1)_Y} = (6/5) Y^2$ where $Y \equiv 
Q_{\rm EM}- T_3$, one has (see eq.(\ref{gasoft}))
\begin{eqnarray}
\defsum N^{U(1)_Y}_R(m) &=& \frac{1}{5} (2 n_{\hat{q}} + 3 n_{\hat{l}}) 
\nonumber \\
\defsum N^{SU(2)_L}_R(m) &=& n_{\hat{l}} \nonumber \\
\defsum N^{SU(3)_c}_R(m) &=& n_{\hat{q}} 
\end{eqnarray}
\noindent
With the Casimir invariant $C_{\bf N}^G$ given by 
\begin{equation}
\Sigma_a T^a_{\bf N} T^a_{\bf N} = C_{\bf N}^{SU(N)} {\bf 1} = 
\frac{N^2-1}{2 N} {\bf 1}
\end{equation}
\noindent
for  the ${\bf N}$  of $SU(N)$, and $C^{U(1)_Y} = (3/5) Y^2$, 
one finds for 
$${\cal N C}(s) \equiv \defsumg \bigg[ \frac{\alpha_G(M_{\rm mes})}{4 \pi}
\bigg]^2  N^G_R(m) C_R^G(s)$$
\noindent
(see eq.(\ref{scalsoft})) the following values:
\begin{eqnarray}
{\cal N C}(\tilde{Q}) &=& \frac{1}{16 \pi^2} \left[ (\frac{n_{\hat{l}}}{100} 
+ \frac{n_{\hat{q}}}{150}) \alpha_1^2 + \frac{3 n_{\hat{l}}}{4} \alpha_2^2 + 
\frac{4 n_{\hat{q}}}{3} \alpha_3^2 \right] \nonumber \\
{\cal N C}(\tilde{U})&=& \frac{1}{16 \pi^2} \left [
(\frac{4 n_{\hat{l}}}{25} + \frac{8 n_{\hat{q}}}{75}) \alpha_1^2 +
\frac{4 n_{\hat{q}}}{3} \alpha_3^2   \right] \nonumber \\
{\cal N C}(\tilde{D})&=& \frac{1}{16 \pi^2} \left[
(\frac{n_{\hat{l}}}{25} + \frac{2 n_{\hat{q}}}{75}) \alpha_1^2 +
\frac{4 n_{\hat{q}}}{3} \alpha_3^2   \right] \nonumber \\
{\cal N C}(\tilde{L})&=& \frac{1}{16 \pi^2} \left[
(\frac{9 n_{\hat{l}}}{100} + \frac{3 n_{\hat{q}}}{50}) \alpha_1^2 +
\frac{3 n_{\hat{l}}}{4} \alpha_2^2 \right] \nonumber \\
{\cal N C}(\tilde{E})&=& \frac{1}{16 \pi^2} \left[
(\frac{9 n_{\hat{l}}}{25} + \frac{6 n_{\hat{q}}}{25}) \alpha_1^2 
\right] \nonumber \\
{\cal N C}(\tilde{H}_u)&=& {\cal N C}(\tilde{H}_d) = {\cal N C}(\tilde{L})
\end{eqnarray} 
The freedom in choosing independently the number of $n_{\hat{q}}$ and $n_{\hat{l}}$
messengers allows to study various model configurations: for instance when the 
messengers are assumed to form complete representations of some grand 
unification group (e.g.  ${\bf 5} + {\bf \bar{5}}$ of SU(5)) where 
$n_{\hat{q}} = n_{\hat{l}}$, or when they transform under larger unification
group factors with some extra discrete symmetries where typically
$n_{\hat{q}} \neq n_{\hat{l}}$ \cite{barbieri}.
[When $n_{\hat{q}} = n_{\hat{l}} = 1$ one retrieves the 
minimal model \cite{gmsb1}. In this case the gaugino masses  
have the same {\sl relative} values as if they were
unified at $M_{\rm GUT}$ despite the fact the boundary conditions are set at
$M_{\rm mes}$ and that scalar masses are flavor independent.
Furthermore when 
$\Lambda/M_{\rm mes} \ll 1$, one has $f(x) \simeq g(x) \simeq 1$.]   
In addition, some constraints are
in general needed in order to have a viable spectrum, for instance:
$\Lambda/M_{\rm mes} < 1$ to avoid negative mass squared for bosonic members of
the messenger scale and $\Lambda/M_{\rm mes} \lsim 0.9$ to avoid too much
fine--tuning in EWSB. Note also that $n_{\hat{q}} > n_{\hat{l}}$
improves the fine--tuning issue \cite{agashe}.\s

\noindent
Once the boundary conditions are set at $M_{\rm mes}$, the low energy
parameters are obtained via the usual RGEs and the proper breaking of
the EW symmetry is required. 

Therefore, in the GMSB model that we are considering, there are six input 
parameters
\beq
\tan \beta \ , \ {\rm sign}(\mu) \ ,  \ M_{\rm mes} \ , \ \Lambda \ , \ n_{\hat{q}} \ , \ n_{\hat{l}}
\eeq
In addition, one has to include as input the mass of the gravitino $\tilde{G}$
which, in this case is the lightest SUSY particle. This mass, $m_{\tilde
G}=F/(\sqrt{3} M_P)$ with $M_P$ the reduced Planck mass, will depend on an
additional free parameter $F$ which parameterizes the scale of the
full SUSY breaking and whose typical size is of 
${\cal O}(F_S)$  in direct 
mediation and much larger in secluded mediation. The choice
of this parameter, which plays a role only for the lifetime of the
next--to--lightest SUSY particle, is left to the user.  

\subsection*{2.6 Non--universal models}

mSUGRA, AMSB and GMSB are well defined models of which the possible
phenomenological consequences and experimental signatures have been widely
studied in the literature. However, none of these models should be
considered as {\sc the} definite model, in the absence of a truly fundamental
description of SUSY--breaking, and some of the basic assumptions inherent to
these scenarii might turn out not to be correct. For instance some of 
the universality conditions postulated in the mSUGRA scenario are naturally 
violated in some cases [47--50] as will be discussed below. \s

To be on the safe side from the experimental point of view, it is therefore
wiser to allow for a departure from these models, and to study the phenomenological
implications of relaxing some defining assumptions.  However, it is often
desirable to limit the number of extra free parameters, in order to retain a
reasonable amount of predictability when attempting detailed investigations of
possible signals of SUSY. Therefore, it is more interesting to relax only one
[or a few] assumption at a time and study the phenomenological implications. Of
course, since there are many possible directions, this would lead to several
intermediate MSSMs between these constrained  models and the phenomenological
MSSM with 22 free parameters discussed in section 2.2.  \s

Taking the most studied model mSUGRA as the reference model, examples of such 
non universal scenarii are for instance: \s

$i)$ non unification of the soft SUSY--breaking gaugino mass terms: 
\beq
M_1 (M_U) \neq M_2(M_U) \neq  M_3(M_U)
\eeq
This occurs for instance in Superstring motivated models in which the SUSY 
breaking is moduli dominated such as in the O--I and O--II models \cite{Pierre},
or in extra dimensional SUSY--GUT models in which the additional dimensions 
lead to the breaking of the large gauge symmetry and/or to Supersymmetry, or 
SUSY models where the breaking occurs through a non SU(5) singlet $F$ term; 
see Ref.~\cite{NM1} for phenomenology oriented discussions. \s

$ii)$ mSUGRA with non--unification of the two first and third generation scalar
masses [i.e. with different scalar mass terms $m_0$ at the high scale
or with a common mass which becomes different at the low--energy scale]: 
\beq
m_{0 \tilde{Q}}= m_{0 \tilde{L}} \cdots \neq m_{0 \tilde{q}} = m_{0 \tilde{l}} 
\cdots
\eeq
This occurs in models where the soft SUSY--breaking scalar masses at the 
GUT scale are influenced by the fermion Yukawa couplings. This is the case
for the so--called inverted mass hierarchy models \cite{NM2} where the 
scalar mass terms of the first two generations can be very heavy ${\cal O}
(10$ TeV),  while those of the third generation sfermions and the Higgs bosons
are rather light, solving thus the SUSY flavor and CP problems, which are 
related to the first two generations, while still satisfying naturalness 
constraints. \s 

$iii)$ mSUGRA-like models, but with non--unification of the sfermion and Higgs
boson scalar masses, e.g.: 
\beq
m_{\tilde{Q}} =m_{\tilde{e}_R}= m_{\tilde{u}_R}  \neq m_{\tilde{d}_R} =
m_{\tilde{L}} \neq  M_{H_u} =M_{H_d}
\eeq
This occurs for instance in SO(10) models with universal boundary conditions 
but with extra D--term contributions to the scalar masses associated to the 
reduction in rank when SO(10) breaks to the SM group \cite{NM3}. In practice,
it amounts to disconnect the Higgs sector from the sfermionic sector and 
introduces two additional input parameters: the pseudoscalar Higgs boson
mass $M_A$ and the higgsino mass parameter $\mu$ [which have a  more direct
``physical" interpretation than the scalar mass terms $M_{H_u}, M_{H_d}$]. 
This allows  to perform more general phenomenological or experimental analyzes;
c.f. some LEP  and LHC Higgs analyzes \cite{Ex-nonuniv} or some recent Dark 
Matter studies  \cite{DM-nonuniv}. \s


$iv)$ Partially unified models where one relaxes one or a few parameters to fit
some collider zoo event or to analyze a phenomenological situation which 
introduces new features. This is the case, for instance, for the light top 
squark scenario which can be set by hand to discuss some theoretical [such as
baryogenesis in the MSSM \cite{baryo} for instance] or  phenomenological [such
as new decay or production modes of top squarks \cite{stop} for instance] situations.
\s 

An easy and practical way to implement these various non--unified or partially
unified scenarii, is to allow for the possibility of choosing all the soft 
SUSY--breaking parameters listed above for the phenomenological MSSM of section 2.2
[the 22 parameters except for $\tan \beta$] at the high--energy or GUT scale,
with the boundary conditions set by hand and chosen at will. One can even chose
the scale at which the boundary conditions are set to account for intermediate
scales. If this scale is the electroweak symmetry breaking scale, then we have
simply the MSSM with the soft SUSY--breaking parameters defined at the low
energy scale, i.e. the phenomenological MSSM.  All these options are
provided by our code.

\section*{3. The Particle Spectrum Calculation with Suspect} 

In this section, we discuss our procedure for calculating the SUSY and Higgs 
particle spectrum. We will take as example the sophisticated cases of the 
constrained MSSMs with universal boundary conditions at the high scale, mSUGRA
AMSB and GMSB, where all ingredients included in the {\tt SuSpect} algorithm 
are present: RGEs, radiative EWSB and calculation of the physical 
particle masses. We will first describe the general algorithm,  then discuss 
the calculation of the soft SUSY--breaking terms, the determination of the
particle masses, the various  theoretical and phenomenological tests that we
impose on the model parameters and show an example of how the parameter
space can be scanned.  


\subsection*{3.1 General algorithm}

As mentioned  previously, there are three main steps for the calculation of
the supersymmetric particle spectrum in constrained MSSMs, in addition to the
choice of the input parameters and the check of the particle spectrum: 

\begin{itemize} 
\vspace{-2mm} 

\item[$i)$] Renormalization group evolution of parameters back and forth 
between the low energy scales, such as $M_Z$ and the electroweak symmetry 
breaking scale, and the high--energy scale, such as the GUT scale or the
messenger scale in GMSB models [17--19]. This is the case for  the SM gauge and
Yukawa couplings and for the soft SUSY--breaking terms (scalar and gaugino
masses, bilinear and trilinear couplings and $\tb$) and $\mu$. This procedure
has to be iterated in order to include SUSY threshold effects  or radiative
corrections due to Higgs and SUSY particles.  In the first step, these
thresholds are only guessed since the spectrum has  not been calculated yet,
and the radiative corrections are not implemented.  \vspace{-2mm}

\item[$ii)$] The implementation of radiative electroweak symmetry breaking 
[20--23] and the calculation of $B$ and $|\mu|$ from the one--loop effective 
scalar potential. Here, we use the tadpole method to include the loop
corrections \cite{potential}. The procedure has to be  iterated until a
convergent value for these two parameters is obtained.  In the first step, the
values of $\mu^2$ and the electroweak symmetry  breaking scale are guessed, and
one of course uses the tree--level  potential since no sparticle or Higgs mass
has been calculated yet.  \vspace{-2mm}

\item[$iii)$] Calculation of the pole masses of the Higgs bosons and the
SUSY particles, including the mixing between the current states 
and the radiative corrections when they are important [24--31]. In this context, we 
will follow the paper of Pierce, Bagger, Matchev and Zhang \cite{PBMZ}, 
to which we will refer as PBMZ. Iterations, which are made to coincide with
those necessary for the RGEs, are also needed to obtain a sufficient accuracy. 
\vspace{-1mm} 
\end{itemize}

\nn The general algorithm is depicted in Figure 1, and we will discuss the 
various steps in some detail in the following subsections and in Appendix A. 
\newpage
\vspace*{-.5cm}
\begin{picture}(1000,470)(10,0)

%
\Line(390,450)(450,450)
\ArrowLine(450,-60)(450,450)
\Line(450,-60)(390,-60)
%

\Line(10,470)(390,470)
\Line(10,410)(390,410)
\Line(10,470)(10,410)
\Line(390,470)(390,410)

\Text(200,460)[]{Choice of low energy input:  $\alpha(M_Z), \sin^2\theta_W, 
\alpha_S(M_Z)$, $m_{t,b,\tau}^{\rm pole}$\, ; $\tan \beta (M_Z)$}

\Text(200,440)[]{Radiative corrections $\Rightarrow$ $g_{1,2,3}^{\rm 
\overline{DR}}(M_Z)$, $\lambda_\tau^{\rm \overline{DR}} (M_Z), \lambda_b^{\rm 
\overline{DR}}(M_Z), \lambda_t^{\rm \overline{DR}} (m_t)$}

\Text(200,420)[]{\it First iteration: no SUSY radiative corrections.} 

\ArrowLine(200,408)(200,392)

\Line(10,390)(390,390)
\Line(10,310)(390,310)
\Line(10,390)(10,310)
\Line(390,390)(390,310)

\Text(200,370)[]{Two--loop RGE for $g_{1,2,3}^{\overline{\rm DR}}$ and $\lambda_{\tau,b,t}^ 
{\overline{\rm DR}}$ with choice: $\begin{array}{l}  g_1=g_2 \cdot \sqrt{3/5} \\ 
 M_{\rm GUT} \sim 2 \cdot 10^{16}~{\rm  GeV} \end{array}$}

\Text(200,340)[]{Include all SUSY thresholds via step functions in $\beta$ 
functions.}

\Text(200,320)[]{\it First iteration: unique threshold guessed.} 

\ArrowLine(200,308)(200,295)

\Text(200,285)[]{Choice of SUSY-breaking model (mSUGRA, GMSB, AMSB, or pMSSM).}
 
\Text(200,265)[]{Fix your high--energy input (mSUGRA: $m_0, m_{1/2}, A_0$, 
sign($\mu)$, etc...).} 

\ArrowLine(200,253)(200,242)

\Line(10,240)(390,240)
\Line(10,180)(390,180)
\Line(10,240)(10,180)
\Line(390,240)(390,180)

\Text(200,220)[]{Run down with RGE to: $\begin{array}{l} - M_Z(m_t)~{\rm for}~
g_{1,2,3}~{\rm and}~\lambda_{\tau,b}(\lambda_t) \\
- M_{\rm EWSB}~{\rm for}~\tilde{m}_i, M_i, A_i, \mu, B \end{array}$} 
\Text(200,195)[]{\it First iteration: guess for $M_{\rm EWSB} = M_Z$.}

\ArrowLine(200,178)(200,162)

\Line(10,160)(390,160)
\Line(10,100)(390,100)
\Line(10,160)(10,100)
\Line(390,160)(390,100)

\Text(200,150)[]{$\mu^2, \mu B = F_{\rm non-linear}(m_{H_u}, m_{H_d}, 
\tan\beta, V_{\rm loop} )$}

\Text(200,130)[]{$V_{\rm loop} \equiv $ Effective potential at 1--loop with 
all masses.}

\Text(200,110)[]{{\it First iteration: $V_{loop}$ not included} }

%
\Line(390,130)(420,130)
\ArrowLine(420,30)(420,130)
\Line(420,30)(390,30)
%

\ArrowLine(200,98)(200,90)

\Text(200,85)[]{Check of consistent EWSB ($\mu$ convergence, no tachyons, 
simple CCB/UFB, etc...) } 

\ArrowLine(200,75)(200,62)


\Line(10,60)(390,60)
\Line(10,0)(390,0)
\Line(10,60)(10,0)
\Line(390,60)(390,0)

\Text(200,50)[]{Diagonalization of mass matrices and calculation of masses /  
couplings}


\Text(200,30)[]{Radiative corrections to the physical Higgs, sfermions, gaugino
masses.}

\Text(200,10)[]{\it First iteration: no radiative corrections.} 

\ArrowLine(200,-2)(200,-17)



\Line(10,-20)(390,-20)
\Line(10,-85)(390,-85)
\Line(10,-20)(10,-85)
\Line(390,-20)(390,-85)

\Text(200,-30)[]{Check of a reasonable spectrum:} 

\Text(200,-45)[]{-- no tachyonic masses (from RGE, EWSB or mix), 
good LSP, etc..\ \hfill } 

\Text(200,-60)[]{-- not too much fine-tuning and sophisticated CCB/UFB 
conditions,\hfill }

\Text(200,-75)[]{-- agreement with experiment: $\Delta\rho$, $(g-2)$, 
$b \to s\gamma$. \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \hfill}
\end{picture}

\vspace*{3.cm}

\noindent {\it Figure 1: Iterative algorithm for the calculation of the SUSY
particle spectrum in {\tt SuSpect} from the choice of input (first step) to the
check of the  spectrum (last step). The steps are detailed in the various 
subsections. The EWSB iteration [calculationally fast] on $\mu$ is performed
until  $|\mu_{i}-\mu_{i-1}| \leq \epsilon |\mu_i|$ (with $\epsilon \sim 10^{-3}$)
while  the RG/RC ``long" iteration [calculationally longer] needs to be
performed 3 to 4 times to reach sufficient stability/accuracy.}

\newpage


\subsection*{3.2 Calculation of the soft SUSY--breaking terms}

For the calculation of the soft SUSY--breaking terms in constrained models 
with boundary conditions at the unification scale, we proceed as follows:

\subsubsection*{3.2.1 Choice and treatment of the SM input}
 
We first chose the low--energy input values of the SM parameters. The gauge
couplings constants are given in the ${\overline{\rm MS}}$ scheme at the
scale $M_Z$ [$\bar{s}_W^2 = 1- \bar{c}_W^2 \equiv
\sin^2\theta_W|^{\overline{\rm MS}}$]:
\beq 
g_1^2= \frac{4 \pi \alpha^{\overline{\rm MS}}_{\rm
em}(M_Z)} {\bar{c}^{2}_W } \ , \ g_2^2= \frac{4 \pi
\alpha^{\overline{\rm MS}}_{\rm em}(M_Z)} {\bar{s}^{2}_W } \ , 
\ g_3^2= 4 \pi \alpha^{\overline{\rm MS}}_s(M_Z)
\eeq
Their values have been obtained from precision measurements at LEP and Tevatron
\cite{PDG}:
\begin{eqnarray}
\alpha^{\overline{\rm MS}}_{\rm em}(M_Z)=1/127.938 \ , \ 
\alpha^{\overline{\rm MS}}_s(M_Z)= 0.1192 \ , \ 
\bar{s}^2_W = 0.23117
\label{defgi}
\end{eqnarray}
%
The pole masses of the heavy SM fermions are chosen as \cite{PDG}: 
%
\begin{eqnarray}
M_{t}= 174.3 \ {\rm GeV} \ \ , \ \ 
M_{b} = 4.87 \  {\rm GeV} \ \ , \ \ 
M_{\tau} = 1.778 \ {\rm GeV} \ \ 
\label{defmfi}
\end{eqnarray}
%
[while the $Z$ boson mass is fixed to $M_Z=91.187$ GeV, the $W$ boson mass is
not a free parameter and is obtained from the relation $M_W=M_Z \bar{c}_W$].
Note, however, that for maximum flexibility, all those SM input default values
in eqs.~(\ref{defgi},\ref{defmfi}) can be changed at will in the input file,
see section 4 for details.\s

Next, the $\overline{\rm DR}$--scheme values of the gauge and Yukawa couplings 
at the scale $M_Z$ ($M_t$ for the top quark) are extracted from these input 
\cite{drbar}. The latter are defined by [note that the SM vacuum expectation 
value at the scale $M_Z$ is $v \simeq 174.1$ GeV]:
%
\beq 
\lambda_t (M_t) = \frac{\overline{m}_t (M_t)}{v \sin \beta} \ , \
\lambda_b (M_Z) = \frac{\overline{m}_b (M_Z)}{v \cos \beta} \ , \
\lambda_\tau (M_Z) = \frac{\overline{m}_\tau (M_Z) }{v \cos \beta} \ .
\eeq
For the bottom and top quark pole masses \cite{qqcd}, one obtains the running $\overline{
\rm DR}$ masses using the two loop relations. The relation  between
the pole masses ($M_Q$) and the running $\overline{\rm MS}$ masses
(${\overline{m}}_{Q}$) at the scale of the  pole mass are given by \cite{broad}
\begin{eqnarray} \label{run-pole}
{\overline{m}}_{Q}(M_{Q})= M_{Q} \bigg[ 1+\frac{4}{3}
\frac{\alpha_{s}(M_Q)}{\pi} + K_Q \left(\frac{\alpha_s(M_Q)}{\pi}\right)^2\bigg]^{-1}
\end{eqnarray}
with the numerical values of the NNLO coefficients reading $K_t\simeq 10.9$
and $K_b \simeq 12.4$. The evolution from $m_{b}$ upward to a renormalization 
scale $\mu$ close to $M_Z$ is given by \cite{runmass}
\begin{eqnarray}
{\overline{m}}_{b}\,(\mu )&=&{\overline{m}}_{b}\,(M_{b})
\,\frac{c\,[\alpha_{s}\,(\mu)/\pi ]}{c\, [\alpha_{s}\,(M_{b})/\pi ]}
\ {\rm with} \ 
c(x)=\left(\frac{23}{6}\,x\right)^{\frac{12}{23}} \, [1+1.175x+1.501\,x^{2}]
\end{eqnarray}
One then determines the $\overline{\rm DR}$ masses at the scale $M_Z$ for the 
$b$--quark and $M_t$ for the top quark \cite{mbdr}. For the $b$--quark we use:
\begin{eqnarray}
m_b(M_Z)^{\overline{\rm DR}} &=&
m_b(M_Z)^{\overline{\rm MS}} \left[1 - \frac{\alpha_s}{3 \pi} - \frac{35
\alpha_s^2}{72 \pi^2} + \frac{3 g_2^2}{128 \pi^2} + \frac{13 g_1^2}{1152 \pi^2} \right]
\end{eqnarray}
while for the top quark, we include only QCD corrections:
\begin{eqnarray}
m_t(M_t)^{\overline{\rm DR}} &=&
m_t(M_t)^{\overline{\rm MS}} \left[1 - \frac{\alpha_s}{3 \pi} - 0.975 \alpha_s^2
\right]
\end{eqnarray}
Once the Supersymmetric particle spectrum has been obtained [see below], we
include all the important SUSY radiative corrections to the gauge and Yukawa
couplings. In the case of the gauge couplings, only the large logarithmic
corrections are implemented by including the multiple SUSY particle (and top
quark) thresholds [via step functions] in the $\beta$ functions
\cite{gutthresh}.  In the case of the Yukawa couplings, we include all relevant
SUSY corrections to the third generation fermion masses. For the bottom quark
($\tau$ lepton) mass,  we include the SUSY--QCD and stop--chargino
(sneutrino--chargino) one--loop corrections at zero--momentum transfer \cite{mbcor}
which, according to PBMZ, is an extremely good approximation. These corrections to the
$b$ and $\tau$ masses are enhanced by terms $\propto \mu \tb$ and can be rather
large. We therefore re--sum these corrections in the case of the $b$--quark
\cite{sumb}: 
\beq
m_{b}(Q)^{\overline{\rm DR}}_{\rm SUSY} = \bar{m}_b(Q)^{\overline{\rm DR}}_{\rm SM}  
(1+ \Delta^{\rm SUSY} m_b/m_b) \to \bar{m}_b (Q)^{\overline{\rm DR}}_{\rm SM} / 
(1- \Delta^{\rm SUSY}  m_b/m_b) 
\eeq
For the top quarks, the inclusion of only the leading corrections at zero
momentum transfer is not an accurate approximation, and we include the 
full one--loop SUSY--QCD [i.e stop and gluino loops] and electroweak [i.e. 
with gauge, Higgs boson and  chargino/neutralino exchange] corrections 
{\it \`a la} PBMZ \cite{PBMZ}. More details are given in Appendix A. 


\subsubsection*{3.2.2 Renormalization Group Evolution}

All gauge and (third generation) Yukawa couplings are then evolved up to the
GUT scale using the two--loop RGEs \cite{RGE2,drbar}. In the initial step, no
SUSY particle threshold is taken into account (since no particle spectrum has
been yet determined). The GUT scale, $M_{\rm GUT} \simeq 2 \cdot 10^{16}$ GeV
can be either fixed by hand or, by appropriate user's choice in the input
file,  calculated consistently to be the scale at which the electroweak gauge
coupling constants [with the adequate normalization] unify, $g_1 = g_2 \cdot
\sqrt{3/5}$. In contrast, we do not enforce exact $g_2 = g_3$  unification at
the GUT scale and assume that the small discrepancy, of at most a few percent,
is accounted for by unknown GUT--scale threshold corrections
\cite{gutthresh}.\s 

One can then chose the parameter $\tan\beta$, given at the scale $M_Z$, the
sign of the $\mu$ parameter and, depending on the chosen model, the high energy
and the low energy input. For instance, one can set the high--energy scale
$E_{\rm High}$, which in mSUGRA or AMSB can be either forced to be $M_{\rm
GUT}$ [the scale at which $g_1$ and $g_2$ unify] or chosen at will [any
particular intermediate scale between $M_Z$ and $M_{\rm GUT}$ can be allowed
in general  and in the case of the GMSB model this scale corresponds to the
messenger  scale $M_{\rm mes}$]. Similarly the low energy scale $E_{\rm Low}$,
where the RGEs  start or end may be chosen [which is in general taken to be
$M_Z$ or the EWSB scale to be discussed later]. The additional input in the
various models are: 
\begin{itemize}
\vspace*{-2mm}
\item \underline{mSUGRA}: the universal trilinear coupling $A_0$, the common 
scalar mass $m_0$ and the common gaugino mass $m_{1/2}$, all defined at the 
scale $M_{\rm GUT}$.  
\vspace*{-2mm}

\item \underline{AMSB}: the common scalar mass $m_0$, the gravitino mass 
$m_{3/2}$ and  the set of coefficients $c_{S_i}$ for the non--anomalous 
contributions, to be as general as possible. 
\vspace*{-2mm}

\item \underline{GMSB}: the scale  $\Lambda$, the messenger scale $M_{\rm mes}$ 
which corresponds to $E_{\rm High}$, as well as the numbers of messengers $n_q$ 
and $n_l$. 
\vspace*{-2mm}

\item \underline{pMSSM} with boundary conditions: the 
various soft SUSY--breaking parameters listed in section 2.2 [21 parameters in 
total, in addition to $\tan\beta$] defined at the scale $E_{\rm High}$. These
input can also be chosen at will at the low--energy scale $E_{\rm Low}$ which
is also provided as input. In this case, one simply has to set  
the appropriate input choice [see section 4 for more details] and the RGE part
will be switched off. Note also that here, a very convenient option is provided
which allows to trade the input parameters $M_{H_u}^2$ and  $M_{H_d}^2$ with
the more ``physical" parameters $M_A$ and $\mu$ [again in such a way that  EWSB
is consistently realized, with a warning flag whenever it is not the case].
\vspace*{-2mm}
\end{itemize}

Given these boundary conditions, all the soft SUSY breaking parameters and 
couplings are evolved down to the weak scale, using one--loop RGEs for 
the scalar masses and trilinear couplings and two--loop RGEs for the gaugino
masses\footnote{The full two--loop RGEs in the MSSM have been recently derived
\cite{Martin}. However, their impact for the soft SUSY--breaking scalar masses
and trilinear couplings should be rather modest. We nevertheless plan to
include them in a future upgrade of the code.}; see Appendix A. Our
default  choice for the EWSB scale is the geometric mean of the two top squark
masses,  \beq
M_{\rm EWSB} = (m_{\tilde{t}_1} m_{\tilde{t}_2})^ {1/2}
\eeq
which minimizes the scale dependence of the one--loop effective
potential  \cite{Vscale} discussed below [before the stop masses are
calculated, we use the geometric mean of the soft SUSY--breaking stop masses
instead as a first guess]. Note, however, that other arbitrary values of
the EWSB scale can be chosen easily by an appropriate input setting; see input
file in section 4. Since $\tb$ is defined at $M_Z$, the vevs have to be
evolved down  from $M_{\rm EWSB}$ to $M_Z$. \s

Once the SUSY spectrum is calculated [as will be discussed later], the heavy
(s)particles are taken to contribute to the RGEs of the gauge coupling constants 
at scales larger than their mass, i.e. multiple thresholds are included in the running 
of the couplings via step functions. The one--loop soft scalar 
masses and trilinear couplings and the two--loop SUSY breaking gaugino masses 
are then frozen at the scale $M_{\rm EWSB}$. \s

\subsubsection*{3.2.3 Electroweak Symmetry Breaking} 

At some stage, we require that the electroweak symmetry is broken radiatively
and use eq.~(\ref{eq:ewsb}) to determine the parameters $\mu^2(M_{\rm EWSB})$
and $B(M_{\rm EWSB})$. It is well known that the one--loop radiative
corrections to the Higgs potential play a major role in determining the values
of these two parameters, which at tree level are given  in terms of the soft 
SUSY--breaking masses of the two Higgs doublet fields. We treat these
corrections using the tadpole method. This means that we can still use
eq.~(\ref{eq:ewsb}) to determine $\mu^2(M_{\rm EWSB})$, one simply has to add
one--loop tadpole corrections \cite{potential,PBMZ} 
\beq
m^2_{H_u} \to m^2_{H_u} -t_u/d_u \ {\rm and} \  m^2_{H_d} \to m^2_{H_d}
-t_d/v_d \eeq
We include the dominant third generation fermion/sfermion loops, as well as 
sub--dominant contributions from sfermions of the
first two generations, gauge bosons, the MSSM Higgs bosons, charginos and
neutralinos\footnote{The contributions of the charginos and neutralinos can be
rather sizable and are very important to minimize the scale dependence of the
one--loop effective potential \cite{Spanos}.}, with the running parameters
evaluated at $M_{\rm EWSB}$. The analytical expressions of the tadpoles
are given in Appendix A for completeness. \s

As far as the determination of $\mu^2$ and $B\mu$ is concerned, this is
equivalent to computing the full one--loop effective potential at scale $M_{\rm
EWSB}$. Since $|\mu|$ and $B$ affect the masses of some (s)particles appearing
in these corrections, this gives a non-linear equation for $|\mu|$ (see  
Fig.~1), which is  solved by a standard iteration algorithm until stability is
reached and a consistent value of $\mu$ is obtained. From a practical point of
view this   requires only three or four iterations for an accuracy of ${\cal
O}(10^{-4})$, if one starts from the values of $|\mu|$ and $B$ as determined
from minimization of the RG--improved tree--level potential at scale $M_{\rm
EWSB}$ and the procedure is extremely fast in CPU as compared to the (iterated)
RGE calculation. \s

At this stage, \sus\ includes a  check on whether the complete scalar potential
has charge and/or  color breaking (CCB) minima  which can be lower than the
electroweak minimum, or whether the tree-level scalar potential is unbounded
from below (UFB). In the present version of the code, we consider only the
following simple  (tree--level) criteria \cite{CCBold}
\beq
{\rm CCB1}: && A^2_f < 3 \, (m^2_{\tilde f_L} +m^2_{\tilde f_R}+ \mu^2 +
m^2_{H_u} ). \label{CCBcons} \\
{\rm UFB1}: && m^2_{H_u} + m^2_{H_d} \geq 2 |B\mu| \ \ {\rm at\, scale} \  
Q^2 >M_{\rm EWSB}^2  \label{UFBcons}
\eeq
\noindent

where $f$ denotes any of the three fermion generations.  Eq.~(\ref{CCBcons})
ensures that there is no deep CCB breaking minimum [due to very small Yukawa
couplings]  in some D--flat directions. One can either take this as a
consistency necessary constraint on the MSSM parameters, or disregard it
appealing  to the fact that such minima are usually well separated from the
electroweak minimum so that the latter can be reasonably stable at
cosmological  scales\footnote{But one would still lack for a compelling reason
why the EW minimum is chosen in the first place!}. For the third generation and
in particular in the top sector, the CCB minimum is not much deeper than the
electroweak minimum, since $y_t$ is not very small,  and not much separated
from it. In this case one should  apply eq.~(\ref{CCBcons}) with some caution
since tunneling effects can be important. On the other hand the
``boundedness-from-below" condition of eq.~(\ref{UFBcons})  is actually an
indication of possible dangerous non physical minima which could form when
radiative corrections are included. At any rate, since both
eqs.~(\ref{CCBcons}) and (\ref{UFBcons}) are merely tree--level conditions,
they should be checked at the highest energy scale.  Note that in the present
version of the code, the calculation is still performed, even if these
conditions are not fulfilled, but a warning  flag is given [see the output file
content in section 4 for more details]. An upcoming version of \sus\ will have
more sophisticated treatments, taking into account loop corrections \cite{CCB}
as well as the geometric configurations of the true minima
\cite{lemouel,Kusenko} as will be discussed later.  \s 

Finally, we reject of course all points in the parameter space which lead to 
tachyonic pseudo--scalar Higgs boson or sfermion masses:
%
\beq
{\rm No\,  Tachyon}: && M_A^2 >0 \ \ , \ \ m^2_{\tilde f} >0 . 
\eeq 
%
Again the occurrence of such problems in the spectrum is signaled in \sus\ 
by appropriate flags as will be discussed in section 4. The electroweak 
symmetry breaking  mechanism is assumed to be consistent when all these 
conditions are satisfied. 

\subsection*{3.3 Calculation of the physical particle masses} 

Once all the soft SUSY--breaking terms are obtained and eventually EWSB is
radiatively realized [as should be the case in unified models] one can then
calculate all the physical particle masses. The  whole procedure (namely, RGE +
EWSB + spectrum calculation) is iterated at least twice until stability is
reached (see the overall algorithm in Fig 1), in order to take into account:
$(i)$ realistic (multi--scale) particle thresholds in the RG evolution of the
dimensionless couplings via step functions in the $\beta$ functions for each
particle threshold and $(ii)$ radiative corrections to SUSY particle masses,
using the expressions given in Ref.~\cite{PBMZ}, where the renormalization
scale is set to $M_{\rm EWSB}$.  \s

Our conventions for the mass matrices in the gaugino, sfermion and
Higgs sectors will be specified below. We basically follow the conventions of
PBMZ with some important exceptions: $(i)$ The $\mu$ parameter is defined with
the opposite sign (see below). $(ii)$ The vevs are different by a factor
$\sqrt{2}$ and  in our case $v=174.1$ GeV. $(iii)$ The sfermion masses are
defined such that $\tilde{f}_1$ and $\tilde{f}_2$ are, respectively, the
lightest and the heaviest one. $(iv)$ The matrices diagonalizing the
chargino and neutralino mass matrices are taken to be real.\s

For the calculation of the physical masses and the implementation of the 
radiative corrections, the various sectors of the MSSM are then treated as 
follows [with some details on the notation and conventions we use; more 
details, in particular on the radiative corrections, will be given in the 
Appendix]: 

\subsubsection*{3.3.1. The sfermion sector}

In the third generation sfermion sector [$\tilde{t},\tilde{b}, \tilde{\tau} $],
mixing between ``left'' and ``right'' current eigenstates is included 
\cite{sfmix}. The
radiatively corrected running fermion masses [essentially the Yukawa coupling
times vevs] at scale $M_{\rm EWSB}$ are employed in the sfermion mass matrices
[this is important at large $\tb$, where these corrections can be quite
sizable].  As mentioned above, contrary to PBMZ, the masses are defined such
that $m_{\tilde{f}_1}$ and $m_{\tilde{f}_2}$ correspond to the mass of
respectively, the lightest and the heaviest sfermion, and therefore, care
should be made in interpreting the sfermion mixing angle $\theta_{\tilde f}$ as
compared to PBMZ.  [Note that a protection which prevents negative
mass squared for third generation sfermions in the presence of too large
mixing is provided.] The sfermion mass matrices and the physical masses and
mixing angles are given  by: 
\begin{eqnarray}
 M_{\tilde{f}}^2 \ = \ 
\left[ \begin{array}{cc} m_{\tilde{f}_L}^2 + ( I^3_f - e_{f} s_W^2) 
M_Z^2 \cos2\beta + m_f^2 & m_f (A_f - \mu r_f) 
\\ m_f (A_f - \mu r_f)  & m_{\tilde{f}_R}^2 - e_{f} s_W^2
M_Z^2 \cos2\beta + m_f^2 \end{array} \right]
\label{defMsf}
\end{eqnarray}
where $m_{\tilde{f}_{L,R}}, A_f, \mu$ and $m_f$ are respectively, 
the $\overline{\rm DR}$ soft SUSY scalar masses, trilinear couplings, higgsino
mass parameter and running fermion masses at the scale $M_{\rm EWSB}$ 
and $r_{b} = r_\tau =1/r_t= \tb$. These matrices are diagonalized by orthogonal
matrices; the mixing angles $\theta_f$ and the squark eigenstate masses are 
given by 
\begin{eqnarray}
\sin 2\theta_f = \frac{2 m_f (A_f -\mu r_f)} { m_{\tilde{f}_1}^2
-m_{\tilde{f}_2}^2 } \ \ , \ \ 
\cos 2\theta_f = \frac{m_{\tilde{f}_L}^2 -m_{\tilde{f}_R}^2} 
{m_{\tilde{f}_1}^2 -m_{\tilde{f}_2}^2 } \hspace*{0.8cm}  \non \\
m_{\tilde{f}_{1,2}}^2 = m_f^2 + \frac{1}{2} \left[ 
m_{ \tilde{f}_L}^2 + m_{\tilde{f}_R}^2 \mp \sqrt{
(m_{\tilde{f}_L}^2 - m_{\tilde{f}_R}^2)^2 + 4m_f^2 (A_f -\mu r_f)^2 } 
\right] 
\end{eqnarray}
The radiative corrections to the sfermion masses are included according to
Ref.~\cite{PBMZ}, i.e. only the QCD corrections for the superpartners of
light quarks [including the bottom squark] plus the leading electroweak
corrections to the two top squarks; the small electroweak radiative corrections
to the slepton masses [which according to PBMZ are at the level of one percent]
have been neglected in the present version. 

\subsubsection*{3.3.2 The gaugino sector}

The $2 \times 2$ chargino and $4\times 4$ neutralino mass matrices  
depend on the $\overline{\rm DR}$ parameters $M_1, M_2, \mu$ at the scale
$M_{\rm EWSB}$ and on $\tb$. The chargino mass matrix given by: 
\begin{eqnarray}
{\cal M}_C = \left[ \begin{array}{cc} M_2 & \sqrt{2}M_W \sin \beta
\\ \sqrt{2}M_W \cos \beta & \mu \end{array} \right]
\label{defMc}
\end{eqnarray}
is diagonalized by two real matrices $U$ and $V$. The chargino masses are
obtained analytically, with the convention that $\chi_1^+$ is the lightest
state [see Appendix A]. \s

The neutralino mass matrix, in the $(-i\tilde{B},
-i\tilde{W}_3, \tilde{H}^0_1,$ $\tilde{H}^0_2)$ basis, has the form  
\begin{eqnarray}
{\cal M}_N = \left[ \begin{array}{cccc}
M_1 & 0 & -M_Z s_W \cos\beta & M_Z  s_W \sin\beta \\
0   & M_2 & M_Z c_W \cos\beta & -M_Z  c_W \sin\beta \\
-M_Z s_W \cos\beta & M_Z  c_W \cos\beta & 0 & -\mu \\
M_Z s_W \sin \beta & -M_Z  c_W \sin\beta & -\mu & 0
\end{array} \right]
\label{defMn}
\end{eqnarray}
It is diagonalized using analytical formulae \cite{egypte} by a single matrix
$Z$ which is chosen to be real, leading to the fact that some (in general one)
of the neutralino eigenvalues is negative [see Appendix A]. The physical masses
are then the absolute values of these eigenvalues with some reordering such
that the neutralinos $\chi_{1,2,3,4}^0$ are heavier with increasing subscript
and $\chi_1^0$ is the lightest neutralino. \s

For the gluino, the  running $\overline{\rm DR}$ mass $m_{\tilde g}$ at scale
$M_{\rm EWSB}$ is identified with $M_3(M_{\rm EWSB}^2)$
\beq
m_{\tilde g}^{\rm tree}= M_3(M_{\rm EWSB}^2)
\eeq
The full one--loop QCD radiative corrections to the gluino mass are
incorporated \cite{drbar}, while in the charginos/neutralinos case the
radiative corrections to the masses are simply included in the
gaugino and higgsino limits, which is a very good approximation \cite{PBMZ}.
These radiative corrections are explicitly given in Appendix A. 

\subsubsection*{3.3.3. The Higgs sector}

The running $\overline{\rm DR}$ mass of the pseudoscalar Higgs boson at the
scale $M_{\rm EWSB}$, $\bar{M}_A$, is obtained from the soft SUSY--breaking
Higgs mass terms frozen at $M_{\rm EWSB}$ and including the full one--loop
tadpole corrections \cite{PBMZ}
\beq
\bar{M}_A^2 (M_{\rm EWSB}) &=& \frac{1}{\cos 2\beta} \bigg( m_{H_d}^2- \frac{t_d}{v_d} - 
m_{H_u}^2 + \frac{t_u}{v_u} \bigg)-\bar{M}_Z^2 + \sin^2\beta \frac{t_d}{v_d} + 
\cos^2 \beta \, \frac{t_u}{v_u}  
\eeq
This mass, together with the $Z$ boson mass $\bar{M}_Z$
at scale $M_{\rm EWSB}$ are then used as input in the CP--even Higgs boson 
$2 \times 2$ mass matrix ${\cal M}_S$. Including the dominant contributions of 
the self--energies of the unrotated CP--even neutral Higgs fields $H_u^0$ and 
$H_d^0$ (as well as the tadpole contributions), this matrix reads at a given 
scale $q^2$ 
\begin{eqnarray}
{\cal M}^S(q^2) = \left[ 
\begin{array}{cccc}
\bar{M}_Z^2\cos\beta^2 + \bar{M}_A^2 \sin^2\beta - s_{11} (q^2) &
- \frac{1}{2}(\bar{M}_Z^2 + \bar{M}_A^2) \sin2\beta - s_{12}(q^2) \\
- \frac{1}{2} (\bar{M}_Z^2+ \bar{M}_A^2) \sin2\beta - s_{12} (q^2) 
& \bar{M}_Z^2 \sin^2\beta + \bar{M}_A^2 \cos^2\beta - s_{22}(q^2) 
\end{array} \right]
\end{eqnarray}
One obtains the running CP--even Higgs boson masses in terms of the matrix 
elements ${\cal M}^S_{ij}$
\beq
\bar{M}_{h,H}^2 = \frac{1}{2} \bigg[ {\cal M}^S_{11}+{\cal M}^S_{22} \mp
\sqrt{ ( {\cal M}^S_{11}-{\cal M}^S_{22})^2+ 4 ({\cal M}^S_{12})^2 } \bigg] 
\eeq
The mixing angle $\alpha$ which diagonalizes the matrix ${\cal M}^S$ and rotates 
the fields $H^0_u, H_d^0$ into the physical CP--even Higgs boson fields $h, H$ 
\begin{eqnarray} 
 \left( \begin{array}{c} H \\ h \end{array}  \right)  = 
 \left( \begin{array}{cc} \cos \alpha & \sin \alpha  \\ -\sin \alpha & 
\cos\alpha \end{array} \right) \ \left( \begin{array}{c} H^0_d \\ H_u^0  
\end{array} \right) 
\end{eqnarray}
is given by 
\beq
\sin 2 \alpha = \frac{ 2 {\cal M}^S_{12} }{ \bar{M}_H^2- \bar{M}_h^2 } \ \ , \ 
\cos 2 \alpha = \frac{ {\cal M}^S_{11} - {\cal M}^S_{22} }{ \bar{M}_H^2- \bar{M}_h^2 }
\ \ \ \bigg( -\frac{\pi}{2} < \alpha < \frac{\pi}{2} \bigg) 
\eeq
The running charged Higgs boson mass at the EWSB scale is given by
\beq
\bar{M}_{H^\pm}^2&=& \bar{M}_A^2 + \bar{M}_W^2 - \sin^2 \beta \, \frac{t_d}{v_d} - 
\cos^2 \beta \, \frac{t_u}{v_u} 
\eeq
The pole masses of all the Higgs bosons are then obtained by including the
self--energy corrections evaluated at the masses of the Higgs bosons 
themselves. \s

In the evaluation of the radiative corrections in the MSSM Higgs sector which 
are known to be very important \cite{RCH}, we have made several options
available: \s

$(i)$ Approximate one--loop and two--loop contributions to the self--energies
(and tadpole) corrections $s_{ij}$ in the mass matrix ${\cal M}^S$. These
expressions, given in Ref.~\cite{FeynHiggsFast}, provide an excellent approximation 
(at the percent level) for the masses of the CP--even Higgs bosons and the  angle
$\alpha$ for a wide range of input parameters. This approximation  (see the
Appendix) is sufficient for most practical purposes and since it makes the
program running faster, it is set as the default choice. A full one loop 
calculation of these  corrections, supplemented by the two--loop QCD and Yukawa
corrections  at zero--momentum transfer \cite{BDSZ} is under
implementation and will  appear soon.\s

$(ii)$ For a very accurate determination of the Higgs masses and couplings,
we have implemented the radiative corrections in the MSSM Higgs sector {\it \`a 
la} {\tt HDECAY} \cite{HDECAY} i.e.\\vspace*{-2mm} the program is interfaced  with the three most
commonly used routines\footnote{We thank Michael Spira for saving us a lot
of time, in performing these interfaces.}: 
\begin{itemize}
\vspace*{-2mm}

\item[--] The routine {\tt subhpolem} of Carena, Quiros and Wagner \cite{SUBH}
which calculates the two--loop QCD corrected Higgs masses in the effective 
potential approach [with the update including the contributions of the gluinos 
which can be important].
\vspace*{-2mm}


\item[--] The routine {\tt HMSUSY} of Haber, Hempfling and Hoang \cite{HHH} 
which approximates the one and two--loop corrections again in the effective 
potential approach. 
\vspace*{-2mm}

\item[--] The routine {\tt FeynHiggsFast} of Heinemeyer, Hollik and Weiglein 
\cite{FHF,FeynHiggsFast} which calculates the one--loop and two--loop QCD 
corrections in the  Feynman diagrammatic approach.  It  is supplemented with
the routine of Brignole, Degrassi, Slavich and Zwirner  for the contributions
of the ${\cal O} (\alpha_t^4)$ corrections \cite{BDSZ}. 


\end{itemize}

\subsection*{3.4 Theoretical and Experimental Constraints on the
spectra\footnote{The implementation of some of the points discussed in this
subsection is still subject to cross checks. These features will be included in
a next release of the program but we nevertheless discuss them here.} }

Once the SUSY and Higgs spectrum is calculated one can check that some
theoretical and experimental requirements are fulfilled. Examples of theory
requirements are for instance, the absence of charge and color breaking (CCB)
minima and that the potential is not unbounded from below (UFB), the absence of
too much fine--tuning (FT) in the determination of the masses of the $Z$ boson
from EWSB as well as in the determination of the top quark mass. For
experimental requirements on the spectrum, one can demand for instance that it
does not lead to large radiative corrections to the precisely measured
electroweak parameters or too large values for the anomalous magnetic moment
of the muon and the branching ratio of the radiative decay of the
$b$--quark.  The program {\tt SuSpect} will provide such tests.

\subsubsection*{3.4.1 CCB and UFB}

As explained previously, in {\tt Suspect}, the EWSB conditions are
consistently  implemented by iteration on the parameters $\mu$ and $B$ and the
occurrence of a local minimum is checked numerically. In the same time one
needs to check for the non existence of deep CCB minima or UFB  directions.
Avoiding such cases may put strong constraints on the model and we mentioned in
section 3.2.3 that we have already implemented two simple CCB and UFB
conditions \cite{CCBold} and the program gives a  warning when they are not
satisfied. \s

In a near future,  we will address the question of CCB  minima and UFB
directions in the most complete possible way, given the present state of the
art. Three complementary features should be considered in relation to the CCB
minima: $(i)$ the directions in the space of scalar fields along which such
minima can develop $(ii)$ whether they are lower than the EWSB minimum $(iii)$
whether  the EWSB (then false)  vacuum can still be sufficiently stable. In
Ref.~\cite{CCB}  a systematic study of point $(i)$ has been carried out
considering subspaces involving the fields $H_u, \tilde{Q}_u, \tilde{u}_R$
($H_d$ and possibly $\tilde{L}$). However, the identified D--flat directions
contain the true minima only in the case of universal scalar soft masses at the
low energy relevant scales, otherwise they constitute only {\sl sufficient}
conditions for the occurrence of CCB minima. While such directions provide very
good approximations for the first two generations, special attention should be
paid to the third generation sector, as was stressed in  \cite{lemouel}. This
is relevant in particular to codes like \sus\ where various SUSY model
assumptions can be considered, including non--universality. Furthermore, the
check of point $(ii)$ as done in \cite{CCB} involves a numerical scan over field
values. Actually there are cases where field-independent conditions can be
obtained even in the case of 5-field directions $H_u, \tilde{Q},
\tilde{u}_R, H_d, \tilde{L}$, leading to faster algorithms; see \cite{lemouel}
and unpublished study. We will thus optimize in \sus\ the various available
complementary approaches. Point $(iii)$ has also its importance as it can
increase the phenomenologically allowed regions of the MSSM parameter space.
Some simple criteria will be encoded, following for instance
Ref.~\cite{Kusenko}.  Finally, the UFB directions as identified in \cite{CCB},
in particular UFB-3, lead to very strong constraints. Nonetheless, there is 
still room for some improvements by optimizing the criterion of  ``deepest
direction", leading in some cases to even stronger constraints which will be
also implemented in {\tt SuSpect}.


\subsubsection*{3.4.2 Fine--Tuning}

One of the main motivations for low energy SUSY is that it solves technically
the hierarchy and naturalness problems. However, since the  $Z$ boson mass is
determined by the soft SUSY--breaking masses $M_{H_u}^2,  M_{H_u}^2$ and the
parameter $\mu^2$, as can be seen from eq.~(11), naturalness  requires that
there are no large cancellations when these parameters are  expressed in terms
of the fundamental parameters of the model [for instance  $m_0, m_{1/2}, \mu,
B$ in mSUGRA], otherwise fine tuning is re--introduced 
\cite{RGE2,fine-tuneold,fine-tune}.  A similar problem
occurs in the case of  the top quark mass, since it is related to the top
Yukawa coupling and  $\tb$.  Various criteria for quantifying the degree of
fine tuning in the determination of $M_Z$ and $m_t$ have been proposed and some
subjectivity is involved in the statement of how much fine tuning can be
allowed. Therefore, in our case,  we will simply evaluate the sensitivity
coefficients for $M_Z^2$ and $m_t$ with respect to a given parameter $a$
\cite{fine-tune}
\beq
\delta M_Z^2/M_Z^2 = C(M_Z^2, a) \, \delta a/a \ \ \ , \ \ \
\delta m_t/m_t = C(m_t, a) \, \delta a/a 
\eeq
and leave to the user the decision of whether the amount of fine--tuning [large 
values of the $C$ coefficients] is bearable or not. We will evaluate only the 
fine--tuning with respect to variations of the parameters $\mu^2$ and $B\mu$, 
for which the coefficients take the simple form: 
\beq
{\rm FT1MZ} &:&  C(M_Z^2, \mu^2) = \frac{2\mu^2}{M_Z^2} \left[ 1+ t_\beta
\frac{4 \tan^2\beta (\bar{m}_1^2-
\bar{m}_2^2) }{ (\bar{m}_1^2-\bar{m}_2^2)t_\beta-M_Z^2} \right] \non \\
{\rm FT1MZ} &:& C(M_Z^2, B\mu) = 4 t_\beta \, \tan^2\beta  \, \frac{
\bar{m}_1^2-\bar{m}_2^2 }{ M_Z^2 (\tan^2\beta -1)^2} \non \\
{\rm FT1MT} &:&  C(m_t,\mu^2) = \frac{1}{2} C(M_Z^2, \mu^2)+ \frac{2\mu^2}
{\bar{m}_1^2+\bar{m}_2^2} \frac{1}{ \tan^2\beta-1} \non \\
{\rm FT1MT} &:&  C(m_t,B\mu) = \frac{1}{2} C(M_Z^2, B\mu)+ 
\frac{1}{ 1-\tan^2\beta} 
\eeq
with $t_\beta=(\tan^2\beta+1)/(\tan^2\beta-1)$.
Further fine-tuning tests can be made, in particular with respect to the $t,b$
Yukawa couplings and are planned to be included in future versions. 


\subsubsection*{3.4.3 Electroweak precision measurements} 

Loops involving Higgs and SUSY particles can contribute to electroweak
observables which have been precisely measured at LEP, SLC and the Tevatron. In
particular, the radiative corrections to the self--energies of the $W$ and $Z$
bosons, $\Pi_{WW}$ and $\Pi_{ZZ}$, might be sizable if there is a large mass
splitting between some particles belonging to the same SU(2) doublet; this can
generate a contribution which grows as the mass squared of the heaviest
particle. The dominant contributions to the electroweak observables, in
particular the $W$ boson mass and the effective mixing angle $s_W^2$, enter via
a deviation from unity of the $\rho$ parameter \cite{drho0}, which measures the
relative strength of the neutral to charged current processes at zero momentum
transfer, i.e. the breaking of the global custodial SU(2) symmetry:
\beq    
%\Delta M_W \simeq \frac{c_W^2 M_W}{2(c_W^2-s_W^2)} \Delta \rho \ \ , \ \
%\Delta s_W^2 \simeq - \frac{2c_W^2 s_W^2}{c_W^2-s_W^2} \Delta \rho \non \\
\rho = (1-\Delta \rho)^{-1} \ ; \ \Delta \rho = \Pi_{ZZ}(0)/M_Z^2 - 
\Pi_{WW}(0)/M_W^2
\eeq
Most of the MSSM contributions to the $\rho$ parameter are small, $\Delta \rho
\lsim 10^{-4}$ \cite{drhoS}. In the case of the Higgs bosons, the contributions
are logarithmic, $\sim \alpha {\rm Log} (M_h/M_Z)$, and are similar to those of
the SM Higgs boson [and identical in the decoupling limit]. The chargino and
neutralino contributions are small because the only terms in the mass matrices
which could break the custodial SU(2) symmetry are proportional to $M_W$. Since
in general, first/second generation sfermions are almost degenerate in mass,
they also give very small contributions to $\Delta \rho$. Therefore, only the
third generation sfermion sector can generate sizable corrections to the $\rho$
parameter, because left--right mixing and [in case of the stop] the SUSY 
contribution $\propto m_f^2$ leads to a potentially large splitting between the
sfermion masses. \s

We have thus calculated $\Delta \rho$ in the MSSM, taking into account only 
the contributions of  the third generation sfermions. We include full mixing 
and in the case of the stop/sbottom doublet, also the two--loop QCD corrections
due  to gluon exchange and the correction due to gluino exchange in the heavy
gluino limit,  which can increase the contribution by 30\% or so \cite{sloop}.
One can then  require the SUSY contribution not to exceed two standard 
deviations from the SM expectation~\cite{LEPrho}: $\Delta \rho ({\rm SUSY}) 
\lsim 2 \cdot 10^{-3}$. 


\subsubsection*{3.4.4 The muon (g-2)} 

\nn The muon $(g-2)$ anomalous magnetic moment has been very precisely
measured  to be \cite{BNL}: 
\begin{eqnarray} 
(g_\mu-2) \equiv a_\mu^{\rm exp} = (11\, 659\, 202\, \pm 8) \, 10^{-10}, \ 
\end{eqnarray} 
The value predicted in the SM, including the QED, QCD and electroweak 
corrections is: $a_\mu^{\rm SM} = 11\, 659\, 169\ (11) \, 10^{-10}$ 
\cite{SMgm2} where the errors are mainly originating from the hadronic 
uncertainties. The measured value and the SM prediction are consistent at  the
3$\sigma$ level. Therefore, this sets strong constraints on the  additional
contribution from SUSY particles. \s

The contribution of SUSY particles to $(g_\mu-2)$ \cite{g-2old,g-2} is mainly 
due to neutralino--smuon and chargino--sneutrino loops [if no flavor violation 
is present as is the case here]. In many models (such as mSUGRA), the
contribution of chargino--sneutrino loops usually dominates. If the SUSY
particles are relatively heavy, the contribution of $\chi_i^\pm$--$\tilde{\nu}$
loops can be approximated by [$\tilde{m}$ is the mass of the heaviest particle
per GeV]:  $|\Delta a_{\mu}^{\tilde\chi^\pm \tilde{\nu}}| \sim 10^{-5}
\times (\tb / \tilde{m}^2)$, to be compared with the contribution of
$\chi_i^0$--$\tilde{\mu}$ loops, $|\Delta a_{\mu}^{\tilde\chi^0 \tilde{\mu}}|
\sim 10^{-6} \times (\tb / \tilde{m}^2)$, which is an order of
magnitude smaller.  These contributions are large for large values of $\tb$ and
small values of the scalar and gaugino masses and their sign is equal to the
sign of $\mu$. \s

We have included a routine which calculates the full one--loop contributions of
chargino--sneutrino and neutralino--smuon loops in the MSSM, using the
analytical expressions given in Ref.~\cite{g-2}. In this case, the full mixing
in the smuon sector is of course included [this is the only place where the
$A_\mu$ parameter plays a role in the code]. The sum of the   chargino and
neutralino contributions should lie in the 3$\sigma$ range allowed by the
experimental measurement. 

\subsubsection*{3.4.5 The radiative decay $b \to s\gamma$} 

Another observable where SUSY particle contributions might be large is the
radiative flavor changing decay $b\to s\gamma$ \cite{bsg0,bsg1}. In the SM this 
decay is mediated by loops containing charge 2/3 quarks and $W$--bosons but in 
SUSY theories, additional contributions come from loops involving charginos and
stops, or top quarks and charged Higgs bosons [contributions from loops
involving gluinos or neutralinos are very small \cite{bsg0} in the models
considered here].  Since SM and SUSY contributions appear at the same order of
perturbation theory, the measurement of the inclusive $B \ra X_s \gamma$ decay
branching ratio \cite{PDG}
\begin{eqnarray} \label{brbsgex}
{\rm BR}(b \ra s \gamma) = (3.37 \ \pm 0.37 \ \pm 0.34 \ \pm 
0.24^{+0.35}_{-0.16} \ \pm 0.38) \cdot 10^{-4} \label{CLEO}
\end{eqnarray}
[where the first three errors are due respectively to statistics, systematics,
and model dependence, while the fourth error is due to the extrapolation from
the  data to the full range of possible photon energies and the fifth error is
an  estimate of the theory uncertainty] is a very powerful tool for
constraining  the SUSY parameter space. \s

Recently, the authors of Ref.~\cite{bsg1,paolo}  have calculated the
next--to--leading order QCD corrections to the decay rate in the MSSM and
provided a {\sc Fortran} code which gives the most up--to--date
determination of BR($b \to s\gamma)$ where all known perturbative and
non--perturbative effects are implemented, including all the possibly large
contributions which can occur at NLO, such as terms $\propto \tan \beta$ and/or
terms containing logarithms of $M_{\rm EWSB}/M_W$. We have interfaced this
routine with our code\footnote{We thank Paolo Gambino for providing us with
his code and for his help in interfacing it with ours.} and plan to make this
interface available in a next version of \sus. Besides the fermion and gauge
boson masses and the gauge couplings that we have as input, we will use the
values of the other SM input parameters required for the calculation of the
rate given in Ref.~\cite{bsg3}, except for the cut--off on the photon energy,
$E_{\gamma} > (1-\delta)m_b/2$ in the bremsstrahlung process $b \to s\gamma
g$, which we fix to $\delta=0.9$ as in Ref.~\cite{paolo}.  

\subsection*{3.5 Scanning the parameter space}

Using the theoretical and  experimental constraints discussed previously, one
can perform a full scan of the MSSM parameter space with \sus\.  This can be
done straightforwardly upon simply adding 	appropriate {\sc Fortran} (do)
loops on the input parameter space within  the main \sus\ calling routine {\tt
suspect2$\_$call.f} that we will describe later.  In the following, we give for
illustration an example of such a scan taken from an update of the analysis of
the mSUGRA model performed in Ref.~\cite{DDK}. \s

For the values $\tb=40$, $A_0=0$ and with a positive $\mu$ parameter, we vary
the scalar mass  parameter $m_0$ from $10$ to 2500 GeV with a grid of 10 GeV
and the gaugino  mass parameter $m_{1/2}$ from 5 to 1250 GeV with a grid of 5
GeV. This makes  62.500 points to scan in the $(m_{1/2}, m_0)$ plane, which
takes a few hours on a 1 GHz PC as discussed later. We impose the following  
constraints, in addition to the ones which are signaled by default in \sus\ 
(such  as proper EWSB, no CCB and UFB, non--tachyonic particles, etc..): \s

-- The experimental bounds from negative searches of charginos, sleptons and
third  generation squarks at LEP2 and squarks and gluinos at the Tevatron
\cite{PDG}:  $m_{\chi_1^+} \geq 104~{\rm GeV}, m_{\tilde{f}} \geq  100$
GeV with  $\tilde{f}= \tilde{t}_1, \tilde{b}_1, \tilde{l}^\pm, \tilde{\nu}$
and  $m_{\tilde{g}} \geq 300~{\rm GeV}, m_{\tilde{q}_{1,2}} \geq  260$ GeV with
$\tilde{q}= \tilde{u}, \tilde{d}, \tilde{s} , \tilde{c}$. We also require 
that the LSP is the lightest neutralino $\chi_1^0$. \s

-- The Higgs mass constraints \cite{LEPH}: i.e. the 95\% CL lower bound on the
mass of a  SM--like Higgs from  LEP2 searches, $M_{H^0} \geq 114$ GeV [in the
MSSM, this bound is  valid in the decoupling regime where the pseudoscalar $A$
boson is very heavy] and for small values of $M_A$, the combined exclusion
limit of $M_h \sim M_A \geq 92$ GeV  [in the intermediate region an
interpolation has to be made]. We will also display the region where a SM--like 
Higgs boson with a mass $M_{H^0} = 115.5 \pm 1.5$ GeV, as suggested by
the $2\sigma$ excess at LEP2, is possible.  \s

-- Constraints from electroweak precision observables: the dominant
contributions to the deviation from unity of the $\rho$ parameter are due to
the third generation $(\tilde{t}, \tilde{b})$ and $(\tilde{\tau}, \tilde{\nu})$
weak iso--doublets, and one has to require that these contributions stay below
the acceptable [$2\sigma$ deviations from the measurement] level of $ \Delta
\rho (\tilde{f}) \leq 2.2 \cdot 10^{-3}$ \cite{LEPrho}. \s

-- The $b\to s \gamma$ decay branching ratio: where SUSY particle contributions
might be rather large as discussed in subsection 3.4.5. Using the routine {\tt 
bsg.f} which gives the most up--to--date determination in the MSSM of the $b 
\to s \gamma$ decay rate including NLO QCD corrections \cite{paolo}, we allow 
the full SM+SUSY value of the branching ratio to vary in the $2\sigma$ range: 
$2.0 \times 10^{-4} \leq {\rm BR}(b \to s \gamma) \leq 5.0 \times 10^{-4}$.\s

-- The contribution to the muon $g-2$: where the new measurement of the 
Brookhaven experiment differs from the predicted SM average value by 3$\sigma$ 
or 1.5$\sigma$ if one takes into account data from $\tau$ decay \cite{SMgm2}.
We interpret the discrepancy as being a SUSY contribution from
chargino--sneutrino and neutralino--smuon loops. \newpage

The effects of all these  constraints on the $(m_{1/2}, m_0)$ parameter space
are shown in Fig.~2. The most stringent theoretical  constraint is the
requirement of proper electroweak symmetry breaking.  In the small green area,
the pseudoscalar Higgs boson mass takes tachyonic values. The region with
tachyonic sfermion masses is indicated in dark blue. In the yellow area the
iteration to determine $|\mu|$ does not converge to a value $\mu^2 > 0$.  The
latter constraint plays an important role and excludes, depending on the value
of $\tb$ [and/or $m_t, m_b, M_{\rm EWSB}$ as discussed in \cite{DDK} for
instance], many scenarii with $m_0 \gg m_{1/2}$.  The requirement that the LSP
is indeed the lightest neutralino rules out the region (in light blue) of small
values of $m_0$ where the less massive $\tilde{\tau}_1$ slepton is lighter than
$\tilde\chi_1^0$. \s

Turning to the experimental constraints on SUSY particle masses,  the
requirement that the lightest charginos are heavier than $\sim 104$ GeV (brown
area) extends the region of no EWSB while the requirement of heavy enough
sleptons, $m_{\tilde l}  \gsim 100$ GeV (dark area), slightly extends the
region where sfermions  are tachyonic. For small values of $m_0$ the
right--handed side of the boundary does not depend on $m_0$; in this region,
$\tilde\chi_1^\pm$ is wino--like and its mass is approximately given by
$m_{\tilde\chi_1^\pm} \sim M_2 \sim 0.8 m_{1/2}$. For larger values of $m_0$,
one enters the ``focus point" \cite{Focuspoint} region where $\tilde\chi_1^\pm$
is a mixture of higgsino and gaugino states; for even larger values of $m_0$,
$\mu$ becomes smaller and the chargino is higgsino--like with
$m_{\tilde\chi_1^\pm} \sim |\mu|$, until one reaches the ``no EWSB'' region
where no consistent value of $\mu$ is obtained.  Note that for the values of
$\tb$ and $A_0$ used here, there are no points, not already ruled out by the
constraints on EWSB and the SUSY particle mass bounds, which are excluded by
the $\Delta \rho$ constraint, since the splitting between the top squarks
remains moderate. The CCB constraint, which is somewhat related, is also not
effective in this case, because $A_t(M_{\rm EWSB})$ remains moderate compared
to the masses of the stop eigenstates in this mSUGRA scenario.\s

The lightest Higgs boson mass constraint $M_h>114$ GeV (in the light red area
of the top--right figure) is only effective if $m_0 \lsim 1$ TeV and $m_{1/2}
\lsim 300$ GeV since we are in a large $\tb$ scenario where $M_h$ can easily be
sufficiently large. The ``evidence" of a SM--like Higgs boson with a mass
between 114 and 117 GeV (darker red area) covers a much larger parameter space.
The constraint from the measurement of the $b \to s \gamma$ branching ratio
excludes only a small additional part of the parameter space (green area) with
low $m_0$ and $m_{1/2}$ values (medium green area) leading to light charginos
and top squarks [the constraint would have been stronger for $\mu<0$].  The
contribution of SUSY particles to the $(g-2)_\mu$ (blue area) accounting for
the deviation from the central experimental value extends from values $m_0
\lsim 0.8$ TeV for small $m_{1/2}$ to the boundary where the neutralino
$\tilde\chi_1^0$ is not the LSP for large values, $m_{1/2} \sim 0.5$ TeV, except
in a little corner for values $m_{1/2} \sim m_0$ of a few hundred GeV, where
the SUSY contribution exceeds the $3\sigma$ upper bound. In this area,
charginos and smuons have relatively small masses and can give too large a
contribution to $(g_\mu-2)$. 

%%%%%%%%%%%%%%%%%%%%%%%%% FIG1: TB=40 INDIVIDUAL CONSTRAINTS %%%%%%%%%%%%%
\setcounter{figure}{1}
\begin{figure}[htbp]
%\vspace*{-.5cm}
%\begin{center}
%\centerline{\large \protect{$\tan\beta$=40}\ , \ $A_0 = 0$ \ ,\  \protect{sign$(\mu)>0$} }
\hspace*{-.2cm}{\large $m_0$}\\[-.2cm]
\begin{center}
\hspace*{-.2cm}\mbox{\epsfig{figure=fscan.ps,bbllx=85,bblly=350,bburx=515,bbury=720,width=10.cm}}
\end{center}
\vspace*{7.cm}
\hspace*{14.9cm} {\large $m_{1/2}$}
\vspace*{2mm}
\caption[]{Constraints on the $(m_{1/2}, m_0)$ mSUGRA plane for $\tan\beta=40, 
A_0 = 0, {\rm sign}(\mu)>0$. Top--Left: 
individual constraints from non--convergent $\mu$ (yellow region), tachyonic 
$M_A$ (green), tachyonic sfermions (blue), light sfermions (dark), light 
charginos (brown), $\chi_1^0$ non--LSP (light blue). Top--Right: constraint
on the Higgs boson mass (light red) and the LEP2 evidence for a 115.5 GeV 
Higgs (red). Bottom--Left: constraint from BR($b \to s \gamma)$ (green) 
and Bottom--Right: the SUSY contribution to the $(g-2)_\mu$ (blue). The gray 
areas are those already excluded by the contraints of the top--left figure.} 
\end{figure}

\newpage


\section*{4. Running {\tt SuSpect}}

\subsection*{4.1 Basic facts about {\tt SuSpect}}

The program {\tt Suspect} is composed of several files and routines: \s

$i)$ \underline{The input file {\tt suspect2.in}}: here one can select the
model to be investigated, the accuracy of the algorithm, the input data (SM
fermion masses and gauge couplings). Some reasonable default values are set in
the example of input file which is discussed in the next subsection. One would 
then simply select the SUSY model (pMSSM, mSUGRA, GMSB and AMSB), choose the
corresponding input parameters and possibly make a few choices concerning the
physical calculation (such as enforcing or not unification of the gauge
couplings, changing the scale at which EWSB occurs, including or not radiative
corrections to the masses and choosing the routine calculating the Higgs boson
masses).  \s 

$ii)$ \underline{The program {\tt suspect2\_call.f}}: this is an example of a 
routine
which calls the main subroutine {\tt suspect2.f}. This program is necessary to
run \sus\ since it defines the primary algorithm control input parameters needed
by the latter. In particular, there is a parameter ({\tt INPUT}) which allows
to bypass the reading of the input file  {\tt suspect2.in}, in which case all
the parameters and choices are to be defined by the user in this calling
routine.  This is particularly useful for interfacing  \sus\ with other
routines and/or for scans of the parameter space. A file example is
discussed in Appendix B where details can be found.\s 

$iii)$ \underline{The main routine {\tt suspect2.f}}: here all the
calculation of the spectrum is performed, once the input is supplied by {\tt
suspect2.in} or {\tt suspect2\_call.f}. This routine is self--contained, except
for the determination of the Higgs boson masses, where it needs to call the
three routines discussed in subsection 3.3.3 that we also supplied: {\tt
subh\_hdec.f}, {\tt feynhiggs.f} and {\tt hmsusy.f}.  [Note that {\tt
suspect2.f} has its own approximate calculation of the Higgs masses, but these
three routines will be anyway needed for the compilation]. \s

$iv)$ \underline{An output file {\tt suspect.out}}: this file is in principle
generated by default [it can be switched off by an appropriate value of the 
control
parameter {\tt INPUT} in {\tt suspect2\_call.f}] at each run of the program and
gives the results for the output soft SUSY--breaking parameters [when they are
calculated] and the masses and mixing angles of the Higgs and SUSY particles. 
Some warnings and comments are also given when the obtained spectrum is
problematic. Examples of output files are given in subsection 4.3.  \s 

The routine {\tt suspect2.f} consists of about 6.000 lines of code and takes 
about 200 Ko of memory, while the input and the calling routines have only a 
few hundred lines (most of them being comments). However, the accompanying 
routines for the calculation of the Higgs masses are somewhat longer; in 
particular, the routine {\tt FeynHiggsFast} has more than 16.000 lines of code. As 
mentioned previously, these routines are provided separately. The complete
executable code takes about 1.7 Mo space. \s

The {\sc Fortran} files have to be compiled altogether and, running for instance 
on a PC using {\sc gnu Fortran}, the compilation and link commands are:

g77 -c -finit-local-zero suspect2\_call.f suspect2.f hmsusy.f subh\_hdec.f 
                        feynhiggs.f

g77 -o suspect suspect2\_call.o suspect2.o hmsusy.o subh\_hdec.o feynhiggs.o

suspect\s

\nn [The compilation option {\tt -finit-local-zero} is mandatory due to the usual 
non-initialization by default with {\sc gnu Fortran}; no
other compilation option is in principle needed].  The running time for a 
typical model point, for instance the mSUGRA point discussed below, is
about 0.5 seconds on a PC with a 1 GHz processor. \s

In the next sections, we will exhibit the input and output files taking a few 
examples in the various models that we consider [this allows to compare 
with spectra given by other routines]. For illustration, we will use the
benchmark points from the Snowmass Points and Slopes \cite{benchmark}
for the followings models [for the first point, we will calculate the 
SUSY--breaking parameters at the EWSB scale and then inject them as if we 
were in the pMSSM]: 
\begin{eqnarray}
{\rm pMSSM~(SPS6)} &:& 2m_0= \frac{M_1}{1.6}=
M_2=M_3=300~{\rm GeV} \ , \ A_0=0 \ , \  \tb=30 \non  
\ , \ \mu>0 \\
{\rm mSUGRA~(SPS1b)} &: & m_0=200~{\rm GeV}\ , \ m_{1/2}=400~{\rm GeV}
\ , \ A_0=0 \ , \  \tb=30 \ , \ \mu>0 \nonumber \\ 
{\rm GMSB~(SPS8)} &:& \Lambda =100~{\rm TeV} \ , M_{\rm mes}=200~{\rm TeV}
\ , \ n_l=n_q=1 \ , \ \tb=15 \ , \ \mu>0 \nonumber \\
{\rm AMSB~(SPS9)} &:&  m_0=450~{\rm GeV} \ , \ m_{3/2}=60~{\rm TeV} 
\ , \ \tb=10 \ , \ \mu>0 \ , \ c_i=1 \non
\eeq
The input and output files are self--explanatory and will not be 
commented  further, in particular since some details will be given in
Appendix B. Furthermore, for convenience, we will exhibit the warning/error 
message part of the output file which normally appears at each \sus\ run
only once, at the end of the first  point,
since ``everything is fine" for all the chosen input here 
[i.e.\ there is no problem with the spectrum].

\subsection*{4.2 The input file}
\vspace*{-2mm}
\begin{verbatim}
                          SUSPECT2.1 INPUT FILE
                          ---------------------
* Initialize various options (choice of models, algorithm  control etc..)
ICHOICE(1): Choice of the model to be considered:
            Arbitrary soft-terms at low scale (no RGE): 0
            Arbitrary soft-terms at high scale (RGE)  : 1
            mSUGRA (cMSSM)                            : 10
            GMSB   (cMSSM)                            : 11
            AMSB   (cMSSM)                            : 12
          10

ICHOICE(2): All the RGEs are at 1-loop order          : 11
            2-loop RGEs for gauge+Yukawas+gauginos    : 21
          21

ICHOICE(3): GUT scale imposed (HIGH to be given below): 0 
            GUT (at g_1=g_2) scale derived from input : 1
          0

ICHOICE(4): RGE sufficiently accurate and fast        : 1
            RGE very accurate but rather slow         : 2
          1 

ICHOICE(5): No radiative EWSB imposed (only in pMSSM) : 0 
            Consistent EWSB (automatic in cMSSMs)     : 1 
          1

ICHOICE(6): M_A, MU as input     (only in pMSSM)      : 0
            M_Hu, M_Hd as input  (only in pMSSM)      : 1
          1

ICHOICE(7): SUSY radiative corrections to the (s)particles masses: 
            No R.C. (! except for Higgs masses)       : 0 
            R.C also in mb,mt,mtau + Yukawa couplings : 1  
            R.C. to squark/gaugino masses in addition : 2
          2

ICHOICE(8): Default EWSB scale=(mt_L*mt_R)^(1/2)      : 1 
            Arbitrary EWSB scale (to be given below)  : 0 
          1

ICHOICE(9): Nb of (long: RGE + full spectrum) iterations: >= 3 
          3

ICHOICE(10): Routine for the calculation of the Higgs boson masses:
             SUSPECT calculation (gen. sufficient)    : 0
             SUBH_HDEC (Carena et al.) from HDECAY    : 1
             HMSUSY (Haber et al.) routine            : 2
             FEYNHIGGSFAST1.2.2 (Heinemeyer et al.)   : 3
          0

* Initialize "SM" parameters (default values here): 
1/alpha(MZ),   s^2_W(MZ),   alpha_S(MZ),  M_t(pole), M_b(pole),   M_tau
127.938        0.23117       0.1192        174.3      4.9         1.7771

* RGE scales(GeV): HIGH (=GUT scale if imposed), Low RGE ends; EWSB scale: 
1.9d16         91.19                  175.

* mSUGRA model input parameters: 
*  m_0        m_1/2        A_0    tan(beta)   sign(mu)
  200.        400.         0.     30.          1.

* GMSB model input parameters:
* MGM_mes     MGM_susy   tan(beta)   sign(mu) Nl_mes    Nq_mes
  200.d3      100.d3     15.         1.       1         1  

* AMSB model input parameters:
* M_3/2    m_0     tan(beta)   sign(MU)  cQ  cuR  cdR  cL  ceR cHu cHd
  60.d3    450.    10          1.        1.  1.   1.   1.  1.  1.  1.

* Non-universal MSSM input (irrelevant if constrained MSSM chosen): 
M_Hu^2    M_Hd^2  (V_Higgs mass terms)   tan(beta)  sign(mu)
-0.15d6   0.62d5                          10.        1.
M_1       M_2      M_3                           (gaugino mass terms)
200.      230.     700.
M_tauL    M_tauR   M_QL    M_tR    M_bR (3rd gen. L and R mass terms) 
260.      235.     600.    515.    630.
M_eL      M_eR     M_qu    M_uR    M_dR (1/2 gen. L and R mass terms)  
260.      240.     660.    640.    630.
A_tau     A_t      A_b     A_e     A_u    A_d   (trilinear couplings)
-200.    -570.     -850.  -220.   -930.   -910.

M_A   MU   if input instead of M_Hu, M_Hd (not in constrained MSSM):
470.  386.
\end{verbatim}

\newpage

\subsection*{4.3 The output files}

\subsubsection*{4.3.1 The output in the pMSSM case}
\begin{verbatim}
             SUSPECT2.1 OUTPUT: pMSSM CASE
No RGEs: only spectrum calculation at the low energy scale
             -----------------------------
Input values:
-------------
  M_top      M_bot      M_tau      1/alpha    sw**2(M_Z)   alpha_S
  174.3      4.900      1.777      127.94     0.2312       0.1192    

Input non-universal soft terms at M_EWSB
----------------------------------------
  mu         M_A        tan(beta)  sign(mu)
  386.0      469.2      10.00      1.000    
  M_1        M_2        M_3
  200.0      230.0      700.0    
  m_eR       m_eL       m_dR       m_uR       m_qL
  240.0      260.0      630.0      640.0      660.0    
  m_tauR     m_tauL     m_bR       m_tR       m_QL
  235.0      260.0      630.0      515.0      600.0    
  Atau       Abottom    Atop       Al         Ad         Au
 -200.0     -850.0     -570.0     -220.0     -910.0     -930.0    

Mass matrices and mixing angles:
--------------------------------
  tan(beta)  alpha_(h,H)
  10.00    -0.1077    
  thet_tau   thet_b     thet_t
  1.142     0.3227      1.059    
  Z(i,j)
  0.9308     -0.2599      0.2232     -0.1271    
  0.3292      0.9013     -0.2371      0.1517    
  0.4761E-01 -0.8145E-01 -0.6978     -0.7100    
  0.1512     -0.3368     -0.6380      0.6758    
  U(i,j)                  V(i,j)
 -0.9084      0.4181     -0.9639      0.2661    
  0.4181      0.9084      0.2661      0.9639    

Final Higgs and SUSY particle masses: 
------------------------------------- 
  h          A          H          H+
  111.1      469.2      469.5      475.8    

  chi+_1     chi+_2     chi0_1     chi0_2     chi0_3     chi0_4
  218.1      410.0      190.9      221.1     -388.8      411.3    

  gluino
  746.1    

  stop_1     stop_2     sup_1      sup_2
  523.9      666.8      668.5      687.0    

  sbot_1     sbot_2     sdown_1    sdown_2
  629.4      663.5      660.1      691.6    

  stau_1     stau_2     snutau     selec_1    selec_2    snuelec
  231.9      270.4      252.0      243.9      264.2      252.0    

Warning/Error Flags: errmess(1)-(10):
-------------------------------------
   0. 0. 0. 0. 0. 0. 0. 0. 0. 0.
---------------------------------
errmess(i)= 0: Everything is fine.
errmess(1)=-1: tachyon 3rd gen. sfermion from RGE
errmess(2)=-1: tachyon 1,2 gen. sfermion from RGE
errmess(3)=-1: tachyon A    (maybe temporary: see final mass) 
errmess(4)=-1: tachyon 3rd gen. sfermion from mixing
errmess(5)=-1: mu(M_GUT) guess inconsistent 
errmess(6)=-1: non-convergent mu from EWSB 
errmess(7)=-1: EWSB maybe inconsistent        (!but RG-improved only check)
errmess(8)=-1: V_Higgs maybe UFB or CCB       (!but RG-improved only check)
errmess(9)=-1: Higgs boson masses are NaN 
errmess(10)=-1: RGE problems (non-pert and/or Landau poles)
\end{verbatim}

\newpage

\subsubsection*{4.3.2 The output in the mSUGRA case}
\begin{verbatim}
             SUSPECT2.1 OUTPUT: MSUGRA CASE
             ------------------------------

Input values:
-------------
  m_0        m_1/2      A_0        tan(beta)  sign(mu)
  200.0      400.0      0.000      30.00      1.000    

  M_top      M_bot      M_tau      1/alpha    sw**2(M_Z)   alpha_S
  174.3      4.900      1.777      127.94     0.2312       0.1192    

  M_GUT      M_EWSB     E_LOW       (input or ouput scales)
 0.1900E+17  716.9      91.19    

Fermion masses and gauge couplings: HIGH/EWSB
---------------------------------------------
  M_top      M_bot      M_tau     g1**2      g2**2      g3**2
  72.01      1.053      1.473     0.5129     0.5132     0.5008    
  155.1      2.681      1.856     0.2130     0.4255      1.521    

mu parameter and soft terms at M_EWSB:
--------------------------------------
  mu         B          M^2_Hu       M^2_Hd
  493.0      20.99    -0.2416E+06    7432.    

  M_1        M_2        M_3
  166.0      309.7      913.4    

  m_tauR     m_tauL     m_bR       m_tR       m_QL
  221.7      327.5      781.9      669.6      769.8    

  m_eR       m_eL       m_dR       m_uR       m_qL
  251.3      338.1      823.4      828.0      862.8    

  Atau       Abottom    Atop       Al         Ad         Au
 -182.5     -989.0     -724.8     -195.6     -1117.     -965.2    
Mass matrices and mixing angles:
--------------------------------
  tan(beta)  alpha_(h,H)
  29.98    -0.3468E-01

  thet_tau   thet_b     thet_t
  1.190     0.6847      1.126    

  Z(i,j)
  0.9936     -0.2089E-01  0.1041     -0.3742E-01
  0.5208E-01  0.9541     -0.2485      0.1588    
  0.4536E-01 -0.6705E-01 -0.7009     -0.7086    
  0.8893E-01 -0.2911     -0.6604      0.6865    

  U(i,j)                  V(i,j)
 -0.9349      0.3550     -0.9739      0.2271    
  0.3550      0.9349      0.2271      0.9739    

Final Higgs and SUSY particle masses: 
------------------------------------- 
  h          A          H          H+
  113.8      556.0      557.1      562.5    

  chi+_1     chi+_2     chi0_1     chi0_2     chi0_3     chi0_4
  304.8      514.1      162.6      305.0     -497.6      513.4    

  gluino
  969.0    

  stop_1     stop_2     sup_1      sup_2
  682.9      825.3      856.9      890.3    

  sbot_1     sbot_2     sdown_1    sdown_2
  781.8      832.5      853.5      894.0    

  stau_1     stau_2     snutau     selec_1    selec_2    snuelec
  200.1      347.2      321.1      255.1      341.4      331.9    
\end{verbatim}

\subsubsection*{4.3.3 The output in the  GMSB case}
\begin{verbatim}
             SUSPECT2.1 OUTPUT: GMSB CASE
             ----------------------------

Input values:
-------------
  M_mess     M_susy     nl         nq         tan(beta)  sign(mu)
 0.2000E+06 0.1000E+06   1           1        15.00      1.000    

  M_top      M_bot      M_tau      1/alpha    sw**2(M_Z)   alpha_S
  174.3      4.900      1.777      127.94     0.2312       0.1192    

  M_GUT      M_EWSB     E_LOW       (input or ouput scales)
 0.1900E+17  1020.      91.19    

Fermion masses and gauge couplings: HIGH/EWSB
---------------------------------------------
  M_top      M_bot      M_tau     g1**2      g2**2      g3**2
  71.27      1.035      1.391     0.5137     0.5127     0.4999    
  155.2      2.727      1.811     0.2130     0.4256      1.522    

mu parameter and soft terms at M_EWSB:
--------------------------------------
  mu         B          M^2_Hu       M^2_Hd
  411.1      49.51    -0.1531E+06   0.1088E+06

  M_1        M_2        M_3
  144.7      272.2      756.3    

  m_tauR     m_tauL     m_bR       m_tR       m_QL
  170.1      354.3      1057.      975.5      1070.    

  m_eR       m_eL       m_dR       m_uR       m_qL
  172.4      354.9      1062.      1067.      1115.    

  Atau       Abottom    Atop       Al         Ad         Au
 -26.83     -271.4     -245.7     -26.89     -278.1     -263.1    
Mass matrices and mixing angles:
--------------------------------
  tan(beta)  alpha_(h,H)
  15.00    -0.7095E-01

  thet_tau   thet_b     thet_t
  1.458      1.177      1.481    

  Z(i,j)
  0.9895     -0.3415E-01  0.1306     -0.5230E-01
  0.8335E-01  0.9252     -0.3060      0.2084    
  0.5211E-01 -0.7595E-01 -0.6987     -0.7095    
  0.1063     -0.3703     -0.6334      0.6712    

  U(i,j)                  V(i,j)
 -0.8972      0.4416     -0.9535      0.3013    
  0.4416      0.8972      0.3013      0.9535    

Final Higgs and SUSY particle masses: 
------------------------------------- 
  h          A          H          H+
  112.9      553.6      554.0      559.1    

  chi+_1     chi+_2     chi0_1     chi0_2     chi0_3     chi0_4
  262.4      436.4      140.0      262.8     -413.8      436.3    

  gluino
  909.5    

  stop_1     stop_2     sup_1      sup_2
  1023.      1110.      1098.      1144.    

  sbot_1     sbot_2     sdown_1    sdown_2
  1086.      1106.      1094.      1147.    

  stau_1     stau_2     snutau     selec_1    selec_2    snuelec
  172.2      359.1      348.5      177.9      358.0      349.0    
\end{verbatim}

\subsubsection*{4.3.4 The output in the AMSB case}
\begin{verbatim}
             SUSPECT2.1 OUTPUT: AMSB CASE
             ----------------------------

Input values:
-------------
  M_3/2      m_0        tan(beta)  sign(mu)
 0.6000E+05  450.0      10.00      1.000    
  cQ      cuR     cdR     cL      ceR     cHu     cHd
  1.00    1.00    1.00    1.00    1.00    1.00    1.00    
  M_top      M_bot      M_tau      1/alpha    sw**2(M_Z)   alpha_S
  174.3      4.900      1.777      127.94     0.2312       0.1192    
  M_GUT      M_EWSB     E_LOW       (input or ouput scales)
 0.1900E+17  967.6      91.19    

Fermion masses and gauge couplings: HIGH/EWSB
---------------------------------------------
  M_top      M_bot      M_tau     g1**2      g2**2      g3**2
  73.76      1.026      1.390     0.5111     0.5123     0.4960    
  156.6      2.639      1.793     0.2132     0.4255      1.512    

mu parameter and soft terms at M_EWSB:
--------------------------------------
  mu         B          M^2_Hu       M^2_Hd
  998.9      109.7    -0.9798E+06   0.1009E+06

  M_1        M_2        M_3
  554.1      167.9     -1272.    

  m_tauR     m_tauL     m_bR       m_tR       m_QL
  322.4      399.2      1200.      865.0      1123.    

  m_eR       m_eL       m_dR       m_uR       m_qL
  336.2      404.8      1216.      1221.      1285.    

  Atau       Abottom    Atop       Al         Ad         Au
  601.3      2502.      1090.      620.2      2905.      2239.    
Mass matrices and mixing angles:
--------------------------------
  tan(beta)  alpha_(h,H)
  9.977    -0.1021    

  thet_tau   thet_b     thet_t
  1.302     0.9955E-01  1.789    

  Z(i,j)
  0.3616E-02 -0.9963      0.8322E-01 -0.2248E-01
  0.9971      0.9836E-02  0.6388E-01 -0.3902E-01
  0.1791E-01 -0.4288E-01 -0.7052     -0.7075    
  0.7326E-01 -0.7423E-01 -0.7012      0.7053    

  U(i,j)                  V(i,j)
 -0.9931      0.1171     -0.9995      0.3170E-01
  0.1171      0.9931      0.3170E-01  0.9995    

Final Higgs and SUSY particle masses: 
------------------------------------- 
  h          A          H          H+
  113.3      1048.      1049.      1054.    

  chi+_1     chi+_2     chi0_1     chi0_2     chi0_3     chi0_4
  174.9      1008.      174.9      544.8     -1004.      1009.    

  gluino
  1193.    

  stop_1     stop_2     sup_1      sup_2
  907.5      1164.      1255.      1317.    

  sbot_1     sbot_2     sdown_1    sdown_2
  1162.      1237.      1252.      1319.    

  stau_1     stau_2     snutau     selec_1    selec_2    snuelec
  318.4      407.5      394.0      339.0      407.5      399.7    
\end{verbatim}

 \newpage

\section*{5. Calculations with {\tt SuSpect}}

\subsection*{5.1 Comparison with other codes} 

Our results for some representative points of the MSSM parameter space have
been carefully cross--checked against other existing codes. Most of the earlier
comparisons have been performed in the context of mSUGRA type models. We obtain
in general a very good agreement, at the percent level, with the program {\tt
SOFTSUSY1.4} \cite{SOFTSUSY} and with the code {\tt SPHENO1.0} \cite{SPHENO}
which will appear publicly very soon\footnote{We thank Ben Allanach, Sabine
Kraml and  Werner Porod for their gracious help in performing these detailed
comparisons of the programs}. We also  find rather good agreement, in general
at the few percent level,  for the SUSY particle  masses computed by the
program {\tt ISASUGRA} \cite{ISASUGRA} version 7.58, once we chose the same
configuration [soft SUSY breaking masses frozen at $M_Z$, some radiative
corrections to sparticle masses are not included, etc..]; a better agreement is
found with the more recent 7.63 version.  A detailed comparison of a previous
version of \sus\ (version 2.005) with these programs has been given in
Ref.~\cite{comp}. Even in the delicate cases of large $\tb$ value [where the
$b$--quark Yukawa coupling, which needs a special treatment and the inclusion
of important radiative corrections, is strong] and large $m_0$ values [the
``focus point" region where EWSB is rather problematic to achieve], the 
discrepancies between \sus\  and the program {\tt SOFTSUSY} for instance, are
rather moderate.\s

In the case of the AMSB and GMSB models, no very detailed comparisons have
been made. We have simply compared our output values for the two SPS points
discussed previously for the minimal versions of these models, with those
obtained with {\tt ISASUGRA} and we find a rather good agreement, in general at
the level of a few percent. [Note that in the numbers given in
Ref.~\cite{nabil}, the difference can go up to 10\% in some cases; however, we
have slightly different values for the input parameters $m_t, \alpha_s, \sin^2
\theta_W$, etc..]. \s

The most sophisticated parameter to obtain in this context is the lightest
Higgs boson mass, since it incorporates all possible ingredients: the RGE's for
the evaluation of $M_{H_u}$ and $M_{H_d}$, the effective potential and the EWSB
for the determination of $M_A$ and the tadpoles, the radiative corrections to
the Higgs sector which involve also the two--loop corrections, etc. The value
that we obtain\footnote{Note that the comparison with the program {\tt 
SuSpect} made in Ref.~\cite{comp}  was with an earlier version which had only a
very approximate determination of the Higgs boson masses. The new version,
since it is linked to several Higgs routines, gives a much better determination
of these parameters.} for $M_h$ is for instance slightly different than the one
from ${\tt ISASUGRA}$ [even if we switch off the ${\cal O}(\lambda_t^2)$
corrections which are not implemented there] and this is presumably
due to the more sophisticated treatment of the Higgs potential made by the
routines to which {\tt SuSpect} is linked. We note however, that there are 
already differences  for $M_h$ obtained with  the three routines used
by \sus\  as well as for the approximation which is  incorporated, 
a reflection of the different degree of accuracy of these routines.  

\subsection*{5.2 Interface with other programs}

In the way it is written, \sus \ can be easily interfaced with other programs
or Monte--Carlo event generators\footnote{To make this interfacing easier, we
have provided a set of obvious commons for the input and output parameters 
needed or calculated by \sus\ and named all commons, subroutines and functions
used with a prefix {\tt SU\_}, not to be in conflict with those used 
by other programs.}. In fact, private versions exist which are already  
interfaced with some programs, and we give a short list of them:

\begin{itemize}
\vspace*{-2mm}
\item {\tt micrOMEGAs} \cite{micromegas}: for the automatic (analytical and then
numerical)  calculation of the cosmological relic density of the lightest 
neutralinos, including all possible annihilation and co--annihilation 
channels\footnote{Note that we have also 
interfaced the program with a private code written by Manuel Drees calculating 
the cosmological relic density of the lightest neutralinos for the complete 
analysis of the mSUGRA parameter space performed in Ref.~\cite{DDK} and 
summarized in Section 3.5.}.
\vspace*{-2mm}

\item {\tt DARKSUSY} \cite{darksusy}: also for the calculation of the relic 
density of the lightest neutralinos and their direct and indirect detection 
rates [the program has its own calculation of the SUSY spectrum, but it is 
rather approximate]\footnote{Note that a private {\tt Suspect/DARKSUSY} 
interface has been already used for prediction studies of indirect
LSP detection \cite{nezri,falvard}} . 
\vspace*{-2mm} 

\item {\tt HDECAY} \cite{HDECAY}: for the calculation of the decay branching 
ratios and total decay widths of the SM and MSSM Higgs bosons [in fact some 
routines, in particular those for the QCD running and for the interface with 
the  routines calculating the Higgs boson masses, are borrowed from there].
\vspace*{-2mm}

\item  {\tt SDECAY} \cite{SDECAY}: for the calculation of the decay widths and 
branching ratios of  SUSY particles including higher order [three--body decays 
for gauginos and stops, four--body decays for the lightest stop and QCD 
corrections to the two--body decays of squarks and gluinos], which will 
appear soon.  
\vspace*{-2mm}

\item {\tt SUSYGEN} \cite{SUSYGEN}: a Monte--Carlo event generator for Higgs 
and SUSY particle production in the MSSM [mainly in $e^+ e^-$ collisions
but some processes in $ep$ and $pp$ collisions are implemented]. The program
is also interfaced with {\tt HDECAY}. 
\vspace*{-2mm}
\end{itemize}

As discussed already, we have also interfaced \sus\  with  the {\sc Fortran}
code {\tt bsf.f}  which calculate the branching ratio of the radiative decay $b
\to s\gamma$ at next-to-leading order \cite{paolo} as well as with  the codes
calculating the radiative corrections to the Higgs boson masses [which is in
fact part of the interface with {\tt HDECAY}].  An interface with two of the
major Monte--Carlo event generators\footnote{We thank by anticipation, 
Stefano Moretti, Peter Richardson and Peter Skands for their help and 
collaboration in implementing the interfaces with these event generators.} {\tt
PYTHIA} \cite{pythia} and {\tt HERWIG} \cite{herwig} is  in progress.  \s

Most of the interfaces with these programs are still under checks and will 
hopefully be made available in a next release of the program.

\newpage

\subsection*{5.3 Future upgrades}

The program is under rapid development and we plan to make several upgrades
in a near future. A brief list of points which will be implemented in the next
releases [maybe not all in the next one] of the program includes [some of 
these points have been discussed previously, but we list them also here for
completeness]:\s

{\it 1)  Implementation of the theoretical and experimental constraints:} the
first improvement which is under checks and which will be done rather quickly,
as was discussed in section 3.4, will be to  include all the routines to
constrain the SUSY spectrum in the MSSM which are almost already available: the
implementation of the more sophisticated CCB and UFB conditions, the
calculation of the fine--tuning criteria parameters for the EWSB mechanism and
the experimental constraints from $\Delta \rho$, the muon $(g-2)$ and the
radiative $b\to s \gamma$ decay.\s

{\it 2) More refined calculations including higher--orders:} we plan to improve
the determination of the SUSY parameters and particle masses by including
several important higher order corrections: the two--loop SUSY--QCD 
corrections to the top and bottom quark masses \cite{bednyakov}, the full one
loop corrections to the Higgs boson masses {\it \`a la} PBMZ \cite{PBMZ},
additional radiative corrections to some SUSY particle masses such
as the full one--loop  corrections to the chargino and neutralinos which are
available  and leading electroweak corrections to squarks and sleptons
\cite{RC0} and possibly,  the full two loop  RGEs for the soft SUSY--breaking
parameters as calculated recently  \cite{Martin}. \s

{\it 3) The interface with other routines:} our first goal would be to 
make the interface fully operative with the programs {\tt HDECAY} and {\tt
SDECAY} for Higgs and SUSY particle decay widths and branching ratios. One
would then, with the three programs [which have many common features already],
have a very complete description of the properties of the new particles in the
MSSM, except from the production part which is in general the {\it chasse
gard\'ee} of the Monte--Carlo event generators. For the later aspect or
purpose, an interface of this new version of \sus\ with {\tt PYTHIA} and {\tt
HERWIG} as well as with {\tt  SUSYGEN}, will be provided quite soon as
mentioned previously.  The interface  with the routines for Dark Matter
calculations such as {\tt MICROMEGAS} and  {\tt DARKSUSY} will also be made
publicly available. \s  

{\it 4) Include additional theoretical models:} the most important upgrade that
we plan for a not too far future is to discuss additional theoretically 
interesting models. Examples of models that we have on our agenda are: \s

\begin{itemize} 
\vspace*{-2mm}

\item[--] The (M+1)SSM with an additional Higgs singlet field. 
The RGEs and the EWSB mechanisms have been discussed in detail by one of the 
authors in Ref.~\cite{MMR} and can be implemented easily in the program. Additional 
work will be needed to discuss the extended superparticle and Higgs spectrum 
[one would have one additional neutralino and one Higgs boson compared to the 
MSSM], in particular if radiative corrections are to be taken into account
\cite{NMSSMpheno}
\vspace*{-2mm}

\item[--] Some other theoretically discussed models, such as
superstring-inspired models, can be dealt with by the present version of the
program, using the pMSSM  machinery with the RGE option. However, some
extensions will need more input to be specified: this is the case with SO(10)
models with right--handed  sneutrinos [in which some additional contributions
to the D--terms of the  scalar masses have to be implemented] \cite{baer} or
the O--I and O--II  string models \cite{Pierre}. This will be done in the
future.  \vspace*{-2mm}

\item[--] Models with R--parity violation \cite{RPV}. The RGE's for the SM 
Yukawa couplings and all the MSSM R--parity violating Yukawa couplings in these models 
[with a discussion of the quasi fixed point properties] have been studied 
in detail by one of us in Ref.~\cite{MM}. The implementation of this 
analysis in \sus\ should not be problematic but some additional work will be 
needed to fully cover the subject. 
\vspace*{-2mm}

\item[--] Models with CP--violation. In principle, this will alter 
substantially only the part where the superparticle and Higgs particle 
spectrum is calculated. For the case of the chargino, neutralino and sfermion 
sectors, this is already available.  Only in the Higgs sector the 
calculation will need extra work \cite{CPHiggs}, since one has to implement 
the radiative corrections which are important in this context.
\vspace*{-2mm}
\end{itemize}

{\it 5) Include additional tools:} finally, there are some tools in the 
context of the MSSM discussed here, which can have some theoretical and  
experimental interest, that are already more or less available as separate
codes and can be interfaced with \sus: 

\begin{itemize}
\vspace*{-2mm}

\item[--] {\tt INVERTER}: this is a routine whose purpose is to determine the 
inverted spectrum relationship [i.e. recovering the Lagrangian parameter values
directly from  physical masses and/or couplings]. The algorithm in its present 
form essentially deals with the non--trivial inversion in the gaugino parameter
sector, where the input can be either two charginos and one neutralino, or two 
neutralinos and one chargino physical masses. The output are the Lagrangian 
parameters, $\mu$, $M_1$, $M_2$. This has been done following the approach of 
Ref.~\cite{inversion} and will be generalized to the case of the sfermion 
and the Higgs sector [the inclusion of radiative corrections might be  
problematic here].
\vspace*{-2mm} 

\item[--] {\tt RG EXACT}: this is a routine which implements an exact RG 
evolution solver limited to one--loop approximation following the approach of 
Ref.~\cite{AG} to  which we refer for a detailed discussion of the procedure. 
We simply mention here, that these exact solutions of the relevant SUSY RGEs 
which have been derived for arbitrary values of $\tan\beta$, should not only 
be useful to improve the general RG evolution algorithm, but more importantly, 
should provide a better control on some non--trivial issues of the 
evolution, such as the occurrence of Landau poles in the Yukawa 
couplings typically. 
\vspace*{-2mm}
\end{itemize}

As stated previously, this rather ambitious program will take some time to be 
fully achieved, but we will definitely try to have everything available 
before the starting of the LHC (and certainly before the advent of VLHC and CLIC)! 
 
\subsection*{5.4 Web information and maintenance}

A web page devoted to the \sus\ program can be found at the http address: \s

\centerline{\tt http://www.lpm.univ-montp2.fr:6714/\~\,kneur/Suspect}\s 

\nn It contains all the information that one needs on the program: 

-- Short explanations of the code and how to run it. 

-- The complete ``users manual" can be obtained in post-script or PDF form.

-- A regularly updated list of important changes/corrected bugs in the
code. 

-- A mailing list to which one can subscribe to be automatically advised about 
future\\ \hspace*{.8cm} \sus\  updates  or eventual corrections. \s

\nn One can also download directly the various files of the program: 

-- {\tt suspect2.in}: the input file of the program.

-- {\tt suspect2\_call.f}: the calling program sample.

-- {\tt suspect2.f}: the main routine of the program.

-- {\tt subh\_hdec.f, hmsusy.f, feynhiggs.f}: the three Higgs routines.

-- {\tt SuSpect2\_New.uu}: all needed routines in uu compressed format 
for the latest version.

-- {\tt SuSpect2\_Old.uu}: the routines for the previous versions of the 
program. \s

\nn A new feature is that we have provided a way to use directly the program
interactively on the web\footnote{We thank our system--manager in Montpellier,
Dominique Caron, for setting-up this possibility.}. For the present time, this
is only possible in the constrained models: mSUGRA, GMSB and AMSB, which need
only a small set of input parameters. The Standard Model input parameters
[fermion masses and gauge couplings], the algorithmic choices for various
accuracy of the program [accuracy and iterations on the RGEs], choice of scales
[GUT and EWSB scales] as well as  the choices for the radiative corrections for
the sparticles and Higgs bosons, have been set to default values which are
those displayed in the input file displayed in section 4.2. On then has simply
to select the model to be considered, i.e. either mSUGRA, GMSB or AMSB, type in
the  corresponding input parameters in the required fields and click on a field
to submit the run of the code. The output will be the usual \sus\ output.
Besides $\tb$ and the sign of the $\mu$
parameter, these input are [see Fig.~3]: \s

--- mSUGRA: the scalar $m_0$ and gaugino $m_{1/2}$ masses 
and the trilinear coupling $A_0$, 

-- GMSB: the scale  $\Lambda$, the messenger scale $M_{\rm mes}$ 
and messenger numbers $n_q$ and $n_l$,

-- AMSB: the common scalar and gravitino masses $m_0$ and 
$m_{3/2}$ and the coefficients $c_{S_i}$.\s


This very easy and friendly way of running \sus\ should be very useful for those
who need to know the spectrum only for a few cMSSM points and do not want to 
download and run the program themselves. 


\begin{figure}[htbp]
\begin{center}
\hspace*{-2cm}
\hspace*{-1cm}
\mbox{\epsfig{figure=mozilla.ps, height=18cm}}
\end{center}
\vspace*{-.5cm}
\caption[]{Web page of interactive \sus\ running where one can rapidly evaluate
some point in the parameter space of the mSUGRA, AMSB and GMSB constrained
models.} \end{figure}

\newpage

\section*{6. List of changes compared to previous versions}

This section, anticipating the next upgrades of the program, will be devoted to 
the summary of all the important changes made after each new release. For the 
present time, we will briefly summarize the history of the program and list the
major changes compared to the earlier versions \sus 1.0 and  \sus 2.0 which 
were available only on our web page. 

\subsection*{6.1 The version \sus 1.0}

This was the first version of the program and was released in 1998. It was
available on the web, but was not intended for a large public and was mainly
used in the framework of the French ``GDR--Supersym\'etrie" for the
experimentalists and the theorists of the working groups to have a common tool
for SUSY\footnote{In fact, the first version of the program was called {\tt
MSSMSpect} but some members of the GDR complained about the name which seemed
to be difficult to pronounce by some of our (presumably not Arabic nor Slavic)
colleagues, probably due to a local cluster of consonants. We then proposed a
change of name to {\tt SUSYSPECT} and then, to make short, to {\tt SuSpect}
(since every code, a priori, is).}.  The code was at a rather preliminary stage
[a patchwork of several bits of codes written by the authors for various
purposes], was largely open to discussions and suggestions and its main
purpose, as mentioned earlier, was to propose some conventions, definitions and
possible flexibility choices in the framework of the GDR. The program was not
very well documented until a short explanation was given in the mid--term
report of the MSSM working group of the GDR in December 1998 \cite{GDR}. \s

At that time, the program had only two extremes models implemented: mSUGRA and 
the pMSSM but with the possibility of RG evolution, and the calculation of
the spectrum  was made using several rough approximations. For instance, simple
threshold effects with a single SUSY scale were included in the running 
of the SM gauge and Yukawa couplings but the important radiative corrections 
to the fermion and SUSY particles masses were not implemented. In addition, the
effective scalar potential for EWSB and the radiative corrections in the Higgs 
sector had only the leading contributions from the third generation (s)fermion 
sector.  Several ``algorithmic" choices [like the choice of the GUT or EWSB 
scales and the ones for the accuracy of the RGEs] were not present. 

\subsection*{6.2 The version \sus 2.0}

An important upgrade was made in the version \sus 2.0 released in 2001, which
still did not have a detailed users manual and was only available on the web 
page [where we started to display some useful information, like the list of
changes, a users E--mail list, etc ...]. For instance, we have included all
dominant radiative corrections to the third generation fermion masses and
Yukawa couplings as well as to the SUSY particle masses. The effective
potential included also the full one-loop contributions from the SUSY
particles. Some refinements and more possibilities were made available for the
various model and approximation choices. A few bugs and inconsistencies had
been fixed. But still, the model choices were limited and the Higgs sector 
was treated only approximately.   

\subsection*{6.3 The version \sus 2.1}

A  major upgrade has been performed, leading to the version that we are
presenting here. The changes compared to the latest version, \sus 2.005, 
displayed on the web page,  can be summarized as follows: \s

$i)$ An upgrade concerning the supersymmetry-breaking models has been performed
by providing the possibility of calculating the MSSM particle spectrum in the
AMSB and GMSB models. Some flexibility in the choice of the input parameters
[in particular the choice of the messenger fields in the GMSB scenario and of
the non--anomalous  contribution to the scalar fields in the AMSB model] has
been made available and should allow the possibility to analyze a large number
of the theoretical scenarii discussed in the literature. \s

$ii)$ A major upgrade was made in the calculation of the Higgs boson
masses. Following the program {\tt HDECAY}, we have provided an interface with 
all the available public routines which evaluate the radiative corrections in 
the MSSM Higgs sector, namely the latest versions of {\tt subhpolem}, {\tt 
FeynHiggsFast} and {\tt HMSUSY}. We have also provided a simple routine 
[included in the program] which gives a rather good approximation of these 
corrections. \s

$iii)$ Some important refinements in the calculation of the radiative 
corrections to the fermion and SUSY particle masses have been made. 
For instance, we have included the two--loop QCD corrections to the 
heavy $t,b$ quark masses, the chargino--neutralino loop corrections in
the determination of the running top quark mass and Yukawa coupling and the 
effective scalar potential, etc.. \s

$iv)$ The program has been completely reorganized and some parts rewritten to
make it easier to read [for instance, many comments on the purpose of the 
subroutines and explanations of the input/output files or commons
have been included and the routines were reorganized according to their actual 
purpose] and to interface with other programs [for instance, we renamed all 
subroutines, functions and commons to start with the 
prefix {\tt SU\_} to minimize the possible conflicts with names used by other 
routines and provided a full list of input/output commons which should be
sufficient for interfacing with any other code]. \s

$v)$ Finally, we have provided an interactive way of using the program
on the web, which we hope will be useful for those who would like to quickly
and easily obtain the Supersymmetric spectrum in the constrained models
mSUGRA, GMSB and AMSB, without downloading all the files and running the 
program themselves. 

\newpage


\section*{7. Conclusion} 

We have presented the version 2.1 of the {\sc Fortran} code {\tt SuSpect}  which
calculates the Supersymmetric and Higgs particle spectrum in the  MSSM. The
calculation can be performed in constrained models  with universal boundary
conditions at high scales such as the gravity (mSUGRA), anomaly (AMSB) or gauge
(GMSB) mediated breaking models, but also in the  non--universal or
unconstrained MSSM case, with up to 22 free input parameters which can be set
either at the electroweak symmetry breaking scale or obtained from boundary
conditions on some common parameter at a high--energy scale. \s

A particular care has been taken to treat all the mandatory features which
are needed to describe accurately these various scenarii: the renormalization
group evolution of parameters between low and  high energy scales, the
consistent implementation of radiative electroweak  symmetry breaking and the
calculation of the physical masses of the Higgs  bosons and supersymmetric
particles taking into account all dominant radiative corrections. The program
provides several  options [for accuracy, scale choice, etc...] to deal with
these aspects. \s  

The program can check the fulfillment of theoretical
constraints, such as the absence of tachyonic particles and improper lightest
SUSY particle, the absence of non desired charge and color breaking as well as
unbounded from below minima and a large fine--tuning in the electroweak
symmetry breaking conditions. A verification that the obtained spectrum is in
agreement with high precision measurements such as the $\rho$ parameter, the 
muon $g-2$ and the radiative $b \to s\gamma$ decay, can also be performed.\s

The  program has a high degree of flexibility in the choice of the model and/or
the input parameters and an adequate level of approximation at different
stages. It is rather precise and quite reliable [since it has been compared
with several other similar existing codes], relatively fast to allow for rapid
comprehensive scans of the parameter space and simple enough to be linked with
 other programs dealing with MSSM particle properties or with Monte--Carlo
event generators. We have also
provided a very simple way to run the code interactively on the web in the
constrained models. \s

The program is also self--contained since it includes all needed routines,
except for the Higgs sector where we have provided links to most of the
publicly available routines which calculate the radiative corrections
[although it can also make an approximate calculation of these corrections; a
more accurate routine is under way]. Several upgrades, which include the
possibility to analyze additional theoretical models and to make the interface
with  programs for (s)particle decay branching ratios and Dark Matter
calculations and with some Monte--Carlo event generators to simulate the
production properties, are planned and will be made available soon.  

\subsection*{Acknowledgments:}

The program \sus\ has been developed in the framework of the {\it Groupe de
Recherche} {\it sur la Supersym\'etrie} (GDR--SUSY), organized by the French {\it 
Centre National de la Recherche Scientifique} (CNRS), and has been checked and
``debugged" during the last few years with the help of several members of the
``MSSM" and ``Tools" working groups of the GDR to whom we are indebted. We
thank in particular, Genevieve B\'elanger, Pierre Binetruy, Fawzi  Boudjema,
Marie-Bernadette Causse,  Jean-Baptiste de Vivie, Laurent Duflot, Nabil
Ghodbane, Jean-Francois Grivaz, Cyril Hugonie, Stavros Katsanevas, Vincent
Lafage, Imad Laktineh, Christophe Le Mou\"el,  Yann Mambrini, Steve Muanza,
Margarete M\"uhlleitner,  Emmanuel Nezri, Jean Orloff, Emmanuelle Perez, Sylvie
Rosier--Lees, Roberto Ruiz de Austri, Aurore Savoy--Navarro and Charling Tao. 
%
We have as well similarly benefited from the more recent working group ``SUSY
Dark Matter" of the GDR {\sl Ph\'enom\`enes Cosmiques de Hautes Energies}. We
thank all members of this group, in particular Julien Guy, Agnieszka 
Jacholkowska, Julien Lavalle, Eric Nuss and Mariusz Sapinski for various 
cross-checks.  
%
We have also benefited from  several discussions, comments and help from: Ben
Allanach, Andreas Birkedal, Francesca Borzumati, Aseshkrishna Datta, Manuel
Drees, Paolo Gambino, Naveen Gaur, Sven Heinemeyer, Jan Kalinowski, Yeong Gyun
Kim, Sabine Kraml, Filip Moortgat, Stefano Moretti, Takeshi Nihei, Werner
Porod, Peter Richardson, Leszek Roszkowski, Pietro Slavich, Peter Skands,
Michael Spira. We thank  them all.  Finally, un grand merci to our
system--manager in Montpellier, Dominique Caron, for setting--up the page where
one can run \sus\ on the web.  

\newpage

\setcounter{equation}{0}
\renewcommand{\theequation}{A.\arabic{equation}}

\section*{Appendix A: Some analytic expressions used in \sus}

In this Appendix, we present for completeness analytical formulae
used in \sus\ for the RG evolution of all parameters, the  determination
of the one-loop effective potential for the EWSB mechanism and the radiative
corrections to the sparticle and Higgs boson masses. 

\subsection*{A.1: Renormalization Group Evolution} 

The RG evolution of the SM and MSSM parameters from the high to low energy
scales [and in the case of SM parameters, also in the reverse direction] is one
of the main ingredients of the \sus\ program [and in fact,  this is the
feature which takes most of the CPU running time]. In the following, we list 
the complete set of the RGE $\beta$ functions used in the program. For many 
purposes, using the one--loop $\beta$ functions is a very good approximation 
and is appropriate, since in particular, it  makes the program run  much faster.
However, the there is an option, {\tt ichoice(2)=21}, which forces the 
program to use the two--loop RGEs for the gauge and the Yukawa couplings as 
well as for the soft SUSY--breaking gaugino mass parameters. This allows for
a more accurate RGE evolution at the expense of rendering the program slower. 
We will therefore also display the two--loop $\beta$ functions for
the couplings. The list of $\beta$ functions given below is ordered as in the 
program \sus [and more precisely, as in in the subroutines {\tt SU$\_$DERIV1} 
and {\tt SU$\_$DERIV2}, for the one and two--loop $\beta$ functions, 
respectively], i.e. it gives the vector ${\tt y(n)}$ with {\tt n=1-31} 
[see Appendix B for details on the routines and their purposes]. \s

\nn $\bullet$ Gauge couplings squared [{\tt y(1)-(y3)}]  with $n_g$ the 
generation number, related to the flavor number by $n_f=2n_g$; the full  SUSY
coefficients $b_i$ (i.e. after the inclusion of the SUSY threshold  effects)
are $b_1=3/5+   2n_g, b_2=-5+2n_g $ and $b_3=-9+2n_g$: 
\begin{eqnarray}
\frac {dg_1^2}{dt}&=&  -\frac{g_1^4}{16 \pi^2}b_1-
\frac{g_1^4}{(16 \pi^2)^2}\bigg[ \bigg( \frac{19}{15}n_f +\frac{9}{25}\bigg)
g_1^2 +\bigg( \frac{3}{5}n_f +\frac{9}{5} \bigg) g_2^2+ \frac{44}{15}n_f \, 
g_3^2 \non \\ 
&& \hspace*{3.6cm} -\frac{26}{5}Y_t^2 -\frac{14}{5}Y_b^2 - \frac{18}{5} Y_\tau^2 \bigg] 
\\
%
\frac {dg_2^2}{dt}&=& - \frac{g_2^4}{16 \pi^2}b_2-
\frac{g_2^4}{(16 \pi^2)^2}\bigg[ \bigg( \frac{1}{5}n_f +\frac{3}{5}\bigg)g_1^2
+(7 n_f - 17)  g_2^2+ 4n_f \, g_3^2 \non \\ 
&& \hspace*{3.6cm} - 6 Y_t^2 -6 Y_b^2 - 2 Y_\tau^2 \bigg] \\
%
\frac {dg_3^2}{dt} &=&  - \frac {g_3^4}{16 \pi^2}b_3 -
\frac{g_3^4}{(16 \pi^2)^2}\bigg[ \frac{11}{3}n_f g_1^2
+ \frac{3}{2}n_f \, g_2^2+ \bigg( \frac{34}{4}n_f - 54\bigg)  g_3^2 \non \\
&& \hspace*{3.6cm} -4  Y_t^2 -2 Y_b^2 \bigg] 
\end{eqnarray}
%
\nn $\bullet$ Third generation Yukawa couplings [{\tt y(4)-y(6)}]
\begin{eqnarray}
{\frac {dY_\tau }{dt}}&=&-{\frac {Y_\tau }{32 \pi^2}} \bigg[ 
4 Y_\tau^2+3 Y_d^2 -3( g_1^2+ g_2^2) \bigg] \non \\
&& -\frac{Y_\tau}{2(16\pi^2)^2} \bigg[-10 Y^4_\tau -9 Y_b^4- 9Y_b^2 Y_\tau^2-
3Y_b^2Y_t^2 \non \\
&& \hspace*{2cm} + \bigg(6 g_2^2 +\frac{6}{5}g_1^2 \bigg) Y_\tau^2 
+ \bigg(-\frac{2}
{5} g_1^2+16g_3^2 \bigg)Y_b^2 \non \\ 
&& \hspace*{2cm} + \bigg(\frac{9}{5}n_f + 
\frac{27}{10} \bigg)g_1^4 + \bigg( 3n_f - \frac{21}{2} \bigg) g_2^4 + \frac{9}{5}
g_1^2 g_2^2 \bigg] \\  
%
{\frac {dY_b}{dt}}&=&-{\frac {Y_b}{32 \pi^2}} \bigg[ 6 Y_b^2 + Y_\tau^2 + 
Y_t ^2   -\bigg({ \frac {7}{9}} g_1^2+3 g_2^2+\frac {16}{3}g_3^2 \bigg)\bigg]
\non \\
&& -\frac{Y_b}{2(16\pi^2)^2} \bigg[-22 Y^4_b - 5Y_t^4 - 5Y_b^2 Y_t^2-
3Y_b^2Y_\tau^2 -3 Y_\tau^2 \non \\
&& \hspace*{2cm} + \frac{4}{5}g_1^2 Y_t^2 + \bigg(
\frac{2}{5} g_1^2+6g_2^2 + 16g_3^2 \bigg)Y_b^2 + \frac{6}{5} g_1^2 Y_\tau^2 
 \non \\
&& \hspace*{2cm} + \bigg(\frac{7}{15}n_f + \frac{7}{18}
\bigg)g_1^4 + \bigg( 3n_f - \frac{21}{2} \bigg) g_2^4 + \bigg( \frac{16}{3}
n_f - \frac{304}{9} \bigg) g_3^4 \non \\ 
&& \hspace*{2cm} +g_1^2 g_2^2 
+\frac{8}{9} g_1^2 g_3^2 + 8 g_2^2g_3^2 \bigg] \\
%
{\frac {dY_t}{dt}}&=&-{\frac {Y_t}{32 \pi^2}} \bigg[6 Y_t^2+Y_b^2  
- \bigg({\frac {13}{9}} g_1^2+3 g_2^2+\frac {16}{3}g_3^2 \bigg) \bigg] 
\non \\
&& -\frac{Y_t}{2(16\pi^2)^2} \bigg[-22 Y^4_t - 5Y_b^4 - 5Y_b^2 Y_t^2-
Y_b^2Y_\tau^2  \non \\
&& \hspace*{2cm} + \frac{2}{5}g_1^2 Y_b^2 + \bigg(
\frac{6}{5} g_1^2+6g_2^2 + 16g_3^2 \bigg)Y_t^2 \frac{6}{5} g_1^2 Y_\tau^2 
 \non \\
&& \hspace*{2cm} + \bigg(\frac{13}{15}n_f + \frac{403}{450}
\bigg)g_1^4 + \bigg( 3n_f - \frac{21}{2} \bigg) g_2^4 + \bigg( \frac{16}{3}
n_f - \frac{304}{9} \bigg) g_3^4 \non \\
&& \hspace*{2cm} + g_1^2 g_2^2 
+\frac{136}{45} g_1^2 g_3^2 + 8 g_2^2g_3^2 \bigg] 
\end{eqnarray}
%
\nn $\bullet$ The vacuum expectation values $v_u$ and  $v_d$ [{\tt y(7)-y(8)}] 
\begin{eqnarray} 
{\frac {dv_u}{dt}}&=&{\frac {v_u}{32 \pi^2}} \bigg[ 3 Y_t^2-{\frac {3}{4}} 
\bigg( {\frac {1}{3}} g_1^2+ g_2^2 \bigg) \bigg] \\
 {\frac {dv_d}{dt}}&=&{\frac {v_d}{32 \pi^2}} \bigg[ 3Y_d^2+Y_\tau^2 -{\frac 
 {3}{4}} \bigg( {\frac {1}{3}} g_1^2+ g_2^2 \bigg) \bigg] 
 \end{eqnarray}
%
\nn $\bullet$ The third generation trilinear $A$ couplings [{\tt y(9)-y(11)}]: 
\begin{eqnarray}
{\frac {d A_t}{dt}}&=&-{\frac {1}{32 \pi^2}} \bigg[ 12 A_t Y_t^2 + 2 A_bY_b^2
+\bigg( {\frac {26}{9}} g_1^2 M_1+6 g_2^2 M_2+{\frac {32}{3}}g_3^2 M_3 
\bigg) \bigg]   \\
 {\frac {d A_b}{dt}}&=&-{\frac {1}{32 \pi^2}} \bigg[ 12 A_b Y_b^2 
+ 2 A_t Y_t ^2 +2 A_\tau Y_\tau^2 +\bigg( {\frac {14}{9}} g_1^2 M_1+
6 g_2^2 M_2+{\frac {32}{3}}g_3^2 M_3 \bigg) \bigg] \\ 
{\frac {d A_\tau}{dt}}&=&-{\frac {1}{32 \pi^2}} \bigg[ 
8 A_\tau Y_\tau^2 +6 A_d Y_d^2  +6( g_1^2 M_1+ g_2^2 M_2) \bigg] 
\end{eqnarray}
%
\nn $\bullet$ The scalar Higgs masses [{\tt y(12)-y(13)]}: here and for the 
scalar fermion masses, factors $P_{\tilde{f}}$ appear and are defined as 
$P_{\tilde{t},\tilde{b}, \tilde{\tau}} \equiv m^2_{H_u, H_d,H_d} +m^2_{ 
{\tilde{Q}} ,{\tilde{Q}} ,{\tilde{L}} } +m^2_{\tilde{t}_R,\tilde{b}_R,
\tilde{\tau}_R}+A^2_{t,b,\tau}$; a term Tr$(Ym^2)$ also appears and is the 
isospin pondered sum of the squared soft masses of the scalar fermions,
Tr$(Ym^2)=\sum_{i=1}^{n_g} (m^2_{ {\tilde{Q}^i}}- m^2_{ {\tilde{u}_R^i}}
+ m^2_{ {\tilde{d}_R^i}} - m^2_{ {\tilde{L}+i}} + m^2_{ {\tilde{e}_R^i}})
+ m^2_{H_u} - m^2_{H_d}$ [in the case of universal soft masses, the trace 
vanishes at any scale, reflecting the anomaly cancellation]: 
\begin{eqnarray}
\label{eqmH1}
{\frac {d m^2_{H_d}}{dt}}&=&-{\frac {1}{16 \pi^2}} \bigg[ 3 Y_b^2 
P_{\tilde{b}} +Y_\tau^2 P_{\tilde{\tau}} - {\frac {1}{2}}g_1^2 {\rm Tr} 
(Y m^2) -( g_1^2 M_1^2+3 g_2^2 M_2^2) \bigg] \\ 
\label{eqmH2}
{\frac {d m^2_{H_u}}{dt}}&=&-{\frac {1}{16 \pi^2}} \bigg[ 
3 Y_t^2 P_{\tilde{t}} +{\frac {1}{2}}g_1^2 {\rm Tr}
(Y m^2)-(g_1^2 M_1^2+3 g_2^2 M_2^2) \bigg]
\end{eqnarray}
%
\nn $\bullet$ The third generation scalar fermion masses [{\tt y(14)-(y18)}]
\begin{eqnarray}
 {\frac {d m^2_{{\tilde{\tau}}_{R}}}{dt}}&=&-{\frac {1}{16 \pi^2}} \bigg[
2 Y_\tau^2 P_{\tilde{\tau}} +g_1^2 {\rm Tr}(Y m^2)-4 g_1^2 M_1^2
\bigg] \\
 {\frac {d m^2_{{\tilde{L}}}}{dt}}&=&-{\frac {1}{16 \pi^2}} \bigg[
Y_\tau ^2 P_{\tilde{\tau}}  
 -{\frac {1}{2}}g_1^2 {\rm Tr} (Y m^2)-( g_1^2 M_1^2+3 g_2^2 M_2^2) \bigg] \\
 {\frac {d m^2_{{\tilde{b}}_{R}}}{dt}}&=&-{\frac {1}{16 \pi^2}} \bigg[
2 Y_b^2 P_{\tilde{b}} +{\frac {1}{3}}g_1^2 {\rm Tr} (Y m^2)- \bigg( 
{\frac {4}{9}} g_1^2 M_1^2+{\frac {16}{3}} g_3^2 M_3^2 \bigg) \bigg]  \\
 {\frac {d m^2_{{\tilde{t}}_{R}}}{dt}}&=&-{\frac {1}{16 \pi^2}} \bigg[
2 Y_t^2 P_{\tilde{t}}   -{\frac {2}{3}}g_1^2 {\rm Tr} (Y m^2)- \bigg(
{\frac {16}{9}} g_1^2 M_1^2+{\frac {16}{3}} g_3^2 M_3^2 \bigg)  \bigg] \\
\frac{d m^2_{{\tilde{Q}}}} {dt} &=&{\frac {-1}{16 \pi^2}} \bigg[
Y_t^2 P_{\tilde{t}}  +Y_b^2 P_{\tilde{b}} +{\frac {1}{6}}g_1^2 
{\rm Tr} (Y m^2)  - \bigg(
{\frac {1}{9}} g_1^2 M_1^2+3 g_2^2 M_2^2+{\frac {16}{3}} g_3^2 M_3^2
\bigg) \bigg]   
\end{eqnarray}
%
\nn $\bullet$ The bilinear soft SUSY--breaking parameter $B$ [{\tt y(19)}]
\begin{eqnarray}
{\frac {d B}{dt}}&=&-{\frac {1}{16 \pi^2}} \bigg[ 
3 A_t Y_t^2+3 A_b Y_b^2+ A_\tau Y_\tau^2 +( g_1^2 M_1+3 g_2^2 M_2) \bigg]
\end{eqnarray}
%
\nn $\bullet$ The gaugino mass parameters [{\tt y(20)-(y22)}]: their RGE's are 
related to those of the gauge couplings [from the corresponding equations at 
one--loop order, one can see that $d/dt(M_i/g_i^2)=0$]; here we will not 
write the two--loop contributions for simplicity. 
\begin{eqnarray}
\frac {dM_1}{dt}&=&\frac{1}{16 \pi^2}\bigg( -1-\frac{10}{3}n_g \bigg) M_1 g_1^2\\
\frac {dM_2}{dt} &=& \frac {1}{16 \pi^2}  (5- 2 n_g ) M_2 g_2^2 \\
\frac {dM_3}{dt} &=& \frac {1}{16 \pi^2}  (9-2n_g) M_3 g_3^2
\end{eqnarray}
%
\nn $\bullet$ The parameter $\mu$  [{\tt y(23)}]: 
\begin{eqnarray} 
 {\frac {d\mu}{dt}}&=&-{\frac {\mu}{32 \pi^2}} \bigg[ 
3 Y_t^2+3 Y_b^2+Y_\tau^2 -( g_1^2+ 3 g_2^2) \bigg] 
\end{eqnarray}
%
\nn $\bullet$ The first and second generation scalar fermion masses 
[{\tt y(24)-(y28)}]
\begin{eqnarray}
 {\frac {d m^2_{{\tilde{e}}_{R}}}{dt}}&=&-{\frac {1}{16 \pi^2}} \bigg[
g_1^2 {\rm Tr}(Y m^2)-4 g_1^2 M_1^2 \bigg] \\
 {\frac {d m^2_{{\tilde{l}}}}{dt}}&=&-{\frac {1}{16 \pi^2}} \bigg[
 -{\frac {1}{2}}g_1^2 {\rm Tr} (Y m^2)-( g_1^2 M_1^2+3 g_2^2 M_2^2) \bigg] \\
 {\frac {d m^2_{{\tilde{d}}_{R}}}{dt}}&=&-{\frac {1}{16 \pi^2}} \bigg[
{\frac {1}{3}}g_1^2 {\rm Tr} (Y m^2)- \bigg( 
{\frac {4}{9}} g_1^2 M_1^2+{\frac {16}{3}} g_3^2 M_3^2 \bigg) \bigg]  \\
 {\frac {d m^2_{{\tilde{u}}_{R}}}{dt}}&=&-{\frac {1}{16 \pi^2}} \bigg[
  -{\frac {2}{3}}g_1^2 {\rm Tr} (Y m^2)- \bigg(
{\frac {16}{9}} g_1^2 M_1^2+{\frac {16}{3}} g_3^2 M_3^2 \bigg)  \bigg] \\
\frac{d m^2_{{\tilde{q}}}} {dt} &=&{\frac {-1}{16 \pi^2}} \bigg[
{\frac {1}{6}}g_1^2 {\rm Tr} (Y m^2)  - \bigg(
{\frac {1}{9}} g_1^2 M_1^2+3 g_2^2 M_2^2+{\frac {16}{3}} g_3^2 M_3^2
\bigg) \bigg]   
\end{eqnarray}
%
\nn $\bullet$ The first and second generation trilinear $A$ couplings 
[{\tt y(29)-y(31)}]: 
\begin{eqnarray}
{\frac {d A_u}{dt}}&=&-{\frac {1}{32 \pi^2}} \bigg[ 6 A_t Y_t^2 + 
{\frac {26}{9}} g_1^2 M_1+ 6 g_2^2 M_2+ {\frac {32}{3}}g_3^2 M_3   \bigg]   \\
 {\frac {d A_d}{dt}}&=&-{\frac {1}{32 \pi^2}} \bigg[ 
 6 A_b Y_b^2 +2  A_\tau Y_\tau^2 + {\frac {14}{9}} g_1^2 
M_1+ 6 g_2^2 M_2+ {\frac {32}{3}}g_3^2 M_3  \bigg] \\ 
{\frac {d A_e}{dt}}&=&-{\frac {1}{32 \pi^2}} \bigg[
 6 A_b Y_b^2 +2  A_\tau Y_\tau^2
 +6 g_1^2 M_1 +6  g_2^2 M_2 \bigg] 
\end{eqnarray}
The evolution parameter $t$ is defined here as $t={\rm Log}
(M_U^2/Q^2)$; this is different from the one used in the RGE's of the program  
where $t= (1/2){\rm Log}(Q^2/M_U^2)$. \s


Finally, to include the threshold effects in the gauge couplings, one
needs to change the coefficients $b_i$ of the one--loop $\beta$ functions to 
include step functions $s_p =
\theta(Q^2 - m_p^2)$ for each new particle $p$ with mass $m_p$ crossing the
threshold $Q$ [the top quark and the supersymmetric
and Higgs particles; the thresholds for the other SM particles have been 
already included in the constant terms]:
\begin{eqnarray}
b_1&=& \frac{103}{30} + \frac{17}{30}s_t + \Sigma_i \bigg( \frac{
s_{\tilde{Q}^i}}{30} + \frac{4s_{\tilde{u}_R^i}}{15} +\frac{
s_{\tilde{d}_R^i}}{15} +\frac{s_{\tilde{l}^i}}{10} + \frac{s_{\tilde{e}_R^i}}{5}
\bigg) + \frac{1}{10} (s_{H_u}+ s_{H_d}) + \frac{1}{5} (s_{\mu}+s_{Z}) \non  \\
%
b_2&=& -\frac{23}{6}+ \frac{1}{2}s_t + \Sigma_i \bigg( \frac{1}{2}
s_{\tilde{Q}^i} + \frac{1}{6} s_{\tilde{l}^i} \bigg) + 
+ \frac{1}{6} (s_{H_u}+ s_{H_d}) + \frac{1}{3} (s_{\mu}+s_{Z}) + \frac{4}{3}
s_{\tilde{W}} \non \\
%
b_3&=& -\frac{23}{3}+ \frac{2}{3}s_t + \Sigma_i \bigg( \frac{1}{3}
s_{\tilde{Q}^i} + \frac{1}{6} s_{\tilde{u}^i_R} + \frac{1}{6} 
s_{\tilde{d}^i_R} \bigg) + 2s_{\tilde{g}} 
\end{eqnarray} 
For simplicity, we have sometimes identified the SUSY particle masses with
their  corresponding soft SUSY--breaking parameters, i.e. we neglected the
mixing  between the current eigenstates (and the D--terms in the case of the
sfermions). In the case of the charginos and neutralinos for instance, the
steps are for the higgsino states with masses $\mu$ and $M_Z$ and the bino
$\tilde{B}$ and wino $\tilde{W}$ states with masses $M_1$ and $M_2$. 
This provides a good approximation.  


\subsection*{A.2: The one-loop scalar potential and EWSB}

To the MSSM tree--level scalar potential $V_{\rm Higgs}$ given by:
\begin{eqnarray} 
V_{\rm Higgs} &=& (m_{H_d}^2+ \mu^2)  H_d^{\dagger} H_d + (m_{H_u}^2 +\mu^2) 
H_u^{\dagger} H_u + B\mu  (H_u \cdot H_d + {\rm h.c.}) \nonumber \\
 &+& \frac{g_1^2+g_2^2}{8}  (H_d^{\dagger} H_d - H_u^{\dagger} H_u)^2 + 
\frac{g_2^2}{2} (H_d^{\dagger}  H_u) (H_u^{\dagger}  H_d)
\end{eqnarray}
we have added the full one--loop corrections, including the contributions
of third generation fermions, all sfermions, Higgs bosons and gauge bosons as
well as the contributions of chargino and neutralino states. We have used 
the tadpole method and implemented {\it \`a la} PBMZ the following 
corrections: 
\beq
16 \pi^2 \, \frac{t_d}{v_d} &=& -6 \lambda_b^2 A_0(m_b) - 2 \lambda_\tau^2
A_0 (m_\tau) + \sum_{\tilde{f}_i} N_c^{\tilde{f}} \frac{g_2}{2M_W \cos\beta}
\lambda_{H_d \tilde{f}_i \tilde{f}_i} A_0(m_{\tilde{f}_i}) \\
&&+  \frac{g_2^2}{8 c_W^2} \bigg[ 2(\cos 2\beta+6 c_W^2)A_0(M_W)+ 
(\cos 2\beta+6) A_0(M_Z) \non \\
&& + 4(c_W^2 - \cos2 \beta) A_0 (M_{H^\pm})- \cos 2 \beta A_0(M_A) \non \\ &&
+ (4 \sin^2 \alpha -1 +\sin2 \alpha \tb) A_0(M_h) 
+ (4 \cos^2 \alpha -1 - 2\sin 2\alpha \tb ) A_0 (M_H) \bigg] \non \\
&& - \frac{g_2^2}{M_W \cos \beta} 
\bigg[ \sum_{i}^4 m_{\chi_i^0} Z_{i3}\bigg(Z_{i2}- \frac{s_W}{c_W} Z_{i1}
\bigg) A_0 (m_{\chi_i^0}) + \sqrt{2} \sum_{i=1}^2 m_{\chi_i^+} V_{i1} U_{i2}
 A_0( m_{\chi_i^+}) \bigg] \non \\
% 
16 \pi^2 \, \frac{t_u}{v_u} &=& -6 \lambda_t^2 A_0(m_t)  + \sum_{\tilde{f}_i} 
N_c^{\tilde{f}} \frac{g_2}{2M_W \sin \beta}
\lambda_{H_u \tilde{f}_i \tilde{f}_i} A_0(m_{\tilde{f}_i})  \\
&&+  \frac{g_2^2}{8 c_W^2} \bigg[  -2(\cos 2\beta-6 c_W^2)A_0(M_W)- 
(\cos 2\beta-6) A_0(M_Z) \non \\
&& + 4(c_W^2 + \cos2 \beta) A_0 (M_{H^\pm})+ 
\cos 2 \beta A_0(M_A) \non \\
&&+ (4 \cos^2 \alpha -1 +\sin2 \alpha {\rm cot}\beta) 
A_0(M_h) + (4 \sin^2 \alpha -1 - 2\sin 2\alpha {\rm cot} \beta ) A_0 (M_H) 
\bigg] \non \\
&& + \frac{g_2^2}{M_W \sin \beta} 
\bigg[ \sum_{i}^4 m_{\chi_i^0} Z_{i4}\bigg(Z_{i2}- \frac{s_W}{c_W} Z_{i1}
\bigg) A_0 (m_{\chi_i^0}) - \sqrt{2} \sum_{i=1}^2 m_{\chi_i^+} V_{i2} U_{i1}
 A_0( m_{\chi_i^+}) \bigg] \non 
\eeq  
with the Passarino--Veltman one--point function defined as usual by:
\beq 
A_0(m)= m^2 \bigg[1 - {\rm Log} \frac{m^2}{Q^2} \bigg]
\eeq
where we have subtracted the pole in $1/\epsilon$ and where $Q$ stands for 
the renormalization scale that we take to be the EWSB scale. The internal loop
masses appearing in the previous expressions should be pole masses while the 
couplings should  be $\overline{\rm DR}$ running couplings at the EWSB scale. 
All these couplings  have been defined previously, except for the $H_u,H_d$ 
couplings to up-- and down--type sfermions which, in the current field 
basis,  are given by: 

\begin{eqnarray}
\lambda_{H_u \tilde{f}_L \tilde{f}_L } &=& - \frac{g_2}{c_W} M_Z 
(I^{3L}_{\tilde{f}} - e_{\tilde{f}} s_W^2) \sin \beta + \delta_{ \tilde{f}_L
\tilde{u}_L } \,  \sqrt{2} \lambda_u m_u \non \\
%
\lambda_{H_u \tilde{f}_R \tilde{f}_R } &=& - \frac{g_2}{c_W} M_Z 
(I^{3R}_{\tilde{f}} - e_{\tilde{f}} s_W^2) \sin \beta + \delta_{ \tilde{f}_R
\tilde{u}_R }\,  \sqrt{2} \lambda_u m_u
\non \\
\lambda_{H_u \tilde{f}_L \tilde{f}_R } &=&  \delta_{ \tilde{f}_L \tilde{d}_R }
\,  \frac{1}{\sqrt{2}}  \lambda_d \mu +
\delta_{ \tilde{f}_L \tilde{u}_R }\,  \frac{1}{\sqrt{2}}  \lambda_u A_u \\
%
\lambda_{H_d \tilde{f}_L \tilde{f}_L } &=& \frac{g_2}{c_W} M_Z 
(I^{3L}_{\tilde{f}} - e_{\tilde{f}} s_W^2) \cos \beta + \delta_{ \tilde{f}_L
\tilde{d}_L } \,  \sqrt{2} \lambda_d m_d \non \\
%
\lambda_{H_d \tilde{f}_R \tilde{f}_R } &=& \frac{g_2}{c_W} M_Z 
(I^{3R}_{\tilde{f}} - e_{\tilde{f}} s_W^2) \cos \beta + \delta_{ \tilde{f}_R
\tilde{d}_R }\,  \sqrt{2} \lambda_d m_d
\non \\
\lambda_{H_d \tilde{f}_L \tilde{f}_R } &=&  - \delta_{ \tilde{f}_L \tilde{u}_R }
\,  \frac{1}{\sqrt{2}}  \lambda_u \mu +
\delta_{ \tilde{f}_L \tilde{d}_R }\,  \frac{1}{\sqrt{2}}  \lambda_d A_d 
\end{eqnarray}
One has then to make rotations to obtain the couplings in the mass eigenvalue 
basis 
\begin{eqnarray}
\left( \begin{array}{cc}
\lambda_{H_i \tilde{f}_1 \tilde{f}_1 } & \lambda_{H_i \tilde{f}_1 \tilde{f}_2}\\
\lambda_{H_i \tilde{f}_2 \tilde{f}_1 } & \lambda_{H_i \tilde{f}_2 \tilde{f}_2 }
\end{array} \right) = \left( \begin{array}{cc} 
c_{\tilde{f}} & s_{\tilde{f}} \\ -s_{\tilde{f}} & c_{\tilde{f}} 
\end{array} \right) 
\left( \begin{array}{cc}
\lambda_{H_i \tilde{f}_L \tilde{f}_L } & \lambda_{H_i \tilde{f}_L \tilde{f}_R}\\
\lambda_{H_i \tilde{f}_R \tilde{f}_L } & \lambda_{H_i \tilde{f}_R \tilde{f}_R }
\end{array} \right) \left( \begin{array}{cc} 
c_{\tilde{f}} & - s_{\tilde{f}} \\ s_{\tilde{f}} & c_{\tilde{f}} 
\end{array} \right) 
\end{eqnarray}
We then apply the minimization conditions on the full one-loop potential
\beq
\frac{\partial V_{\rm Higgs}^{\rm 1-loop}}{\partial H_d^0} = \frac{\partial 
V_{\rm Higgs}^{\rm 1-loop}}{\partial H_u^0} = 0
\eeq
which are equivalent to the requirement that the tree--level plus one--loop
tadpoles vanish, and obtain the loop corrected values of $\mu^2$ and $B \mu$:
%
\begin{eqnarray} 
\mu^2 &=& \frac{1}{2} \bigg\{ \tan 2\beta \bigg[ \bigg(m^2_{H_u} -
\frac{t_u}{v_u} \bigg)  \tan \beta - \bigg(m^2_{H_d} -\frac{t_d}{v_d} \bigg) \cot 
\beta \bigg] - \overline{M}_Z^2 \bigg\} \non \\
B\mu &=& \frac{1}{2} \sin 2\beta \Bigg[ \bigg( m^2_{H_u} +\frac{t_u}{v_u}
\bigg) + \bigg( m^2_{H_d}- \frac{t_u}{v_u} \bigg)  + 2
\mu^2 \Bigg] 
\end{eqnarray}
as well as the running pseudo--scalar Higgs boson mass at the EWSB scale:
\beq
\overline{M}_A^2(M_{EWSB}) &=& \frac{1}{\cos 2\beta} \bigg[ \bigg( m_{H_d}^2- 
\frac{t_d}{v_d} \bigg) - \bigg( m_{H_u}^2 - \frac{t_u}{v_u} \bigg) \bigg] 
-\overline{M}_Z^2 \non \\ 
&& + \sin^2\beta \, \frac{t_d}{v_d} + \cos^2 \beta \, \frac{t_u}{v_u}  
\eeq
[The $Z$ boson mass appearing in the above expressions should be the running 
mass at the EWSB scale; however, the difference between this and the pole 
mass value is rather small and we have neglected it in the 
program]. \s

Once the running pseudoscalar Higgs bosons mass is obtained, it will serve as
input to the calculation of the other Higgs boson masses as discussed in
section 3.3 and also later in this Appendix. One also has to derive the pole
$M_A$ value by including the one--loop (and potentially two--loop)
contributions. This part of the calculation is in principle performed
by the Higgs routines. \bigskip

\subsection*{A.3: The particle spectrum}

\subsubsection*{A.3.1 Diagonalization of the mass matrices}

In section 3.3, we have discussed how to obtain the tree--level Higgs boson 
and SUSY particle mass spectrum from the soft SUSY--breaking parameters. While
this discussion was more or less complete for the sfermion and Higgs boson
sectors, some details will be given here in the case of chargino and 
neutralino sectors. \s
 
The general $2\times 2$ chargino mass matrix ${\cal M}_C$ given in eq.~(47) is 
diagonalized by two real matrices $U$ and $V$, 
\begin{eqnarray}
U^* {\cal M}_C V^{-1} \ \ \ra \ \ U={\cal O}_- \ {\rm and} \ \ V = 
\left\{
\begin{array}{cc} {\cal O}_+ \ \ \ & {\rm if \ det}{\cal M}_C >0  \\
            \sigma_3  {\cal O}_+ \ \ \ & {\rm if \ det}{\cal M}_C <0  
\end{array}
\right. 
\end{eqnarray}
where $\sigma_3$ is the Pauli matrix and the rotations matrices  are given by:
\begin{eqnarray}
{\cal O}_\pm = \left[ \begin{array}{cc} \cos \theta_\pm & \sin \theta_\pm
\\ -\sin \theta_\pm & \cos \theta_\pm \end{array} \right] 
\end{eqnarray}
with the mixing angles defined by: 
\begin{eqnarray}
\tan 2 \theta_- &= & \frac{ 2\sqrt{2}M_W(M_2 \cos \beta
+\mu \sin \beta)}{ M_2^2-\mu^2-2M_W^2 \cos \beta} \non \\
\tan 2 \theta_+ & = & \frac{ 2\sqrt{2}M_W(M_2 \sin \beta
+\mu \cos \beta)}{M_2^2-\mu^2 +2M_W^2 \cos \beta} 
\end{eqnarray}
This leads to the two chargino  $\chi_{1,2}^+$ masses
\begin{eqnarray}
m_{\chi_{1,2}^+} = && \frac{1}{\sqrt{2}} \left[ M_2^2+\mu^2+2M_W^2
\right. \\
&& \left. \mp \left\{ (M_2^2-\mu^2)^2+4 M_W^4 \cos^2 2\beta+4M_W^2 (M^2_2+\mu^2
+2M_2\mu \sin 2\beta) \right\}^{\frac{1}{2}} \right]^{\frac{1}{2}} \non
\end{eqnarray}

In the case of the neutralinos, the four-dimensional mass matrix eq.~(48)
has be diagonalized analytically by a single real matrix $Z$;
the [positive] masses of the neutralino states $m_{\chi_i^0}$ are given by:
\beq
\epsilon_1 m_{\chi_1^0} &=& C_1 -\left( \frac{1}{2} a- \frac{1}{6}C_2
\right)^{1/2} + \left[ - \frac{1}{2} a- \frac{1}{3}C_2 + \frac{C_3}
{(8a-8C_2/3)^{1/2}} \right]^{1/2} \non \\
\epsilon_2 m_{\chi_2^0} &=& C_1 +\left( \frac{1}{2} a- \frac{1}{6}C_2
\right)^{1/2} - \left[ - \frac{1}{2} a- \frac{1}{3}C_2 - \frac{C_3}
{(8a-8C_2/3)^{1/2}} \right]^{1/2} \non \\
\epsilon_3 m_{\chi_3^0} &=& C_1 -\left( \frac{1}{2} a- \frac{1}{6}C_2
\right)^{1/2} - \left[ - \frac{1}{2} a- \frac{1}{3}C_2 + \frac{C_3} 
{(8a-8C_2/3)^{1/2}} \right]^{1/2} \non \\
\epsilon_4 m_{\chi_4^0} &=& C_1 +\left( \frac{1}{2} a- \frac{1}{6}C_2
\right)^{1/2} + \left[ - \frac{1}{2} a- \frac{1}{3}C_2 - \frac{C_3}
{(8a-8C_2/3)^{1/2}} \right]^{1/2}
\eeq
where $\epsilon_i = \pm 1$; the coefficients $C_i$ and $a$ are given by
\beq
C_1 &=& (M_1+M_2)/4 \non \\
C_2 &=& M_1 M_2 - M_Z^2 -\mu^2 -6 C_1^ 2 \non \\
C_3 &=& 2 C_1 \left[ C_2 + 2 C_1^2 +2 \mu^2 \right]+
M_Z^2 (M_1 c_W^2 + M_2 s_W^2) - \mu M_Z^2 \sin 2 \beta \non \\
C_4 &=& C_1 C_3- C_1^2 C_2 -C_1^4 -M_1 M_2 \mu^2 +(M_1 c_W^2 + M_2 s_W^2)
M_Z^2 \mu \sin 2\beta
\eeq
and
\beq
a = \frac{1} {2^{1/3}} {\rm Re} \left[ S+ i \left( \frac{D}{27} 
\right)^{1/2} \right]^{1/3}
\eeq
with
\beq
S &=& C_3^2+\frac{2}{27} C_2^3 -\frac{8}{3} C_2 C_4 \non \\
D &=& \frac{4}{27} (C_2^2 +12 C_4)^3 -27 S^2 
\eeq

\subsubsection*{A.3.2 Radiative corrections to the fermion masses}

Since the fermion masses provide one of the main input, it is important to 
include the leading radiative corrections to these parameters, in particular 
those due to strong interactions and Yukawa couplings. The fermion 
masses which have to be used in the mass matrices eq.~(45) are 
the masses $\hat{m}_f (Q^2)$, evaluated in the $\overline{\rm DR}$ scheme at 
the scale $Q=M_{\rm EWSB}$ and which, in terms of the pole masses $m_f$, are 
given by:  
\beq 
m_f = \hat{m}_f (Q^2) \, \left(1+ \frac{\Delta m_f}{m_f} \right) 
\eeq
In the case of top quarks, it is in general sufficient to include the 
one--loop QCD corrections originating from standard gluon exchange (first term
of the expression below) and gluino--stop exchange (second term):
\begin{eqnarray}
\frac{\Delta m_t}{m_t} &=& \frac{\alpha_s}{3\pi} \left[3 \log \left( \frac{Q^2}
{m_t^2} \right) +5 \right]  \\
&-& \frac{\alpha_s}{3\pi} \left[ B_1(m_{\tilde{g}}, m_{\tilde{t}_1})+
B_1( m_{\tilde{g}}, m_{\tilde{t}_2}) -\sin 2\theta_t \frac{m_{\tilde{g}}}{m_t}
\bigg(B_0(m_{\tilde{g}}, m_{\tilde{t}_1})-B_0(m_{\tilde{g}}, m_{\tilde{t}_2}) 
\bigg) \right] \non 
\end{eqnarray}
where in terms of $M={\rm max}(m_1,m_2)$, $m={\rm min}(m_1,m_2)$ and $x=
m_2^2/m_1^2$, the two Passarino--Veltman functions $B_{0,1}(m_1,m_2) 
\equiv B_{0,1}(0,m_1^2,m_2^2)$ simply read in this limit
\begin{eqnarray}
B_0 (m_1,m_2) &=& -\log \left( \frac{M^2}{Q^2} \right) +1 + \frac{m^2}{m^2-M^2}
\log \left( \frac{M^2}{m^2} \right) \non \\
B_1 (m_1,m_2) &=& \frac{1}{2} \left[- \log \left( \frac{M^2}{Q^2} \right) 
+\frac{1}{2}  + \frac{1}{1-x}+ \frac{\log x}{(1-x)^2} - \theta (1-x) \log x
\right]
\end{eqnarray}
[one has also to include the two--loop ${\cal O}(\alpha_s^2)$ standard QCD
terms as discussed in Section 3.2]. However, this approximation fails in some
cases and we have incorporated the full one--loop corrections at finite
momentum transfer and including the contributions of all SUSY particles [the
only approximation was to neglect the mixing between gauginos and Higgsinos]. \s

In the case of bottom quarks, the first important correction which has to be 
included is the one due to standard QCD corrections and the running from the 
scale $m_b$ to the high scale $Q$, as was discussed in Section 3.2.  
Once this is done, one has to include the sbottom--gluino and the
stop--chargino  corrections which are the most important ones, in particular
for  large $\tb$ and $\mu$ values:
\begin{eqnarray}
\frac{\Delta m_b}{m_b} &=&-\frac{\alpha_s}{3\pi} \left[ B_1(m_{\tilde{g}}, 
m_{\tilde{b}_1})+B_1( m_{\tilde{g}}, m_{\tilde{b}_2}) -\sin 2\theta_b 
\frac{m_{\tilde{g}}}{m_b} \bigg( B_0(m_{\tilde{g}}, m_{\tilde{b}_1})-
B_0(m_{\tilde{g}}, m_{\tilde{b}_2}) \bigg) \right] \non \\
&-& \frac{\alpha}{8\pi s_W^2} \frac{m_t \mu}{M_W^2 \sin 2\beta}\, \sin2\theta_t
\, [B_0(\mu, m_{\tilde{t}_1})- B_0( \mu, m_{\tilde{t}_2}) ] \\
&-& \frac{\alpha}{4\pi s_W^2} \left[ \frac{M_2\mu \tb}{\mu^2-M_2^2}
\bigg( \cos^2 \theta_t B_0(M_2, m_{\tilde{t}_1})+ \sin^2 \theta_t B_0(M_2, 
m_{\tilde{t}_2}) \bigg) + (\mu \leftrightarrow M_2) \right] \non
\end{eqnarray}
For the $\tau$ lepton mass, the only relevant corrections to be included are 
those stemming from chargino--sneutrino loops, and which simply read
\begin{eqnarray}
\frac{\Delta m_\tau}{m_\tau} &=& -\frac{\alpha}{4\pi s_W^2} \, 
\frac{M_2\mu \tb}{\mu^2-M_2^2} \left[ B_0(M_2, m_{\tilde{\nu}_\tau})
-B_0(\mu, m_{\tilde{\nu}_\tau}) \right] 
\end{eqnarray}

\subsubsection*{A.3.3 Radiative corrections to the sparticle masses}

The gluino mass is given at the tree--level by $m_{\tilde{g}}=M_3(M_{\rm 
EWSB})$. To obtain the pole gluino mass, one has to include the standard 
and SUSY QCD corrections, $m_{\tilde{g}}=M_3+\Delta M_3/M_3$. These
corrections are given by [assuming a universal squark mass for simplicity]:
\beq
\frac{\Delta M_3}{M_3} &=& \frac{3\alpha_s}{2\pi} \left\{ 
2B_0(M_3^2, M_3, 0)- B_1(M_3^2, M_3, 0) -2 B_1(M_3^2, 0, m_{\tilde{q}}) 
\right\}
\eeq
with the finite parts of the Passarino--Veltman two--point functions $B_0$ and 
$B_1$ given by:
\beq
B_0(q^2, m_1,m_2) &=& -{\rm Log}\left(\frac{q^2}{Q^2} \right)-2  \non \\
&& -{\rm Log}(1-x_+)-x_+{\rm Log}(1-x_+^{-1}) 
-{\rm Log}(1-x_-)-x_-{\rm Log}(1-x_-^{-1}) \non \\
B_1(q^2, m_1,m_2) &=& \frac{1}{2q^2} \bigg[ m_2^2 \left(1- {\rm \log} 
\frac{m_2^2}{Q^2} \right) - m_1^2 \left(1- {\rm Log} \frac{m_1^2}{Q^2} 
\right)  \non \\ &&  + (q^2-m_2^2+m_1^2) B_0(q^2, m_1,m_2) \bigg]  
\eeq
with $Q^2$ denoting the renormalization scale which we take to be the EWSB 
scale, and the variables $x_\pm$ are given by:   
\beq
x_{\pm} = \frac{1}{2q^2} \left( q^2-m_2^2+m_1^2 \pm \sqrt{(q^2-m_2^2+m_1^2)^2 
-4q^2(m_1^2- i \epsilon) } \, \right)
\eeq 

In the case of the charginos and neutralinos, we work in an approximation 
where one corrects only the gaugino and higgsino entries in the mass matrices 
and not the states themselves. This gives, according to PBMZ, a very good 
approximation of the complete result. Using the Passarino--Veltman two--point 
functions above, the dominant one--loop corrections to the electroweak
gaugino masses $M_{1}, M_2$ are\cite{PBMZ}:
\beq
\frac{\Delta M_1}{M_1} &=& - \frac{\alpha}{4\pi c_W^2} \left\{ 
11 B_1(M_1^2, 0, m_{\tilde{q}})+ 9 B_1(M_1^2, 0, m_{\tilde{l}}) - \frac{\mu}
{M_1} \sin 2\beta  \right. \\
&& \left. \times \Bigg[ B_0(M_1^2, \mu, M_A) - B_0 (M_1^2, \mu, M_Z) \Bigg] +
B_1(M_1^2, \mu, M_A) + B_1 (M_1^2, \mu, M_Z) \right\} \non \\
\frac{\Delta M_2}{M_2} &=& - \frac{\alpha}{4\pi s_W^2} \left\{ 
9B_1(M_2^2, 0, m_{\tilde{q}})+ 3 B_1(M_1^2, 0, m_{\tilde{l}}) - \frac{\mu}
{M_2} \sin 2\beta  \right. \\
&& \times \Bigg[ B_0(M_2^2, \mu, M_A) - B_0 (M_2^2, \mu, M_Z) \Bigg] +
B_1(M_2^2, \mu, M_A) + B_1 (M_2^2, \mu, M_Z)  \non \\
&&  \left. - 8 B_0(M_2^2, M_2, M_W) + 4 B_1 (M_2^2, M_2, M_W) \right\} \non 
\eeq
while the corrections to the higgsino mass parameter are given by:
\beq
\frac{\delta \mu}{\mu} &=& \frac{- 3 }{32 \pi^2 } \bigg[ \lambda_t^2 \left(
B_1(\mu^2, m_t, m_{\tilde{t}_1}) +B_1(\mu^2, m_t, m_{\tilde{t}_2}) \right) \\
&& \hspace*{.8cm} + \lambda_b^2 \left(
B_1(\mu^2, m_b, m_{\tilde{b}_1}) +B_1(\mu^2, m_b, m_{\tilde{b}_2}) \right)
\bigg] \non \\
 && \frac{-3\alpha}{16 \pi } \bigg[ B_1(\mu^2, M_2,M_A) +B_1(\mu^2,M_2,M_Z)
 +2 B_1(\mu^2, \mu,M_Z) -4B_0( \mu^2,\mu,M_Z) \bigg] \non 
\eeq
\bigskip
 
For the masses of the squarks, except for the stops which need a special 
treatment, one needs to include only the QCD corrections neglecting the masses 
of the partner quarks. This leads to a simple expression for the pole squark
masses squared,
\beq 
m^2_{\tilde{q}} = \hat{m}^2_{\tilde{q}} (Q^2) \, \left(1+ \frac{\Delta 
m^2_{\tilde{q}} }{m^2_{\tilde{q}}} \right) 
\eeq
with
\beq
\frac{\Delta  m^2_{\tilde{q}} }{m^2_{\tilde{q}}}=\frac{2\alpha_s}{3 \pi} 
\bigg[2B_1(m^2_{\tilde{q}}, m_{\tilde{q}},0) + \frac{ A(m_{\tilde{g}})}
{m^2_{\tilde{q}}} - \bigg(1- \frac{ m^2_{\tilde{g}}} {m^2_{\tilde{q}}}
\bigg) B_0 (m^2_{\tilde{q}}, m_{\tilde{g}},0) \bigg]
\eeq
For the two top squarks, simply including the QCD corrections as above is not 
an enough good approximation and one has to incorporate also the electroweak 
corrections  which can be important, in particular those involving the 
possibly large Yukawa couplings. We have incorporated the full set of 
electroweak corrections a la PBMZ. \s

Finally, in the case of the sleptons, the radiative corrections are very 
small, less than one percent according to PBMZ,  and we have neglected them 
in the program. \bigskip
 

\subsubsection*{A.3.4 Radiative corrections to the Higgs boson masses}

We have interfaced \sus\ with several routines calculating the Higgs bosons 
masses in the MSSM. These routines, that we  provide with the main program,
use different methods and approximations but include the most important
contributions. One is therefore in principle guaranteed to have the most
accurate and up--to date  value for these Higgs sector parameters. However, in
some cases an accuracy of a  few percent in the determinations of these masses
is sufficient. To have a  complete and self-contained program, we have
therefore provided a default choice where one uses simple expressions for these
radiative corrections to the Higgs masses, which provide a rather good
approximation [a complete one--loop and leading two--loop routine  is in
preparation]. \s

For the CP--even Higgs bosons masses, we use the procedure described in
Section 3.3.3, with the following values for the corrections $s_{ij}$. 
Defining first, to simplify the expressions, the reduced variables:
\beq
x_t= \bigg( \frac{A_t - \mu {\rm cot}\beta}{M_S}\bigg)^2 \ , \  \ 
y_t= \frac{\bar{m}^2_t}{M_S^2} \ , \ \
z_t= \frac{M_Z^2} {\bar{m}^2_t} \, \  
\eeq
with $\bar{m}_t$ being the $\overline{\rm MS}$ top quark mass corrected 
at one-loop only with pure QCD corrections 
\beq
\bar{m}_t= m_t (1+ 4 \alpha_s/3\pi)^{-1}
\eeq
and $M_S$ an average SUSY scale taken to be in terms of the soft stop masses
\beq
M_S= [\, m_{\tilde{Q}}^2 m_{\tilde{t}_R}^2 + \bar{m}_t^2 (m_{\tilde{Q}}^2 + 
m_{\tilde{t}_R}^2) + \bar{m}_t^4\, ]^{1/4}
\eeq
one obtains for the various $s_{ij}$ corrections at zero--momentum 
transfer \cite{FeynHiggsFast}:
\beq
s_{11}&=& \frac{\sqrt{2}G_F}{\pi^2} M_Z^4 \bigg( \frac{1}{8} - \frac{1}{3}s_W^2
+ \frac{4}{9}s_W^4 \bigg) \cos^2 \beta  {\rm Log}(y_t)  \\
s_{12}&=& \frac{\sqrt{2}G_F}{\pi^2} M_Z^2 {\rm cot} \beta  \bigg[  
\frac{3}{8} \bar{m}_t^2 - \bigg( \frac{1}{8} - \frac{1}{3}s_W^2
+ \frac{4}{9}s_W^4 \bigg) \sin^2 \beta M_Z^2 \bigg] {\rm Log}(y_t)  \\
s_{22}&=& \frac{\sqrt{2}G_F}{\pi^2} \frac{\bar{m}_t^4 }{ 8 \sin^2 \beta} \bigg[
\bigg(12 -6 z_t \sin^2 \beta + z_t^2
\bigg( \frac{1}{8} - \frac{1}{3}s_W^2 + \frac{4}{9}s_W^4 \bigg) \sin^4 \beta
\bigg) {\rm Log}(y_t) \non \\
&& \hspace*{3cm} -2z_t +\frac{11}{10} z_t^2 
+ x_t (-12 +4z_t + 6y_t) + x_t^2 (1-4 y_t+ 3y_t^2)\non \\
&& \hspace*{3cm} + x_t^3 \bigg( \frac{3}{5} y_t - \frac{12}{5} y_t^2 + 2 y_t^3 \bigg)
+ x_t^4 \bigg( \frac{3}{7} y_t^2 - \frac{12}{7} y_t^3 +\frac{3}{2} y_t^4
\bigg) \ \bigg] \non \\
&+& \frac{\sqrt{2}G_F}{\pi^2} \frac{\alpha_s}{\pi} \frac{\bar{m}_t^4}{ 
\sin^2 \beta} \bigg[ 4+ 3 {\rm Log}^2(y_t) + 2 {\rm Log}(y_t) -6 
\sqrt{x_t} - x_t (3 {\rm Log}(y_t)+ 8) + \frac{17}{12} x_t^2 \bigg] \non \\
&-& \frac{9G_F^2}{16\pi^4} \frac{ \bar{m}_t^6} {\sin^2 \beta} \bigg[
{\rm Log}^2(y_t) -2 x_t {\rm Log}(y_t) + \frac{1}{6} x_t^2 {\rm Log}(y_t) 
\bigg] 
\eeq
The radiative corrections to the pseudoscalar and charged Higgs boson masses,
which are in principle generally rather tiny, have not been included in this 
approximation.    

\newpage


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section*{Appendix B: Contents of the Fortran Code}

\subsection*{B.1: The subroutines and their main purpose}

We list below all the subroutines and functions contained in the program 
{\tt SuSpect} and shortly describe their main purpose and content. 
 
\subsubsection*{B.1.1 The main routine}

\begin{verbatim}
         SUBROUTINE SUSPECT2(iknowl,input,ichoice,errmess)
\end{verbatim}
This is the main routine of the program, to be be used as it is or to be
called by any other routine (such as {\tt suspect2\_call.f}, as will be
discussed below). It has the following four basic input control 
parameters: \s

{\tt IKNOWL}: which sets the degree of control on the various parts of the 
algorithm. It has three possible values at present:

\begin{itemize}
\vspace*{-2mm}
\item[--] {\tt IKNOWL=0}: totally blind use of the program, i.e. no control on
any  ``algorithmic" parameter, no warning and other messages. Reasonable
default values are set for the control parameters and the program gives just
the results from the physical input.  
\vspace*{-2mm}

\item[--]  {\tt IKNOWL=1}: in which there is no control on any algorithmic
feature but some warning/error messages are collected in the {\tt suspect.out} 
file (this is the recommended choice in general).  
\vspace*{-2mm}

\item[--]  {\tt IKNOWL=2}: is for a more ``educated" use. One can control some
algorithmic parameters and gets all warning/error messages (with many printed
on the screen). One has to set personally by hand the appropriate values of 
some other parameters control. This option is therefore not recommended 
unless for debugging.  
\vspace*{-2mm}
\end{itemize}

{\tt INPUT}: is for the physical input setting and works in three modes:

\begin{itemize}
\vspace*{-2mm}
\item[--] {\tt INPUT=0}: the model and option parameters {\tt ichoice(1)-(10)} 
as well as the values of the physical input parameters are read off from the
file  {\tt suspect2.in}. 
\vspace*{-2mm}

\item[--] {\tt  INPUT=1}: when you want to define yourself all the relevant
input choices and parameters within your calling program. The required list of
parameters to be defined (with consistent names etc), can be found in the
commons given below, and their meaning is also explained in the {\tt
suspect2.in}  file.
\vspace*{-2mm}

\item[--] {\tt INPUT=11}: same as {\tt  INPUT=1}, but with no output file 
{\tt suspect.out} generated (this option is convenient e.g. for scans of the 
MSSM parameter space).
\vspace*{-2mm}
\end{itemize}   

{\tt ICHOICE}: initializes the various options for the models to be considered,
the degree of accuracy to be required, the features to be included, etc. There
are 10 possible choices at present and the options are described in detail in
the input file: 
\begin{itemize}
\vspace*{-2mm}
\item[--] {\tt ICHOICE(1)}: Choice of the model to be considered.
\vspace*{-3mm}

\item[--] {\tt ICHOICE(2)}: For the perturbative order (1 or 2 loop) of the 
RGEs. 
\vspace*{-3mm}

\item[--] {\tt ICHOICE(3)}: To impose or not the GUT scale. 
\vspace*{-3mm}

\item[--] {\tt ICHOICE(4)}: For the accuracy of the RGEs.
\vspace*{-3mm}

\item[--] {\tt ICHOICE(5)}: To impose or not the radiative EWSB. 
\vspace*{-3mm}

\item[--] {\tt ICHOICE(6)}: To chose different input in general MSSM.
\vspace*{-2mm}

\item[--] {\tt ICHOICE(7)}: For the radiative corrections to the (s)particles 
masses. 
\vspace*{-3mm}

\item[--] {\tt ICHOICE(8)}: To set the value of the EWSB scale.
\vspace*{-3mm}

\item[--] {\tt ICHOICE(9)}: For the number of (RGE + full spectrum) 
iterations.
\vspace*{-3mm}

\item[--] {\tt ICHOICE(10)}: For the routine calculating the Higgs boson masses.
%\vspace*{-2mm}
\end{itemize}

{\tt  ERRMESS}: which provides a useful set of warning/error message flags,
           that are automatically written in the output file {\tt suspect.out}:
\begin{itemize}
\vspace*{-2mm}
\item[--] {\tt ERRMESS(i)= 0}: Everything is fine,
\vspace*{-3mm}

\item[--] {\tt ERRMESS(1)=-1}: tachyon 3rd gen. sfermion from RGE,
\vspace*{-3mm}

\item[--] {\tt ERRMESS(2)=-1}: tachyon 1,2 gen. sfermion from RGE,
\vspace*{-3mm}

\item[--] {\tt ERRMESS(3)=-1}: tachyon $A$ boson (maybe temporary: see final 
mass), 
\vspace*{-3mm}

\item[--] {\tt ERRMESS(4)=-1}: tachyon 3rd gen. sfermion from mixing,
\vspace*{-3mm}

\item[--] {\tt ERRMESS(5)=-1}: $\mu(M_{\rm GUT})$ guess inconsistent, 
\vspace*{-3mm}

\item[--] {\tt ERRMESS(6)=-1}: non--convergent $\mu$ from EWSB, 
\vspace*{-3mm}

\item[--] {\tt ERRMESS(7)=-1}: EWSB maybe inconsistent  (! but RG-improved only check),
\vspace*{-3mm}

\item[--] {\tt ERRMESS(8)=-1}: $V_{\rm Higgs}$ maybe UFB or CCB (! but 
RG-improved only check),
\vspace*{-3mm}

\item[--] {\tt ERRMESS(9)=-1}: Higgs boson masses are NaN, 
\vspace*{-3mm}

\item[--] {\tt ERRMESS(10)=-1}: RGE problems (non-pert and/or Landau poles).
%\vspace*{-2mm}
\end{itemize}

\subsubsection*{B.1.2 Routines for the models}

There are two main routines for the model boundary conditions, one for the 
AMSB and one for the GMSB models [because of historical reasons, the 
calculation in the mSUGRA model is performed directly in the main routine
{\tt suspect2.f}]. 

\begin{verbatim}
          SUBROUTINE SU_AMSBSUB(m0,m32,cq,cu,cd,cl,ce,chu,chd,g12,g22,g32,
     . ytau,yb,yt,al,ad,au,mhu2,mhd2,mtaur2,msl2,mbr2,mtr2,msq2,mer2,mel2,
     . mdr2,mur2,muq2,m1,m2,m3)
\end{verbatim}
Calculates the initial conditions at initial scale where the RGE starts in
the general AMSB model [i.e. including a soft SUSY--breaking scalar mass $m_0$
with a different weight $c_i$ for every Higgs and sfermion scalar mass]. \s

  The input parameters at the initial scale are: \\
  m32: the gravitino mass, \\
  m0 : the soft-SUSY breaking scalar mass term,\\
  cq,cu,cd,cl,ce,chu,chd: weights  of m0 for the different soft terms, \\
  (for the original AMSB model: $c_i=0$ and usual minimal AMSB model: $c_i=1$),
\\ 
  g12,g22,g23: gauge couplings squared, \\
  ytau,yb,yt : third generation Yukawa gauge couplings squared. \s

  The ouputs at the initial scale are: \\
  m1,m2,m3: gaugino mass terms,  \\
  au,ad,al,au1,ad1,l1: 3d and 1st/2d generation trilinear couplings, \\
  au,ad,al,au1,ad1,l1: 3d and 1st/2d generation trilinear couplings, \\
  mhu2,mhd2,mtaur2,msl2,mbr2,mtr2,msq2,mer2,mel2,mdr2,mur2,muq2: 
  Higgs and sfermion soft mass terms squared. 

\begin{verbatim}
      SUBROUTINE SU_GMSBSUB(mgmmess,mgmsusy,nl,nq, g12,g22,g32,
     . al,ad,au,mhu2,mhd2,mtaur2,msl2,mbr2,mtr2,msq2,mer2,mel2,
     . mdr2,mur2,muq2,m1,m2,m3)
\end{verbatim}
Calculates the  GMSB model initial conditions at the messenger scale $M_{\rm 
Mes}$ where the RGE start in this case. \s

The input at the messenger scale are:  \\
  mgmmess,mgmsusy: messenger and SUSY-breaking scales, \\
  nl, nq number of lepton/ quark messengers (in minimal GMSB, $n_l=n_q=1$),  \\
  g12,g22,g23: gauge couplings squared. \s

  The output parameters at the messenger scale are:  \\
  m1,m2,m3: gaugino masses,  \\
  au,ad,al,au1,ad1,al1: trilinear sfermion couplings,   \\
  mhu2,mhd2,mtaur2,msl2,mbr2,mtr2,msq2,mer2,mel2,mdr2,mur2,muq2: 
  Higgs and sfermion soft mass terms squared.  \s

  The routine needs to evaluate a Spence function which is supplied: 
\begin{verbatim}
      REAL*8 FUNCTION SU_PLI2(x)
\end{verbatim}

\subsubsection*{B.1.3. Routines for the fermion masses and $\alpha_s$}

The following three routines are for the evaluation of the (SUSY) radiative 
corrections to the generation fermion masses. They will need to evaluate 
the one--loop real ($A$) and two-loop complex ($B_0$ and $B_1$) 
Passarino--Veltman functions which are supplied:
\begin{verbatim}
      REAL*8 FUNCTION SU_A(m)
      COMPLEX*16 FUNCTION SU_B0(qsq,m1,m2)
      COMPLEX*16 FUNCTION SU_B1(s,mi,mj)
\end{verbatim}
The arguments are the internal pole masses and the momentum transfer squared.

\begin{verbatim}
       SUBROUTINE SU_TOPMSCR(alpha_s,mt,mb,rmt,rmb,yt,yb,tbeta,
     .            mql,mur,mdr,at,ab,mu, delmtop)
\end{verbatim}
  Calculates the radiative corrections to the top quark mass including the
  standard and SUSY QCD corrections (the standard corrections are also 
  calculable with RUNM) and the electroweak corrections including the 
  contributions of gauge bosons, Higgs bosons, charginos and neutralinos.
  The input are respectively: the strong coupling constant, the pole masses,
  running masses and Yukawa couplings of the top and bottom quarks, $\tan\beta$,
  the 3d generation squark mass terms and trilinear couplings and $\mu$. 
  The output {\tt delmtop} is the radiative correction to the top quark mass. 
%
\begin{verbatim}
        SUBROUTINE SU_BMSUSYCR(alphas,mb,rmt,rmb,yt,tbeta,m2,mgluino,
     .             mql,mur,mdr,at,ab,mu, delmb)          
\end{verbatim}
  Calculates the SUSY radiative corrections to the bottom mass including
  the SUSY QCD corrections (the standard ones are calculated with RUNM)
  and the dominant electroweak corrections due to the Yukawa couplings.
  The input are respectively: the strong coupling constant, pole b mass,
  the running top and bottom masses, the top Yukawa coupling, $\tan\beta$, 
  the SU(2) gaugino mass, the gluino mass, the 3d generation squark mass 
  terms, the 3d generation trilinear couplings and the parameter $\mu$. 
  The output  {\tt delmb} is the SUSY radiative correction to the bottom mass.
  These corrections are then re-summed in the main routine.  
%
\begin{verbatim}
        SUBROUTINE SU_TAUMSCR(tgbeta,mu,m2,mnstau, delmtau)
\end{verbatim}
  Calculates the dominant SUSY radiative corrections to the $\tau$ lepton  mass 
  with the contribution of charginos/stau-sneutrinos without re--summation. 
  The input are respectively: $\tan\beta$, the higgsino mass parameter $\mu$, 
  the SU(2) gaugino mass parameter and the 3d generation sneutrino mass. 
  The output {\tt delmtau} is the radiative correction to the tau lepton mass.
\bigskip

There are also routines for the QCD running of the quark masses and for
the evaluation of the strong coupling constant $\alpha_s$ at various scales. 
They are given in the following. 
\begin{verbatim}
           SUBROUTINE ALSINI(ACC)
\end{verbatim}
Subroutine for initialization in the evaluation of the strong coupling 
constant $\alpha_s$. It needs the two iteration functions to determine the
improved values of QCD scale $\Lambda_{\rm QCD}$ for a given number of quark 
flavor and masses, loop order, etc..: 
\begin{verbatim}
          DOUBLE PRECISION FUNCTION XITER(Q,XLB1,NF1,XLB,NF2,ACC)
          DOUBLE PRECISION FUNCTION XITLA(NO,ALP,ACC)
\end{verbatim}
There are also two important functions for the calculation of the 
running of the QCD coupling at scale $Q$ and perturbative order $N$:        
\begin{verbatim}
          DOUBLE PRECISION FUNCTION ALPHAS(Q,N)
\end{verbatim}
and the running of the quark masses at scale Q and with NF quark flavors:
\begin{verbatim}
          DOUBLE PRECISION FUNCTION RUNM(Q,NF)
\end{verbatim}
These routines are borrowed from the program {\tt HDECAY} version 2.2 


\subsubsection*{B.1.4 Routines for the SUSY and Higgs particle masses}

  The following routines are for the evaluation of the chargino/neutralino,
  sfermion and Higgs boson masses including the radiative corrections {\it 
  \`a la PBMZ}. For these radiative corrections, they also need the one-- and 
  two--loop Passarino--Veltman functions discussed above.
\begin{verbatim}
      SUBROUTINE SU_GAUGINO(mu,m1,m2,m3,b,a,mc,mn,xmn)
\end{verbatim}
Calculates the chargino and neutralino masses and mixing angles (with 
analytical expressions) including radiative corrections in the higgsino and 
gaugino limits. \s

  The input parameters at EWSB scale are: \\
  mu,m1.m2,m3: Higgs mass parameter and gaugino mass parameters,  \\
  b,a: the angle $\beta$ and the mixing angle $\alpha$ in the Higgs sector.\s

The output parameters are: \s

mc: the two chargino masses,\\
mn: the four neutralino masses (absolute values),\\
mx: the four neutralino masses (including signs). \s 

The  masses are ordered with increasing value. The diagonalizing 
(ordered) mass matrices $U,V$ for charginos and $Z$ for neutralinos are 
given in the common block  {\tt SU\_MATINO/u,v,z}.
%
\begin{verbatim}
       SUBROUTINE SU_CINORC(ml1,mq1,mq3,mu3,md3,ma,yt,yb,m1,m2,mu,tb,
     .            rcm1,rcm2,rcmu)
\end{verbatim}
Calculates the radiative corrections to the gaugino and higgsino mass 
parameters {\it \`a la PBMZ}. \s 

The input parameters at EWSB scale are: \\
ml1,mq1,mq3,mu3,md3: sfermion mass parameters of 1st and 3d generations\\
ma,tb: pseudoscalar Higgs boson mass and tan(beta), \\
yt,yb: top and bottom Yukawa couplings,\\
m1,m2,mu: bare gaugino and Higgs mass parameters. \s

The outputs are the radiative corrections {\tt rcm1, rcm2, rcmu} to $M_1,M_2, 
\mu$.
%
\begin{verbatim}
       SUBROUTINE SU_GINOCR(alphas,m3, mb,mt, delgino)
\end{verbatim}
Calculates the radiative correction to the gluino mass, {\tt delgino} 
(output).  \s

The input parameters at EWSB scale are: \\
alphas,m3: the strong coupling constant and the SU(3) gaugino mass, \\
mb, mt: the bottom and top pole masses;\\
msu1,msu2,msd1,msd2,msb1,msb2,mst1,mst2: the squark masses (input via
the common/SU\_bpew/.. calculated by the subroutine SU\_SFERMION).  \s   

\begin{verbatim}
       SUBROUTINE SU_SFERMION(mql,mur,mdr,mel,mer,mql1,mur1,mdr1,mel1,mer1,
     .            al,at,ab,mu, mst,msb,msl,msu,msd,mse,msn)
\end{verbatim}
 Calculates the sfermion masses including radiative corrections {\it \`a la 
PBMZ} and the mixing angles for the third generation sfermions. \s

The input parameters at EWSB scale are: \\
mql,mur,mdr,mel,mer,mql1,mur1,mdr1,mel1,mer1: sfermion mass terms, \\
al,at,ab,mu: 3d generation trilinear couplings and the parameter $\mu$. \s

The outputs are the sfermions masses: mst,msb,msl,msu,msd,mse,msn. \s

The masses msf=msf(1) and msf(2) are ordered such that the lightest is 1 and 
the heaviest is 2. The mixing angles of third generation sfermions are in the 
common block {\tt COMMON/SU\_MIXANG/thet,theb,thel} which is to be treated with
care because of the ordering of the sfermion masses, when compared to other 
calculations.
\begin{verbatim}
       SUBROUTINE SU_SQCR(alphas,mgluino,msquark,dmsquark)
\end{verbatim}
Calculates the QCD (standard+SUSY) correction to squark (except stop)
masses. The input are: the strong coupling constant $\alpha_s$, the gluino 
and tree-level squark masses and the output is the correction to the 
squark mass dmsquark. Squark mixing and Yukawa's are neglected. 

\begin{verbatim}
        SUBROUTINE SU_STOPCR(alphas,mgluino,mu,ma,thet,bet,mst1,mst2,msb,
     .             yt,yb,at,ab, crll,crlr,crrr)
\end{verbatim}
  Calculates radiative corrections to the two stop masses, including standard 
and SUSY-QCD corrections and the Yukawa corrections {\it \`a la PBMZ}.
  The input at the EWSB scale are, respectively: the strong coupling 
  constant, the gluino mass, mu parameter, pseudoscalar Higgs boson mass,
  stop mixing angle, the angle beta, the two stop masses, the right sbottom mass
  parameter, the top and bottom Yukawa couplings and trilinear couplings. 
  The outputs are the radiative corrections to the LL, LR, RR entries of the 
  stop squark mass matrix. 

\begin{verbatim}
         SUBROUTINE SU_SUSYCP(TGBET)
\end{verbatim}
Calculates the MSSM Higgs bosons masses and the angle $\alpha$ including
radiative corrections for a given input value of the parameter $\tan \beta$.
The other input parameters (soft SUSY--breaking parameters, sparticle
masses and mixing angles, SM parameters), are called via common blocks. 
This routine is adapted from the one in the program HDECAY version 3.0.  
It returns the masses of the pole masses of the CP-odd (ama), lighter 
CP--even (aml), heavier CP--even (amh), charged Higgs boson (amch) as well as 
the running CP--odd (amar) Higgs masses, which are given in the block: 
\begin{verbatim}
        COMMON/SU_HMASS/ama,aml,amh,amch,amar
\end{verbatim}
It gives also the couplings of the angle beta at the EWSB scale, the mixing
$\alpha$ and the Higgs boson couplings to standard particles in:
\begin{verbatim}
        COMMON/SU_HCOUP/b,a,gat,gab,glt,glb,ght,ghb,ghvv,glvv
\end{verbatim}
It returns also the couplings of the Higgs bosons to sfermions 
\begin{verbatim}
        COMMON/SU_CPLHSF/gcen,gctb,glee,gltt,glbb,ghee,ghtt,ghbb
      .                  gatt,gabb,gaee
\end{verbatim}
and the Higgs couplings to charginos and neutralinos:
\begin{verbatim}
         COMMON/SU_CPLHINO/ac1,ac2,ac3,an1,an2,an3,acnl,acnr
\end{verbatim}
For the radiative correction in the Higgs sector, there is the default
option where the calculation is made in an approximation based on the
of work Heinemeyer, Hollik and Weiglein and which is in 
general sufficient, or uses the {\tt HDECAY} procedure which depending on the 
flag {\tt IMODEL=ichoice(10)}, calls the following routines: 
\begin{verbatim}
     1:  SUBH_HDEC from Carena, Quiros and Wagner adapted by HDECAY 
     2:  HMSUSY from Haber, Hempfling and Hoang 
     3:  FEYNHIGGSFAST1.2.2 from Heinemeyer, Hollik and Weiglein 
\end{verbatim}
as follows: 
\begin{verbatim}
       CALL SUBH_HDEC(ama,tgbet,amsq,amur,amdr,amt,au,ad,amu,amchi,
     .            amlr,amhr,amch,sa,ca,tanba,amglu)

       CALL HMSUSY0(tgbet,sa,ca)

       CALL FEYNHIGGS(ama,tgbet,amt,xmst1,xmst2,stt,xmsb1,
     .                xmsb2,stb,amu,amglu,am2,amlr,amhr,sa,ca)
\end{verbatim}

\subsubsection*{B.1.5 The routine for the EWSB}

The following routine is for the one--loop effective scalar potential 
\begin{verbatim}
      SUBROUTINE SU_VLOOP2(q2,MU,AT,AB,AL,  dVdvd2,dVdvu2) 
\end{verbatim}
which is the main and in fact only subroutine for the EWSB and calculates the 
tadpole corrections to the Higgs mass terms squared. \s

The input at the EWSB scale are: \\
 q2: the scale at which EWSB is supposed to happen,  \\
 MU: the higgsino parameter mu at EWSB scale, \\
 AT,AB,AL: the third generation trilinear couplings at EWSB scale,\\
Ytau, Yt, Yb: the Yukawa couplings (at EWSB scale), input via the 
common/SU\_yukaewsb/..,\\
 msta1,msta2,msb1,msb2,mst1,mst2,..,thet,theb,thel: masses and mixing of
 tau,b,top,.. etc sfermions at EWSB scale (input via common/su\_bpew/..,
calculated by the subroutine SU\_SFERMION).\s

Other important input parameters, such as the Higgs, chargino, neutralino 
masses and couplings as well as SM parameters are called via commons.  \s

The output, {\tt dVdvd2} and {\tt dVdvu2}, are (up to some appropriate 
overall constants) the derivatives of the full one--loop scalar potential 
including the contributions of all SM and SUSY particles a la PBMZ.
The consistency of the EWSB mechanism is performed by the main program. 

\subsubsection*{B.1.6 Routines for the RGE}

  The following routines are for the numerical RGE evolution of the parameters 
\begin{verbatim}
           SUBROUTINE SU_ODEINT(y,n,x1,x2,eps,h1,hmin,nok,nbad,
     .                          SU_DERIVS,SU_RKQC) 
\end{verbatim}
This is the routine for the RGE evolution of parameter between low and high 
energy scales, borrowed from Numerical Recipes. It returns a set of n mass and 
coupling parameters "$y$" at a specified scale $exp(x2)$ when given at an 
initial scale exp(x2). It uses the two routines:
\begin{verbatim}
           SUBROUTINE SU_RKQC(y,dydx,n,x,htry,eps,yscal,hdid,hnext,SU_DERIVS)
           SUBROUTINE SU_RK4(y,dydx,n,x,h,yout,SU_DERIVS)
\end{verbatim}
which are the fourth order Runge--Kutta numerical algorithms solving 
differential equations by Numerical Recipes\cite{numrec}. \s

The four routines: 
\begin{verbatim}
           SUBROUTINE SU_DERIV1(x,y,dydx)		  
           SUBROUTINE SU_DERIV2(x,y,dydx)
           SUBROUTINE SU_DERIV1T(x,y,dydx)
           SUBROUTINE SU_DERIV2T(x,y,dydx)
\end{verbatim}
are the derivatives of the RG running parameters $y(xN)$, i.e the beta 
functions $\beta(y)=d(y)/dln(Q)$. The analytic expressions of the functions 
are taken from (up to some sign conventions which have been changed) from
Castano, Ramond and Piard and from Barger, Berger and Ohmann. \s
Thus y(n) is a  vector containing all the n RG evolving parameters at 
various possible scales depending on evolution stages. The parameters are
\begin{verbatim}
  y(1) = g_1^2   U(1) gauge coupling squared
  y(2) = g_2^2   SU(2)_L gauge coupling squared
  y(3) = g_3^2   SU(3) gauge coupling squared
  y(4) = Y_\tau  tau lepton Yukawa coupling 
  y(5) = Y_b     bottom  quark Yukawa coupling
  y(6) = Y_t     top quark Yukawa coupling
  y(7) = Ln(v_u) logarithm of the vev vu 
  y(8) = Ln(v_d) logarithm of the vev vd 
  y(9) = A_\tau  trilinear coupling for stau 
  y(10)= A_b     trilinear coupling for sbottom
  y(11)= A_t     trilinear coupling for stop
  y(12)=(m_Hu)^2 scalar phi_u mass term squared
  y(13)=(m_Hd)^2 scalar phi_d mass term squared  
  y(14)=m_\taur^2 right-handed stau mass term squared
  y(15)= msl^2   left-handed stau mass term squared
  y(16)= mbr^2   right-handed sbottom mass term squared
  y(17)= mtr^2   right-handed stop mass term squared 
  y(18)= msq^2   left-handed stop mass term squared
  y(19)= B       the (dimensionful) bilinear parameter B 
  y(20)= Ln|M_1| logarithm of the bino mass term
  y(21)= Ln|M_2| logarithm of the wino mass term
  y(22)= Ln|M_3| logarithm of the gluino mass term
  y(23)= Ln|\mu| logarithm of the mu parameter
  y(24)= mer^2   right-handed selectron (smuon) mass term squared
  y(25)= mel^2   left-handed selectron (smuon) mass term squared
  y(26)= mdr^2   right-handed sdown (sstrange) mass term squared
  y(27)= mur^2   right-handed sup (scharm) mass term squared
  y(28)= muq^2   left-handed sup (scharm) mass term squared
  y(29)= A_l     trilinear coupling for selectron (smuon) 
  y(30)= A_d     trilinear coupling for sdown (sstrange)
  y(31)= A_u     trilinear coupling for sup (scharm). 
\end{verbatim}
  Note that the number of running parameters does not coincide with the 22
  parameters of the phenomenological MSSM since one has to add the gauge
 and the Yukawa couplings, as well as those which are linearly dependent. \s

Note that: \s
 
{\tt  DERIV1} : includes only 1-loop RGE with simple (unique scale) threshold.
 
{\tt  DERIV2} : includes 2-loop RGE for gauge, Yukawa couplings and gaugino 
masses.

{\tt  DERIV1T}: includes 1-loop RGE with realistic multi scale threshold.

{\tt  DERIV2T}: includes 2-loop RGEs and multi-scale thresholds. \s

\subsubsection*{B.1.7 Routines for the checks of the spectrum}

There are already three routines which allow to check the particle spectrum
which are already implemented in \sus\ but which are not called [and no output
is given yet]:
\begin{verbatim}
      SUBROUTINE SU_GMINUS2(mel,mer,Amu,mu,tb,u,v,z,mn,mc1,mc2,gmuon)
\end{verbatim}
Calculates the leading chargino and neutralino loop SUSY contributions
c to the muon anomalous magnetic moment. The inputs are: \s

mel,mer,Amu: relevant soft terms for the 2d generation smuon sector,

mu, tb: $\mu$ and $\tb$, 

U,V,Z, mn, mc1,mc2: chargino and neutralino mixing matrices and masses. \s

\nn The output {\tt gmuon} is $a_\mu = g_\mu -2$ in standard units. 

\begin{verbatim}
     SUBROUTINE SU_DELRHO(mt,gmst,gmsb,gmstau,msn,thetat,thetab,thel,drho) 
\end{verbatim}

Calculates the leading one--loop SUSY contributions of third generation 
sfermions (plus leading two--loop QCD contributions in the case of squarks)
to the $\rho$ parameter. The inputs are: \s
 
mt, gmst(2), gmsb(2), gmstau(2), msn: top and 3d generation sfermion masses. 

thetat,thetab,thel: stop, sbottom, stau mixing angles. \s

\nn The output {\tt drho} is the SUSY contribution to $\rho-1$.  
 
\begin{verbatim}
    SUBROUTINE SU_FINETUNE(mu,tb,mhd2,mhu2,czmu,czbmu,ctmu,ctbmu)
\end{verbatim}
Calculates the degree of fine--tuning in a given model (at the moment with 
respect to $M_Z$ and $m_t$ only). The inputs are: \s 

mu,tbeta, mHd2, mHu2: $\mu, \tb, M_{H_u}^2, M_{H_d}^2$ at the EWSB scale. 

\nn The output  {\tt czmu, czbmu, ctmu, ctbmu} are the (dimensionless) measures
of the degree of fine--tuning  on $M_Z$ and $m_t$ with respect to $\mu$ and 
$B\mu$, respectively. The larger those numbers $(\gg 1)$, the more the model  
is "fine--tuned". \bigskip

Two additional routines will be included very soon (some checks are being
performed presently): one for the evaluation of the $b \to s\gamma$ branching 
ratio and one for the test of the CCB and UFB minima. 


\newpage

\subsection*{B.2: List of the various COMMONs}

We list below the various {\tt COMMON}s used in the program with some short 
explanations. The {\tt COMMON}s for the input and output parameters are
important since they are possibly called by {\tt suspect\_call.f} and are 
needed for interfacing with other codes. 

\subsubsection*{B.2.1 COMMONs for input parameters} 
 
\hspace*{.5cm} Standard Model input parameters (couplings and fermion masses):\\
\hspace*{2cm} {\tt COMMON/SU\_SMPAR/dalfinv,dsw2,dalphas,dmt,dmb,dmtau}\sx

RG evolution scale parameters (EWSB scale, high and low RGE ends):\\
\hspace*{2cm} {\tt       COMMON/SU\_RGSCAL/dqewsb,dehigh,delow}\sx

Soft SUSY--breaking MSSM parameters of the scalar potential:\\
\hspace*{2cm} {\tt       COMMON/SU\_MSSMHPAR/dmhu2,dmhd2,dMA,dMU}\sx

The U(1), SU(2), SU(3) SUSY--breaking gaugino masses:\\
\hspace*{2cm} {\tt       COMMON/SU\_MSSMGPAR/dm1,dm2,dm3}\sx 

The soft-SUSY breaking slepton mass terms (3d and then 1/2 generations):\\
\hspace*{2cm} {\tt       COMMON/SU\_MSSMSLEP/dmsl,dmtaur,dmel,dmer}\sx

The soft-SUSY breaking squark mass terms (3d and then 1/2 generations):\\
\hspace*{2cm} {\tt       COMMON/SU\_MSSMSQUA/dmsq,dmtr,dmbr,dmuq,dmur,dmdr}\sx

The soft-SUSY breaking trilinear couplings (3d and then 1/2 generations):\\
\hspace*{2cm} {\tt       COMMON/SU\_ATRI3/dal,dau,dad}\\
\hspace*{2cm} {\tt       COMMON/SU\_ATRI12/dal1,dau1,dad1}\sx

The sign of $\mu$ and the input $\tb$ value:\\
\hspace*{2cm} {\tt       COMMON/SU\_RADEWSB/sgnmu0,tgbeta}\sx

mSUGRA case input parameters:\\
\hspace*{2cm} {\tt       COMMON/SU\_MSUGRA/m0,mhalf,a0}\s

GMSB case input parameters:\\
\hspace*{2cm} {\tt       COMMON/SU\_GMSB/mgmmess,mgmsusy,nl,nq}\sx

AMSB case input parameters:\\
\hspace*{2cm} {\tt       COMMON/SU\_AMSB/m32,am0,cq,cu,cd,cl,ce,chu,chd}\sx


\subsubsection*{B.2.2 COMMONs for output masses and mixing angles}

\hspace*{.5cm} Light $h$, heavy $H$, charged Higgs $H^+$ Higgs masses and mixing angle 
$\alpha$:\\
\hspace*{2cm} {\tt      COMMON/SU\_OUTHIGGS/dml,dmh,dmch,alfa}\sx

Charginos $\chi_{1,2}^\pm$ masses, neutralinos $\chi^0_{1..4}$ masses, gluino 
$\tilde{g}$ mass:\\
\hspace*{2cm} {\tt COMMON/SU\_OUTGINOS/dmc1,dmc2,dmn1,dmn2,dmn3,dmn4,mgluino}\sx

Stop $\tilde{t}_{1,2}$ masses and Sup $\tilde{u}_{1,2}$, Scharm 
$\tilde{c}_{1,2}$ masses:\\
\hspace*{2cm} {\tt       COMMON/SU\_OUTSQU/dmst1,dmst2,dmsu1,dmsu2}\sx

Sbottom $\tilde{b}_{1,2}$ masses and Sdown $\tilde{d}_{1,2}$, Sstrange
$\tilde{s}_{1,2}$ masses:\\
\hspace*{2cm} {\tt       COMMON/SU\_OUTSQD/dmsb1,dmsb2,dmsd1,dmsd2}\sx

Stau $\tilde{\tau}_{1,2}$ masses and Selectron $\tilde{e}_{1,2}$, Smuon
$\tilde{s}_{1,2}$ and Sneutrino masses:\\
\hspace*{2cm} {\tt COMMON/SU\_OUTSLEP/dmsl1,dmsl2,dmse1,dmse2,dmsn1,dmsntau}\sx

The soft-SUSY breaking trilinear couplings (3d and then 1/2 generations):\\
\hspace*{2cm} {\tt       COMMON/SU\_ATRI3/dal,dau,dad}\\
\hspace*{2cm} {\tt       COMMON/SU\_ATRI12/dal1,dau1,dad1}\sx

Stop, sbottom, stau mixing angles:\\
\hspace*{2cm} {\tt         COMMON/SU\_MIX/thet,theb,thel}\sx

The values of $\tb$ and the angle $\alpha$ at the EWSB scale:\\
\hspace*{2cm} {\tt             COMMON/SU\_HMIX/beta,adum}\sx

$U,V$ chargino and $Z$ neutralino diagonalyzing matrices:\\
\hspace*{2cm} {\tt       COMMON/SU\_MATINO/U,VV,Z}\sx

Final bottom, top tau masses and gauge couplings at EWSB scale:\\ 
\hspace*{2cm} {\tt        COMMON/SU\_YUKAEWSB/ytauewsb,ybewsb,ytewsb,alsewsb,g2ewsb,g1ewsb}\sx

\subsubsection*{B.2.3 Internal COMMONs} 

These commons are internal to the \sus\ routine and the user should not need
to care about any of them in principle, except in case of debugging. We list
them without any detailed comment, in case they are needed: \s

\begin{verbatim}
      COMMON/SU_strc/irge,isfrc,inorc
      COMMON/SU_stepwi/wistep,h1,kpole
      COMMON/SU_stegut/ifirst,jfirst,ygut
      COMMON/SU_errsf/sterr,sberr,stauerr,stnuerr
      COMMON/SU_qcdflag/nnlo,idrflag
      COMMON/SU_hflag/ihflag
      COMMON/SU_tachyrc/tachsqrc
      COMMON/SU_good/iflop
      COMMON/SU_sthresh/rmtop,susym,egut
      COMMON/SU_gunif/kunif
      COMMON/SU_param/gf,alpha,mz,mw
      COMMON/SU_cte/nf,cpi,zm,wm,tbeta
      COMMON/SU_als/xlambda,mc0,mb0,mt0,n0
      COMMON/SU_fmasses/mtau,mbpole,mtpole
      COMMON/SU_runmasses/mtaurun,mbrun,mtrun
      COMMON/SU_yuka/ytau,yb,ytop
      COMMON/SU_treesfer/msbtr1,msbtr2,msttr1,msttr2
      COMMON/SU_hmass/ma,ml,mh,mch,marun
      COMMON/SU_break/msl,mtaur,msq,mtr,mbr,al,au,ad,
     .                mu,m1,m2,m3
      COMMON/SU_break2/mel,mer,muq,mur,mdr
      COMMON/SU_smass/gmn,xmn,gmc,gmst,msb,gmsl,gmsu,gmsd,gmse,gmsn
      COMMON/SU_hcoup/bcoup,a,gat,gab,glt,glb,ght,ghb,ghvv,glvv
      COMMON/SU_cplhsf/gcen,gctb,glee,gltt,glbb,ghee,ghtt,ghbb,
     .                 gatt,gabb,gaee
      COMMON/SU_cplhino/ac1,ac2,ac3,an1,an2,an3,acnl,acnr
      COMMON/SU_cteloop/vu,vd,atop,ab,atau,rmllt,rmllb,rmlltau,
     .                 rmrrt,rmrrb,rmrrtau
      COMMON/SU_soft/rmtaur,rml,rmbr,rmtr,rmq
      COMMON/SU_cpl/g22,sw2
      COMMON/SU_sgnm123/sgnm1,sgnm2,sgnm3
      COMMON/SU_renscale/scale
\end{verbatim}

\newpage

\subsection*{B.3: Example of a calling routine}

Here is an example of a program calling the main routine {\tt suspect2.f} and
that one can use to inteface with other programs or to make scans of 
the parameter space. The file is provided with the program and is called 
 {\tt suspect2\_call.f}

\begin{verbatim}
c  ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
c                    The calling program suspect_call.f 
c  ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
c  VERSION 2.1
c  Last changes : November 20, 2002 
c  ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
c  This program is the example routine calling the main program SuSpect2.f.
c  It has to be compiled together with suspect2.f in all cases, but it is
c  particularly useful when performing e.g. a scan of the parameter space   
c  (and not only to obtain the spectrum for one point as can be done in the 
c  SuSpect2.f routine by setting the control parameter INPUT to the value 1) 
c  and/or to interface SuSpect with another program. In this routine you have  
c  to set the four control parameters which are the inputs arguments of the  
c  main program:

c         SUBROUTINE SuSpect2(iknowl,input,ichoice,errmess) 
c  The input are (see details in the comments of begining of SuSpect2.f): 
c  IKNOWL which sets the degree of control on various parts of the algorithm:
c  =0: blind use of the program, no control on parameters and no warning.
c  =1: no control on the algorithm but warning/error messages in output file.
c  =2: control some algorithmic parameters and all warning/error messages.
c  INPUT is for the physical input setting and works in three modes:
c  =0: model and option parameters and physical input read in SuSpect.in
c  =1: define yourself IN THIS FILE the relevant input choices and parameters.
c  =11: same as input=1, but with no output file SuSpect.out generated
c       (more convenient e.g. for scan over the model parameter space).
c  ICHOICE intialises the various model/accuracy options to be considred: 
c  - ICHOICE(1): Choice of the model to be considered.
c  - ICHOICE(2): For the perturbative order (1 or 2 loop) of the RGEs. 
c  - ICHOICE(3): To impose or not the GUT scale. 
c  - ICHOICE(4): For the accuracy of the RGEs.
c  - ICHOICE(5): To impose or not the radiative EWSB. 
c  - ICHOICE(6): To chose different (scalar sector) input in general MSSM.
c  - ICHOICE(7): For the radiative corrections to the (s)particles masses. 
c  - ICHOICE(8): To set the value of the EWSB scale.
c  - ICHOICE(9): For the number of (long: RGE + full spectrum) iterations: 
c  - ICHOICE(10): For the routine calculating the Higgs boson masses.
c  ERRMESS provides a useful set of warning/error message flags in output file.
c  - ERRMESS(i)= 0: Everything is fine.
c  - ERRMESS(1)=-1: tachyon 3rd gen. sfermion from RGE
c  - ERRMESS(2)=-1: tachyon 1,2 gen. sfermion from RGE
c  - ERRMESS(3)=-1: tachyon A    (maybe temporary: see final mass) 
c  - ERRMESS(4)=-1: tachyon 3rd gen. sfermion from mixing
c  - ERRMESS(5)=-1: mu(M_GUT) guess inconsistent 
c  - ERRMESS(6)=-1: non-convergent mu from EWSB 
c  - ERRMESS(7)=-1: EWSB maybe inconsistent  (!but RG-improved only check)
c  - ERRMESS(8)=-1: V_Higgs maybe UFB or CCB (!but RG-improved only check)
c  - ERRMESS(9)=-1: Higgs boson masses are NaN 
c  - ERRMESS(10)=-1: RGE problems (non-pert and/or Landau poles)
c  ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
c                      The program starts here
c  ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
      PROGRAM main
c 
      implicit real*8(a-h,m,o-z)
      dimension ichoice(10),errmess(10)
      dimension u(2,2),vv(2,2),z(4,4)
c
c
c=========================  COMMONs for input ============================
c   These are the commons for the parameters that can be read in the file 
c   suspect2.in (together with the various ichoices). 
c   !Important note: to interface your program with SuSpect2.f, these 
c    commons (plus the output ones below) are the only ones needed.
c
c   "Standard model" INPUT parameters (couplings and fermion masses):
       COMMON/SU_SMPAR/alfinv,sw2,alphas,mt,mb,mc,mtau
c   RG evolution scale parameters (EWSB scale, high and low RGE ends):
       COMMON/SU_RGSCAL/qewsb,ehigh,elow
c   (Soft-SUSY breaking) MSSM parameters of the scalar potential:     
       COMMON/SU_MSSMHPAR/mhu2,mhd2,ma,mu
c   The U(1), SU(2), SU(3) SUSY-breaking gaugino masses
       COMMON/SU_MSSMGPAR/m1,m2,m3 
c   The soft-SUSY breaking slepton mass terms (3d and then 1/2 gen.): 
       COMMON/SU_MSSMSLEP/msl,mtaur,mel,mer
c   The soft-SUSY breaking squark mass terms (3d and then 1/2 gen.):
       COMMON/SU_MSSMSQUA/msq,mtr,mbr,muq,mur,mdr
c   The soft-SUSY breaking trilinear couplings (3d and then 1/2 gen.):
       COMMON/SU_ATRI3/atau,at,ab
       COMMON/SU_ATRI12/al,au,ad
c   mSUGRA case input parameters:
       COMMON/SU_MSUGRA/m0,mhalf,a0
       COMMON/SU_RADEWSB/sgnmu0,tgbeta
c   GMSB case input parameters:
       COMMON/SU_GMSB/mgmmess,mgmsusy,nl,nq
c   AMSB case input parameters:
       COMMON/SU_AMSB/m32,am0,cq,cu,cd,cl,ce,chu,chd
c
c========================  COMMONs for output ============================= 
c
c      COMMON/SU_OUTHIGGS/ml,mh,mch,alfa
c   light, heavy, charged Higgs masses, Higgs mix angle alpha 
       COMMON/SU_OUTGINOS/mc1,mc2,mn1,mn2,mn3,mn4,gluino
c   charginos 1,2 masses, neutralinos 1-4 masses, gluino mass 
       COMMON/SU_OUTSQU/mst1,mst2,msu1,msu2
c   stop 1,2 and sup 1,2 = scharm 1,2 masses
       COMMON/SU_OUTSQD/msb1,msb2,msd1,msd2
c   sbottom 1,2 and sdown 1,2 = sstrange 1,2 masses
       COMMON/SU_OUTSLEP/msl1,msl2,mse1,mse2,msn1,msntau
c   stau 1,2 ; selectron (=smuon) 1,2; sneut_e,mu, sneut_tau masses
       COMMON/SU_OUTMIX/thet,theb,thel
c   stop, sbottom, stau mixing angles
       COMMON/SU_MATINO/u,vv,z
c   U,V chargino and Z neutralino diagonalizing matrices
      COMMON/SU_YUKAEWSB/ytauewsb,ybewsb,ytewsb,alsewsb,g2ewsb,g1ewsb
c   (final) bottom, top tau masses and gauge couplings at EWSB scale 
c Note for soft terms: OUTPUT values are contained in the same commons as
c for their input values: MSSMhpar, MSSMgpar, MSSMslep,
c                         MSSMsqua, MSSMAtri
c 
c (NB if meaning ambiguous, see detailed parameter definitions and 
c  conventions in suspect2.f file)
c
c========================  Setting the running input ======================
c   Here you set your command for reading the input SuSpect2.in and/or writing 
c   (see functions in the comments above) in the output file SuSpect.out
       IKNOWL = 1
       INPUT  = 0
c  other possible choice: INPUT = 11:
c Same as INPUT = 1 , but NO OUTPUT File (suspect2.out) generated
c (convenient e.g. for scan on MSSM/mSUGRA parameters)
c  In case your INPUT choice is 1 or 11, the following lines will be read
c  (so that you have to set yourself ICHOICE(1)-(10) and the physical input 
c   parameters, see details in the input file suspec2.in or in the comments of 
c   the main suspect2.f file). 
c=======  Example of choice for the model/accuracy, etc, parameters  
      if(input.eq.0) goto 99
c control parameters input:
      ichoice(1) = 10
c (minimal SUGRA case)
c
      ichoice(2) = 21
c (2-loop RGE for gauge, yukawas, gauginos)
      ichoice(3) = 0
c (ichoice(3)= 0: GUT scale imposed (then EHIGH = input!); 
c            = 1: gauge unif scale calculated from gauge cpls. input
c
      ichoice(4) = 1
c  (RG accuracy: 1: moderately accurate and fast (generally sufficient)
c                 2: very accurate but rather slow!
      ichoice(5) = 1
c (consistent EWSB)
      ichoice(6) = 1
c (M_Hu, M_Hd (= m_0 in mSUGRA) input)
      ichoice(7) = 2
c ICHOICE(7):  SUSY radiative corrections to the (s)particles masses: 
c                      No Radiative corrections     : 0 
c                      only in mb,mt,mtau +Yukawas : 1  
c                      all squarks + gaugino R.C. in addition: 2
      ichoice(8) = 1
c (ichoice(8) = 1 for default EWSB scale=(m_t_L*m_t_R)^(1/2), =0 if not)
c then IF ichoice(8)=0 EWSB scale is set by user from input file/calling
c routine by the value of Qewsb
      ichoice(9) = 3
c ichoice(9) >= 3: Nb of (long: RGE + Full spectrum) iterations
      ichoice(10) = 1
c ICHOICE(10): Higgs mass options:
c             SUSPECT approximate m_h calculation      : 0
c             SUBH_HDEC (Carena et al.) from HDECAY    : 1
c             HMSUSY (Haber et al.) routine            : 2
c             FEYNHIGGSFAST1.2.2 (Heinemeyer et al.)   : 3
c
c======= Then define the needed SM and SUSY input parameters (example below)
c        (these are the parameters contained in the commons for input above):
c  "SM-like" input:
      alfinv= 127.938d0
      sw2 = .23117d0
      alphas =.1192d0
      mt =175.d0
      mb = 4.9d0
      mtau =1.7771d0
c
c RG evolution parameters: 
      ehigh = 1.9d16
      elow =91.19d0
      qewsb = 200.d0
c (!! qewsb value only relevant if ichoice(8) = 0, see above)
c   
c  minimal SUGRA case input sample (SNOWMASS point 1):
c
      m0 = 400.d0
      mhalf =400.d0
      A0 = 0.d0
      sgnmu0 = 1.d0
      tgbeta = 40.d0
c
c   
c  Gauge Mediated Supersymmetry Breaking (GMSB) input sample:
c
CC      mgmmess = 50.d3
CC      mgmsusy = 5.d3
CC      nl = 1
CC      nq = 1
CC      tgbeta = 30.d0
CC      sgnmu0 = 1.d0
c
c   
c  Anomaly Mediated Supersymmetry Breaking (AMSB) input sample:
c
CC      m32 = 40.d3
CC      am0  = 100.d0
CC      tgbeta = 30.d0
CC      sgnmu0 = 1.d0
CC      cq  =1.d0
CC      cu = 1.d0
CC      cd = 1.d0
CC      cl = 1.d0
CC      ce = 1.d0
c
c   non-universal case input sample:
c
CC        MHU2     = .5d4
CC        MHD2     = 5.d5
CC        M1       = 50.D0
CC        M2       = 200.D0
CC        M3       = 350.D0
CC        MSL      = 4.7D2
CC        MTAUR    = 4.7D2
CC        MSQ      = 367.5d0
CC        MTR      = 123.5d0
CC        MBR      = 4.7D2
CC        MEL      = 4.7D2
CC        MER      = 4.7D2
CC        MUQ      = 4.7D2
CC        MUR      = 4.7D2
CC        MDR      = 4.7D2
CC        Atau     = 1.5D3
CC        At       = -300.d0
CC        Ab       = 1.5D3
CC        AL       = 1.5D3
CC        AU       = -300.d0
CC        AD       = 1.5D3
c  special case of MA, MU input (instead of MHU2, MHD2)
CC        MA       = 1000.d0
CC        MU       = 100.d0
c      
  99  continue
c    At this stage you can call the main subroutine suspect:
c%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
c
       CALL suspect2(IKNOWL, INPUT, ICHOICE,ERRMESS)
c
c  (ALL relevant OUTPUT will be written in suspect.out file;
c   except if INPUT=11 chosen, and you may continue with output 
c   values within this program)
c
c   ......sequel of your own program continues e.g. here 
c   ....  Bonne route!
c
      end
c  +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

\end{verbatim}

\newpage
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%
%%%%%%%%%%%%%%%%  Introduction %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%
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%
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%
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%
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%
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%
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%
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%
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%
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%
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%
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%
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%
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%
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%
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% 
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%
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\end{document}









