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\newcommand{\drbar} {\overline{DR}}
\newcommand{\eq} [1] {Eq.~(\ref{#1})}
\newcommand{\fig} [1] {Fig.~\ref{#1}}
\newcommand{\msbar} {\overline{MS}}
\newcommand{\sect} [1] {Sect.~\ref{#1}}
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\begin{document}

\title{
\begin{flushright} \small \rm
   ZU-TH 01/03
\end{flushright}
       {\bf SPheno}, a program for calculating \\ supersymmetric spectra,  \\
       SUSY particle decays \\ and SUSY particle production at 
       $e^+ e^-$ colliders}
\author{W.~Porod\\[1cm] %}
     Institut f\"ur Theoretische Physik, Universit\"at Z\"urich, \\
         CH-8057 Z\"urich, Switzerland}
\maketitle
\begin{abstract}
SPheno is a program that accurately calculates the supersymmetric
particle spectrum within a high scale theory, such as minimal
supergravity, gauge mediated supersymmetry breaking, 
anomaly mediated supersymmetry breaking, or string effective field theories.
An interface exists for an easy implementation of other models. 
The program solves the renormalization group equations numerically to 
two--loop order with user-specified boundary conditions.
The complete one--loop formulas for the masses are used which are supplemented
by two--loop contributions in case of the neutral Higgs bosons and the
$\mu$ parameter.
The obtained masses and mixing matrices are used to calculate
 decay widths and branching ratios
 of supersymmetric particles as well as of Higgs bosons,
$b \to s \gamma$, $\Delta \rho$ and $(g-2)_\mu$. Moreover, 
the production cross sections of all supersymmetric particle as well as
Higgs bosons at $e^+ e^-$ colliders can be calculated including initial
state radiation and longitudinal
polarization of the incoming electrons/positrons. 
The program is structured such that it can 
easily be extend to include non-minimal models and/or complex parameters.
\end{abstract}

%\input{summary}

\tableofcontents

\section{Introduction}

Supersymmetry (SUSY) \cite{Wess:tw,Nilles:1983ge,habkan} 
provides an attractive extension of the Standard Model 
(SM). It provides a qualitative understanding of various phenomena in
particle physics: It stabilizes
the gap between the Grand Unification scale / Planck scale and the
electroweak scale \cite{Witten:nf}. It allows the unification of the three
gauge couplings at a scale $M_U \simeq 2 \cdot 10^{16}$~GeV in a
straight forward way \cite{GUT}. The large top mass generates radiative 
electroweak symmetry breaking \cite{Ibanez:fr}. In addition it provides
the lightest supersymmetric particle as a cold dark matter candidate
 \cite{Ellis:1983ew}.
Therefore, the search for supersymmetric particles is one of the main topics in
the experimental program of present and future high energy colliders
\cite{Carena:1997mb,LHC,LC,Abdullin:1999zp}.

The Minimal Supersymmetric Standard Model (MSSM) consists of taking the
Standard Model and adding the corresponding supersymmetric partners
\cite{habkan}. In
addition a second Higgs doublet is needed to obtain an anomaly--free theory.
The second Higgs doublet is also needed to give mass to u-type quarks and
down-type quarks at the same time. 
The MSSM in its most general from contains
more than 100 unknown parameters \cite{Haber:1997if} which are clearly
to many for an exhaustive study.  This number drastically reduces if
one embeds the MSSM in a high scale theory, such as minimal supergravity 
theories \cite{sugra}, gauge mediated supersymmetry breaking\cite{gmsb},
or anomaly mediated supersymmetry breaking\cite{Giudice:1998xp}.
There is not yet a theoretical preferred scheme for supersymmetry breaking.
For this reason it is important to know whether the precision of
on-going and future experiments
is sufficient: (i) To distinguish between the various schemes. (ii)
To which extend it is possible to reconstruct the underlying theory.
It has been 
demonstrated that the expected experimental accuracies at future  $e^+ e^-$
colliders complemented with data from the LHC 
allow for a successful reconstruct of such an underlying
supersymmetric high scale theory \cite{Blair:2000gy}.  Connected with these
questions is the question if the theoretical accuracy matches the
experimental one. The present version of the  program  
\verb+SPheno+\footnote{SPheno stands for {\bf S}upersymmetric
{\bf Pheno}menology}
is thought as a further step in getting accurate
theoretical results to match finally the experimental precision.

In the view of ongoing and future experiments it 
is highly desirable to have various and independent tools at hand
performing the calculation of the supersymmetric spectrum, of decay widths,
of branching ratios and of production cross sections. This allows for a 
cross check of the tools and by comparing the implemented methods
and approximations one can also get a rough understanding of the
theoretical error. \verb+SPheno+ is a program performing an accurate
calculation of the supersymmetric spectrum, of the branching ratios of
supersymmetric particles and the Higgs bosons and of the production cross
sections of supersymmetric particles and the Higgs bosons 
in $e^+ e^-$ annihilation including longitudinal beam polarization. 
Moreover, the spectrum is used to calculate the branching of the rare
decay $b \to s \gamma$, the supersymmetric contributions to the
anomalous magnetic of the muon $a_\mu$ as well as supersymmetric
contributions to the $\rho$ parameter.  

 For the calculation of the spectrum the programs
 ISASUSY \cite{Baer:1999sp}, SOFTSUSY \cite{Allanach:2001kg}
and SUSPECT \cite{suspect}  are widely used. A comparison of 
the results among these programs and with \verb+SPheno+
is given in \cite{Allanach:2002pz}. The calculation of the
branching ratios of supersymmetric particles as well as the production
cross sections in $e^+ e^-$ annihilation can  be done with \verb+SPheno+ , 
ISASUSY \cite{Baer:1999sp}, SPYTHIA \cite{Mrenna:1996hu} and 
SUSYGEN \cite{Ghodbane:1999va}. A comparison of the results of these
programs will be given in a future paper.

\verb+SPheno+ has been written in Fortran90. The main focus has been
on accuracy and on stable numerical results and less on speed. However,
on a modern PC a typical running time is in the order of one second.
 The calculation is done using two-loop renormalization
group equations (RGEs) \cite{Martin:1993zk}, complete
one-loop correction to all SUSY and Higgs masses \cite{Pierce:1996zz}
supplemented by the 2-loop corrections  to the neutral Higgs bosons 
\cite{Degrassi:2001yf,Dedes:2002dy} 
and to the $\mu$ parameter\cite{Dedes:2002dy}.
The present version of \verb+SPheno+ does all calculations for real parameters
neglecting the flavour structure in the fermion as well as in the
sfermion sector. Decay widths and cross sections are calculated using
tree-level formulas. However, the couplings involved are running couplings
and thus important numerical effects of higher order corrections are
already taken into account.
The program
has been structured in such a way that the future inclusion of
complex phases and mixing between the generations has already been considered
in the design of the interfaces as well as in the definition of the various
variables. Moreover, extensions of the MSSM, e.g.~models with broken R-parity,
 can be implemented easily. 

The aim of this paper is to provide a manual of the program, version 2.0, 
to describe
the approximations used and to display the results of a run. 
In \sect{sect:MSSM} we will summarize the MSSM parameters and we give the
tree-level formulas for the supersymmetric particles. Moreover, a 
short summary of the implemented high scale models is given.
In \sect{sect:decays} we list the implemented decay modes of supersymmetric
particles and the Higgs bosons. We also discuss shortly 
the approximations used. 
In \sect{sect:prod} we present the implemented cross sections in
$e^+ e^-$ annihilation. In \sect{sec:constraints} we discuss give
details on the implemented low energy constraints.
In \sect{sec:calc} we discuss the implemented algorithm in some detail.
In \sect{sec:example} the main program is presented in detail providing
the necessary information so that this program can be easily adapted to
the user's requirement. In the appendices we discuss the possible
switches for influencing the program as well as a detailed discussion
of possible input files. Moreover, we list the output of the program
for a typical example. The source code as well as precompiled versions
of the program can be obtained from the author via email: 
\verb+porod@physik.unizh.ch+; or it can be downloaded from
\verb+http://www-theorie.physik.unizh.ch/~porod/SPheno.html+.

\section{MSSM parameters, particle spectrum, and High Scale Models}
\label{sect:MSSM}

In this section we fix our notation concerning the parameters and
present the tree-level formulas for the masses as well as the mixing matrices.
In the following we assume that the physical masses are ordered:
$m_i \le m_j$ if $i<j$ except for the sfermions as explained below.
We also give a short overview over various high scale models which
are implemented in the program.

\subsection{Ingredients for the Lagrangian}

The pure supersymmetric Lagrangian is specified by the K\"ahler potential
giving the gauge interactions
and by the Superpotential $W$ giving the Yukawa interactions:
\begin{eqnarray}
W = \epsilon_{ab} \left( Y^L_{ij} {\hat L}^a_i {\hat H}^b_1 {\hat E}^c_j 
  + Y^D_{ij} {\hat Q}^a_i {\hat H}^b_1 {\hat D}^c_j
  + Y^U_{ij} {\hat Q}^b_i {\hat H}^a_2 {\hat U}^c_j
  - \mu {\hat H}^a_1 {\hat H}^b_2\right)
\end{eqnarray} 
where ${\hat L}$, ${\hat E}$, ${\hat Q}$, ${\hat D}$, and ${\hat U}$
denote the matter superfields. The $SU(2)_L$ representation indices
are denoted by $a, b =1,2$ and the generation indices by $i,j=1,2,3$;
$\epsilon_{ab}$ is the totally antisymmetric tensor with $\epsilon_{12}=1$.
Note that the sign of $\mu$ is identical to the one in ISASUSY 
\cite{Baer:1999sp} and SOFTSUSY \cite{Allanach:2001kg} but opposite 
to the convention in \cite{Pierce:1996zz}. Presently, real Yukawas
$Y^L$, $Y^D$, $Y^U$ only are included. They and the
gauge couplings $g_i$ are $\drbar$ quantities. $g_1$ is defined
in the Grand Unification normalization $g_1 = \sqrt{5/3} g'$ where
$g'$ is the Standard Model hypercharge gauge coupling.

The next ingredient is the soft SUSY breaking Lagrangian, which  is given by
mass terms for the gauginos
\begin{eqnarray}
L_{soft,1} &=& \frac{1}{2} \left( M_1 \tilde B \tilde B
              + M_2 \tilde W_a \tilde W^a
              + M_3 \tilde g_\alpha \tilde g^\alpha \right) + h.c. \, \, ,
\end{eqnarray}
mass terms for scalar matter fields and Higgs fields
\begin{eqnarray}
L_{soft,2} &=&  - M^2_{H_1} H^*_{1a} H^a_1 - M^2_{H_2} H^*_{2a} H^a_2
     - M^2_{\tilde L,ij} {\tilde L}^*_{ia} {\tilde L}^a_{j}
     - M^2_{\tilde E,ij} {\tilde E}^*_{i} {\tilde E}_{j}  \nonumber  \\
  && - M^2_{\tilde Q,ij} {\tilde Q}^*_{ia} {\tilde Q}^a_{j}
     - M^2_{\tilde U,ij} {\tilde U}^*_{i} {\tilde U}_{j}
     - M^2_{\tilde D,ij} {\tilde D}^*_{i} {\tilde D}_{j}
\end{eqnarray}
and trilinear couplings of scalar matter fields and Higgs fields
\begin{eqnarray}
L_{soft,3} &=& -
  \epsilon_{ab} \left( A^L_{ij} {\tilde L}^a_i  H^b_1 {\tilde E}^*_j 
  + A^D_{ij} {\tilde Q}^a_i  H^b_1 {\tilde D}^*_j
  + A^U_{ij} {\tilde Q}^b_i  H^a_2 {\tilde U}^*_j
  - B \mu  H^a_1  H^b_2\right) \nonumber \\ &&+ h.c.
\end{eqnarray}
 

\subsection{Masses and Mixing Matrices}

The masses of the various particles are induced by the soft SUSY
breaking parameters and the vacuum expectation values $v_i$ of the neutral
Higgs fields $v_i = <H^0_i>$. The ratio of the vacuum expectation values
is denoted by $\tan\beta = v_2 / v_1$. The sum of the vacuum expectation values
(vevs) squared is fixed by the gauge boson masses:
\begin{eqnarray}
m^2_W = \frac{1}{4} g^2 (v^2_1 + v^2_2) , \hspace{1cm}
m^2_Z = \frac{1}{4} (g^2 + {g'}^2) (v^2_1 + v^2_2)
\end{eqnarray}
Neglecting the mixing between different generations, the Standard Model 
fermion masses  are given by:
\begin{eqnarray}
m_{u_i} = \frac{1}{\sqrt{2}} Y^U_{ii} v_2 , \hspace{1cm}
m_{d_i} = \frac{1}{\sqrt{2}} Y^D_{ii} v_1 , \hspace{1cm}
m_{l_i} = \frac{1}{\sqrt{2}} Y^L_{ii} v_1
\end{eqnarray}
for u-quarks, d-quarks and leptons, respectively. 

The gluino mass is given by $m_{\tilde g} = |M_3|$. The charginos
are combination of the charged winos 
$\tilde w^\pm = (\tilde w^1 \mp i \tilde w^2) / \sqrt{2}$ and 
the charged higgsinos $\tilde h^-_1, \tilde h^+_2$. The Lagrangian
contains the chargino mass term 
$-(\tilde \psi^-)^T X \tilde \psi^+$ where
$\psi^- = (-i \tilde w^-, \tilde h^-_1)^T$, 
$\psi^+ = (-i \tilde w^+, \tilde h^+_2)^T$ and 
\begin{eqnarray}
X = \left( \begin{array}{cc} M &  \frac{g}{\sqrt{2}} v_2 \\
           \frac{g}{\sqrt{2}} v_1 & \mu \end{array} \right).
\end{eqnarray}
The matrix is diagonalized by two unitary matrices $U$ and $V$:
\begin{eqnarray}
M_{D,\tilde \chi^\pm} =  U^* X V^{-1} \, . 
\end{eqnarray}
The neutral gauginos $\tilde b, \tilde w^3$
as well as the
neutral higgsinos $\tilde h^0_1, \tilde h^0_2$ form the neutralinos. 
In the basis 
$\tilde \psi^0 = (\tilde b, \tilde w^3, \tilde h^0_1, \tilde h^0_2)^T$
one finds the mass term $- (\tilde \psi^0)^T Y \tilde \psi^0$ with
\begin{eqnarray}
Y = \left( \begin{array}{cccc}
         M_1 & 0   & - \frac{g'}{2} v_1 &   \frac{g'}{2} v_2 \\
          0  & M_2 & \frac{g}{2} v_1    & - \frac{g}{2} v_2 \\
      - \frac{g'}{2} v_1   & \frac{g}{2} v_1 & 0 & -\mu \\
        \frac{g'}{2} v_2 &   - \frac{g}{2} v_2    & -\mu & 0
 \end{array} \right)
\end{eqnarray}
This matrix is diagonalized by an unitary matrix $N$:
\begin{eqnarray}
M_{D,\tilde \chi^0} = N^* Y N^\dagger \,.
\end{eqnarray}

The CP-even electroweak eigenstates $(H^0_1, H^0_2)$ are rotated by the
angle $\alpha$ into the Higgs mass eigenstates $(h^0, H^0)$ as follows:
\begin{eqnarray}
\left( \begin{array}{c} h^0 \\ H^0 \end{array} \right) =
\left( \begin{array}{cc} -\sin\alpha & \cos\alpha \\
                          \cos\alpha & \sin\alpha \end{array} \right) 
\left( \begin{array}{c} H^0_1 \\ H^0_2 \end{array} \right) 
\end{eqnarray}
with $m_{h^0} < m_{H^0}$. The CP-odd and the charged Higgs masses are
given by
\begin{eqnarray}
 m^2_{A^0} = B \, \mu \, (\tan \beta + \cot \beta) \, ,
\hspace{1cm} m^2_{H^+} = m^2_{A^0} + m^2_W 
\end{eqnarray}
at tree level.

Neglecting generation mixing, the sneutrino masses are given by:
\begin{eqnarray}
M^2_{\tilde \nu_i} &=& M^2_{{\tilde L}_ii} + \frac{1}{2} m_Z^2 \cos 2 \beta
\end{eqnarray}
The other sfermion mass matrices are $2 \times 2$ matrices: 
\begin{eqnarray}
M^2_{\tilde l,i} &=& 
      \left( \begin{array}{cc}
        M^2_{\tilde L,ii} -\left(\frac{1}{2} - s^2_W \right) c_{2 \beta} m_Z^2
          + m_{l,i}^2 &
     \frac{1}{\sqrt{2}} \left( v_1 (A^L_{ii})^* - \mu Y^L_{ii} v_2 \right)   \\
     \frac{1}{\sqrt{2}} \left( v_1 A^L_{ii} - (\mu Y^L_{ii})^* v_2  \right)  &
        M^2_{\tilde E,ii} - s^2_W  c_{2 \beta}  m_Z^2  + m_{l,i}^2
          \end{array} \right) \\
M^2_{\tilde u} &=& 
      \left( \begin{array}{cc}
        M^2_{\tilde Q,ii} + \left(\frac{1}{2} - \frac{2}{3} s^2_W \right)
               c_{2 \beta}   m_Z^2 + m_{u,i}^2 &
    \frac{1}{\sqrt{2}} \left(  v_2 (A^U_{ii})^* - \mu Y^U_{ii} v_1\right)   \\
    \frac{1}{\sqrt{2}} \left(  v_2 A^U_{ii} - (\mu Y^U_{ii})^* v_1 \right)   &
        M^2_{\tilde U,ii} + \frac{2}{3} s^2_W c_{2 \beta}  m_Z^2 + m_{u,i}^2
          \end{array} \right) \\
M^2_{\tilde d} &=& 
      \left( \begin{array}{cc}
        M^2_{\tilde Q,ii} -\left(\frac{1}{2} - \frac{1}{3} s^2_W \right)
            c_{2 \beta}  m_Z^2  + m_{d,i}^2 &
   \frac{1}{\sqrt{2}} \left(   v_1 (A^D_{ii})^* - \mu Y^D_{ii} v_2  \right) \\
   \frac{1}{\sqrt{2}} \left(   v_1 A^D_{ii} - (\mu Y^D_{ii})^* v_2  \right)  &
        M^2_{\tilde D,ii} - \frac{1}{3} s^2_W  c_{2 \beta} m_Z^2 + m_{d,i}^2
          \end{array} \right) 
\end{eqnarray}
where $c_{2 \beta} = \cos \ 2 \beta$ and $s^2_W = \sin^2 \theta_W$.
These matrices are diagonalized by $2 \times 2$ matrices $R_{\tilde f,i}$ with
\begin{eqnarray}
m^2_{\tilde f} = R^\dagger_{\tilde f} M^2_{\tilde f} R_{\tilde f}
\end{eqnarray}
Sfermions are first ordered according to the generation and inside 
a generation according to their masses.
For example, in the slepton sector the ordering
is $\tilde e_1$, $\tilde e_2$, $\tilde \mu_1$, $\tilde \mu_2$, 
$\tilde \tau_1$, $\tilde \tau_2$ and similarly for squarks.

\subsection{High scale models}
\label{sect:models}

In this section we summarize the key ingredients of the high scale models
implemented in \verb+SPheno+. We also present the formulas for the boundary
conditions in the various models.
In all cases the modulus $|\mu|$ is determined
by requiring correct radiative symmetry breaking. At tree level the
corresponding formula reads as:
\begin{eqnarray}
|\mu|^2 = \frac{1}{2} \left[ \tan 2 \beta \left(
   M^2_{H_2} \tan\beta - M^2_{H_1} \cot\beta \right) - m^2_Z \right] \, .
\end{eqnarray}
Moreover, in all cases the high scale parameters are supplemented by the
sign of $\mu$ and $\tan\beta$.

\subsubsection{Minimal Supergravity}

The minimal supergravity (mSUGRA) scenario is characterized by a set
of universal parameters \cite{sugra,Nilles:1983ge} at the
GUT scale $M_{GUT}$: the gaugino mass parameter
 $M_{1/2}$, the
scalar mass parameter $M_0$, and the trilinear coupling $A_0$: 
\begin{eqnarray}
 M_i(M_{GUT}) &=& M_{1/2} \\
 M^2_{\tilde j}(M_{GUT}) &=& M^2_0 \\
 A_i(M_{GUT}) &=& A_0 Y_i(M_{GUT})
\end{eqnarray}


\subsubsection{Minimal Supergravity including right handed neutrinos}

In addition to the parameters of the mSUGRA model above the following 
parameters appear in this
case: $m_{\nu_R}$, a common mass for all right handed neutrinos, and
$m_{\nu_i}$ ($i=1,2,3$), the light neutrino masses. In this case
the MSSM RGEs are run up to the scale $m_{\nu_R}$ where the neutrino
Yukawa couplings are calculated using the formula 
$Y_{\nu,i} = \sqrt{m_{\nu_R} m_{\nu_i}}/v_2$. In the range between
$m_{\nu_R}$ and $M_{GUT}$ the effect of neutrino Yukawa couplings is
included in the RGEs of gauge and Yukawa couplings. At the GUT-scale
the right sneutrino mass parameters  as well as the trilinear coupling
$A_{\nu,i}$ are given by:
\begin{eqnarray}
 M^2_{\tilde R}(M_{GUT}) &=& M^2_0 \\
 A_{\nu,i}(M_{GUT}) &=& A_0 Y_{\nu,i}(M_{GUT})
\end{eqnarray}
 The corresponding RGEs are used in the running
from $M_{GUT}$ to $m_{\nu_R}$. At the scale $m_{\nu_R}$ the neutrino
Yukawa couplings $Y_{\nu,i}$, the trilinear couplings $A_{\nu,i}$
and the soft masses $M^2_{R,i}$ for the right sneutrinos are taken out
of the RGEs and below the  $m_{\nu_R}$ the usual set of MSSM RGEs are used. 

 
\subsubsection{Gauge Mediated Supersymmetry Breaking}
\label{sect:gmsb}

Gauge mediated supersymmetry breaking \cite{gmsb,Giudice:1998bp} 
(GMSB) is characterized by the mass $M_M \sim$ $\langle S \rangle $ 
of the messenger
fields and the mass 
scale $\Lambda = {\langle F_S \rangle} / {\langle S \rangle}$ 
setting the size of the gaugino and scalar masses. 
The gaugino masses  
\begin{equation}
M_i(M_M) = (N_5+3 N_{10}) g\left(\Lambda/M_M\right)
\alpha_i(M_M) \Lambda
\label{bc1}
\end{equation}
are generated by loops of scalar and fermionic messenger component
fields; $N_i$ is the multiplicity of  messengers in the
$5+\overline{5}$ and $10+\overline{10}$ vector-like multiplets, and
\begin{eqnarray}
g(x) &=&{1+x\over x^2}\log(1+x)  +   (x\rightarrow-x)
\end{eqnarray}
is the messenger--scale threshold function \cite{Martin} which
approaches unity for $\Lambda \ll M_M$. Masses of the scalar fields in the
visible sector
are generated by 2-loop effects of gauge/gaugino and messenger fields:
\begin{equation}
M^2_{\tilde j} (M_M) = 2  (N_5 + 3 N_{10}) f\left(\Lambda/M_M\right)
\sum_{i=1}^3  k_i   C_j^i \alpha^2_i(M_M) \Lambda^2
\label{bc2}
\end{equation}
with $k_i=1,1,3/5$ for $SU(3)$, $SU(2)$, and $U(1)$, respectively;
the coefficients $C_j^i$ are the quadratic Casimir invariants,
being 4/3, 3/4, and $Y^2/4$ for the fundamental representations ${\tilde j}$ 
in the groups $i = SU(3), SU(2)$ and $U(1)$, with $Y=2(Q-I_3)$ denoting 
the usual hypercharge; also
the threshold function \cite{Martin} 
\begin{eqnarray}
f(x)&=& {1+x\over x^2}\biggl[\log(1+x) -2{\rm Li}_2
\left({x\over1+x}\right)  +\ {1\over2}{\rm Li}_2
\left({2x\over1+x}\right)\biggr] \nonumber \\ &&
  +   (x\rightarrow-x)
\end{eqnarray} 
approaches unity for $\Lambda \ll M_M$.
As evident from \eq{bc2} scalar particles with identical Standard--Model 
charges squared have equal
masses at the messenger scale $M_M$.
%
In the minimal version of GMSB, the $A$ parameters
are generated at 3-loop level and they are practically zero at $M_M$.
However, the program permits to set a value for $A_0$ different from zero
but universal for all sfermions.

\subsubsection{Anomaly Mediated  Supersymmetry Breaking}

In anomaly mediated supersymmetry breaking (AMSB) the SUSY breaking
is transmitted from the hidden sector to the visible sector via
the super--Weyl anomaly \cite{Giudice:1998xp}.
The soft SUSY breaking parameters are given by:
\begin{eqnarray}
 M_a &=& \frac{1}{g_a} \beta_a m_{3/2} \\
 A_i &=& \beta_{Y_i} m_{3/2} \\
 M^2_j &=& \frac{1}{2} \dot\gamma_j m^2_{3/2}
\label{eq:m0sqamsb}
\end{eqnarray}
where $\beta_a$ and $\beta_{Y_i}$ are the beta functions of gauge and Yukawa
couplings, respectively. The $\gamma_j$ are the anomalous dimensions of
the corresponding matter superfield and $m_{3/2}$ is the gravitino mass. 
Equation~(\ref{eq:m0sqamsb}) leads to
negative mass squared for the sleptons which is phenomenologically 
not acceptable. There are several possibilities to solve this problem
\cite{AMSBmodels} and the simplest one is to add a common scalar mass $M_0$ so
that eq.~(\ref{eq:m0sqamsb}) reads as 
\begin{eqnarray}
 M^2_j &=& M^2_0 + \frac{1}{2} \dot\gamma_j m^2_{3/2}
\label{eq:m0sqamsb1}
\end{eqnarray}
This extension has been implemented in the program.

\subsubsection{String Effective Field Theories}

Four--dimensional
strings naturally give rise to a minimal set of fields for inducing
supersymmetry breaking; they play the r\^ole of the fields in the hidden
sectors: the dilaton $S$ and the moduli $T_m$ chiral
superfields which are generically present in large classes of
4--dimensional heterotic string theories. The vacuum expectation
values of $S$ and $T_m$, generated by genuinely non--perturbative
effects, determine the soft supersymmetry breaking parameters 
\cite{cvetic,Binetruy:2001md}.

In the following we assume that all moduli fields get the same vacuum
expectation values and that they couple in the same way to matter fields.
Therefore, we omit the index $m$ and take only one
moduli field $T$.
%
 The properties of the supersymmetric theories
are quite different for dilaton and moduli dominated scenarios
as discussed in \cite{cvetic,Binetruy:2001md}.
The mass
scale of the supersymmetry parameters is set by  the gravitino mass
$m_{3/2}$.

In the program we implemented the complete 1-loop formulas given in
\cite{Binetruy:2001md}. Three classes of models are implemented 
in the program: two versions of $OII$ compactification defined
by the sets A and B of boundary conditions in  \cite{Binetruy:2001md}
as well as an $OI$ compactification scheme. For the implementation of
the   $OI$ compactification scheme we have used formulas Eqs.~(3.21) --
(3.23) of \cite{Binetruy:2001md}:
\begin{eqnarray}
M_i &=&  - g_i^2 m_{3/2}  \left\{ s {\sqrt{3} \sin \theta} +
\left[ b_{i} + 
   {s \sqrt{3}\sin\theta} 
 g_{s}^{2}\left(C_i
-\sum_{j}C_{i}^{j}\right) \right. \right.
 \nonumber \\ && \hspace*{1cm} + \left. \left. 2 \, t
\cos\theta\,  G_{2}(t)
    \left( \delta_{\rm GS} + b_{i}
           - 2  \sum_{j}C_{i}^{j} (1+n_j)   \right)
 \right] / {16\pi^2}  \right\}  \\
%
M_{\tilde j}^2 &=& m^2_{3/2} \Bigg\{ \left(
  1 + n_j \cos^2 \theta \right) +  {2 \sqrt{3} s \sin\theta} 
 \left[ \sum_{i} \gamma_{j}^{i} g_{i}^{2} -
 \frac{1}{2s}
   \sum_{km} \gamma_{j}^{km} \right] \nonumber \\
    & & \hspace*{1cm} +
     \gamma_{j} + 2 t \cos \theta \, G_2(t)
  \sum_{km} \gamma^{km}_j (n_j + n_k + n_m+3) \Bigg\} \\
%
A_{jkm}&=& m_{3/2} \bigg[ \frac{ \sin \theta }{\sqrt{3}}- 2 t
 \cos\theta  (n_j + n_k + n_m + 3) G_2(t) 
   + \gamma_j + \gamma_k + \gamma_m
 \bigg] \label{eq:a1}
\end{eqnarray}
$s = \langle S \rangle$ is the vacuum expectation values of the dilaton 
field.
$t = \langle T \rangle / m_{3/2}$ is the vacuum
expectation value of the moduli field(s), and 
$G_2(t) = 2\zeta(t) + 1/2t$ is the 
non-holomorphic Eisenstein function with
$\zeta$ denoting the Riemann zeta function.
$\delta_{GS}$ is the parameter 
of the Green-Schwarz counterterm.
$\gamma_j$ are the anomalous 
dimensions of the matter
fields, the $\gamma^i_j$ and $\gamma^{km}_j$ are their gauge and Yukawa parts,
respectively.
%; $b^0_i = b_i / 16 \pi^2$
$C_i$, $C^j_i$ are the quadratic Casimir operators for the gauge group 
$G_i$, respectively, in the adjoint representation and in the matter 
representation. The indices $i,j,k$ denote $H_1$, $H_2$, $\tilde E$, 
$\tilde L$, $\tilde D$, $\tilde U$ and $\tilde Q$. The A-parameters are
finally given by:
\begin{eqnarray}
 A_{e,n}(GUT) &=& Y_{e,nn}(GUT) A_{\tilde E_n \tilde L_n H_1} \\ 
 A_{d,n}(GUT) &=& Y_{d,nn}(GUT) A_{\tilde D_n \tilde Q_n H_1} \\ 
 A_{u,n}(GUT) &=& Y_{u,nn}(GUT) A_{\tilde U_n \tilde Q_n H_2}
\end{eqnarray}
where $n$ denotes the generation.

 In case of the $OII$ compactification
scheme the gaugino masses are given by  Eqs.~(3.11) of \cite{Binetruy:2001md}:
\begin{eqnarray}
M_i&=&- g_i^2 m_{3/2} \Bigg\{ \frac{\sqrt{3} \sin\theta}
                                 {2 k_{s\overline{s}}^{1/2}} +
 \frac{1}{16 \pi^2} \bigg[  2 t \cos\theta G_{2}
                           \left( \delta_{\rm GS} + b_i \right) + b_i
 \nonumber \\
 && \hspace*{4.7cm} + 
\frac{g_s^2 \sin\theta}{k_{s\overline{s}}^{1/2}} ( C_i
-\sum_{j}C_{i}^{j} ) \bigg] \Bigg\}\, .
\label{MaO2}
\end{eqnarray}
%
For the sfermion parameters we have implemented two sets of boundary
conditions: set $(A)$ is specified by formulas Eqs.~(3.15) and (3.19)
of \cite{Binetruy:2001md}:
\begin{eqnarray}
M_i^{2} &=&m^{2}_{3/2} \Bigg\{ \sin^{2}\theta + \gamma_{i} +
\frac{\sqrt{3}\sin\theta }{k_{s\overline{s}}^{1/2}}
    \bigg[ \sum_{a} \gamma_{i}^{a} g_{a}^{2} -
   \frac{1}{2} 
   \sum_{jk} \gamma_{i}^{jk} (k_{s} + k_{\overline{s}}) \bigg] \Bigg\},
\label{massO2A} \\
%
A_{ijk} &=& m_{3/2} \Bigg\{ \gamma_{i} + \gamma_{j} + \gamma_{k}
   + \frac{\sin\theta}{\sqrt{3} k_{s\overline{s}}^{1/2}} \Bigg\}
\label{eq:a2}
\end{eqnarray}
%
Set $(B)$ is specified by  formulas Eqs.~(3.16) and (3.20)
 of \cite{Binetruy:2001md}:
\begin{eqnarray}
M_i^2&=&m^2_{3/2} \Bigg\{
\frac{\sqrt{3}\sin\theta}{k_{s\overline{s}}^{1/2}}
   \bigg[ 1 + 2 t \cos\theta G_{2} \bigg] \bigg[ \sum_{a} g_{a}^{2}
\gamma_{i}^{a} - \frac{1}{2} \sum_{jk} \gamma_{i}^{jk} \left(k_{s} +
k_{\overline{s}}\right) \bigg]  \nonumber \\
 & & \hspace{1cm}
   + \sin^{2} \bigg[ 1 + \gamma_{i} + \ln\big[2 t 
     |\eta(t)|^4\big] \big( \sum_{a} \gamma_{i}^{a} -2 \sum_{jk}
   \gamma_{i}^{jk} \big) - \sum_{a} \gamma_{i}^{a} \ln(g_{a}^{2}) \bigg]
   \nonumber \\
 & &  \hspace{1cm} -\frac{9 \sin^{2}\theta}{k_{s\overline{s}}}
    \bigg[ \sum_{a}
   \gamma_{i}^{a} \left(\frac{g_{a}^{4}}{4}\right) \left(\ln(g_{a}^{2})
   +\frac{5}{3}\right)  \nonumber \\
 & &   \hspace{2.5cm}
+ \ln\big[(t +
   \overline{t})|\eta(t)|^4\big] \big( \sum_{a} \gamma_{i}^{a}
   \big(\frac{g_{a}^{4}}{4}\big) +\frac{1}{3} \sum_{jk} \gamma_{i}^{jk}
   k_{s} k_{\overline{s}} \big) \bigg] \Bigg\} \, , \\
%
A_{ijk} &=&  m_{3/2} \Bigg\{
  (\gamma_{i} + \gamma_{j} + \gamma_{k} )\bigg[ 1 + 2 t \cos\theta 
  G_{2} \bigg] \nonumber \\
 && \hspace*{1cm} +\frac{\sqrt{3} \sin\theta}{k_{s\overline{s}}^{1/2}}
\bigg[ k_{s} + \sum_{a} \frac{g_a^2}{2}
 ( \gamma_{i}^{a} +  \gamma_{j}^{a} +  \gamma_{k}^{a} )
(1 - \ln(g_a^2))  \nonumber \\
 & &  \hspace{2.8cm} -\ln\bigg[(t + \overline{t})
     |\eta(t)|^4\bigg]
  \big( \sum_{a} g_{a}^{2}( \gamma_{i}^{a} + \gamma_{j}^{a} + \gamma_{k}^{a} )
 \nonumber \\ && \hspace{5.8cm} -
  \sum_{lm} k_{s} (\gamma_{i}^{lm} + \gamma_{j}^{lm} + \gamma_{k}^{lm})
   \big) \bigg] \Bigg\} \, .
\label{eq:a3}
\end{eqnarray}
%
 In all three cases we have assumed that terms
proportional to the $\log(\tilde \mu_i)$ can be neglected
($\tilde \mu_i$ denote the Pauli Villar masses).

\subsubsection{General High Scale Model}

It is clear from the examples above that up to now there is no
unique mechanism for supersymmetry breaking. Therefore, we have implemented
the possibility to specify rather freely a high scale model. This model
is specified by: a set of three in principal non--universal gaugino mass 
parameters $M_{1/2}[U(1)]$,  $M_{1/2}[SU(2)]$,  $M_{1/2}[SU(3)]$;
a scalar mass for each type of sfermion, resulting in
fifteen parameters: $M^0_{\tilde E,ii}$, $ M^0_{\tilde L,ii}$, 
$ M^0_{\tilde D,ii}$,
$ M^0_{\tilde U,ii}$, $ M^0_{\tilde Q,ii}$; two Higgs mass parameters
$M^0_{H_1}$ and $M^0_{H_2}$; nine different $A$ parameters $A_{0,e,ii}$,
 $A_{0,d,ii}$ and  $A_{0,u,ii}$. Here $ii$ denotes that only the
diagonal entries can be set, because in the current version the
effects of generation mixing is not taken into account.
 A model of this kind has been used in \cite{Bartl:2001wc} 
for the study of low energy observables and the supersymmetric
spectrum. It also can be used, for example, to set the boundary conditions
for the gaugino mediated supersymmetry breaking \cite{Kaplan:1999ac}.
This general model will be denoted by SUGRA.

\section{Decays of supersymmetric particles and Higgs bosons}
\label{sect:decays}

The programs calculates the most important two- and three-body decays
of supersymmetric particles at tree level. 
 In case of three-body decays the formulas are
implemented such, that the effects of decay widths in the propagators
are taken into account \cite{ToBePublished}. 
Therefore, it is possible to perform the
calculation even in case that some of the intermediate particles are
on-shell. This is useful in the case that the two--body decays
have small phase space, because then the calculation of the three-body
decays gives a more accurate result, 
e.g.~$\Gamma(\tilde \chi^+_1 \to \tilde \chi^0_1 W^+) \times 
      \mathrm{BR}(W^+ \to \nu l^+)$ can be quite different from
$\Gamma(\tilde \chi^+_1 \to\tilde \chi^0_1 \nu l^+)$ if the 
decay $\tilde \chi^+_1 \to \tilde \chi^0_1 W^+$ has only small
phase space.


The following sfermion decays are calculated:
\begin{eqnarray}
 \label{eq:sfermiondecays}
 {\tilde f}_i &\to& f  \, {\tilde \chi}^0_k , \, \,
                    f'  \, {\tilde \chi}^\pm_l \\
 {\tilde f}_i  &\to& {\tilde f}_j  \, Z^0 , \, \,  {\tilde f}'_j  \, W^\pm \\
 { \tilde f}_i  &\to& {\tilde f}_j  \, (h^0, H^0, A^0), \, \,
                       {\tilde f}'_j  \, W^\pm
\end{eqnarray}
In case of the lighter stop, it is possible that all two-body decays
modes are kinematically 
forbidden at tree--level. In this case the following decay
modes are important \cite{Hikasa:1987db,Porod:1996at,djouadi3}:
\begin{eqnarray}
{\tilde t}_1 &\to& c \, {\tilde \chi}^0_{1,2} \\
{\tilde t}_1 &\to& W^+ \, b \, {\tilde \chi}^0_1 , \, \, 
                   H^+ \, b \, {\tilde \chi}^0_1 \\
{\tilde t}_1 &\to& b \, \nu \, {\tilde l}^+_i , \, \,
                   b \, l^+ \, {\tilde \nu}
\end{eqnarray}
where $l=e, \mu , \tau$. The corresponding widths are calculated within
SPheno using the formulas given in \cite{Porod:1996at}. In case of
GMSB models scenarios exist where the charged sleptons are next to
lightest supersymmetric particles (NLSP) and the gravitino $\tilde G$ is
the LSP. In this case the sleptons decay according to:
\begin{eqnarray}
 \label{eq:sleptondecays}
 {\tilde l}_i &\to& l  \, {\tilde G}
\end{eqnarray}
Here we use the formulas given in \cite{Giudice:1998bp}.

It is well known that the partial widths of sfermions can receive
considerable radiative corrections \cite{Kraml:1996kz}. However, the branching
ratios are not that strongly affected \cite{Bartl:2000kw}.
 Therefore, for the moment
being tree-level formulas are implemented. Some important numerical
effects of higher order
corrections are nevertheless implemented by using 1-loop corrected masses
and running couplings in the formulas.  The complete implementation of
higher-order corrections is left for future versions of the program.


In case of charginos and neutralinos the following decay modes are
calculated:
\begin{eqnarray}
 {\tilde \chi}^0_i &\to& Z^0  \, {\tilde \chi}^0_j , \, \,
                         W^\pm     \, {\tilde \chi}^\mp_k \\
 {\tilde \chi}^0_i &\to& (h^0, H^0, A^0)  \, {\tilde \chi}^0_j , \, \,
                         H^\pm     \, {\tilde \chi}^\mp_k \\
 {\tilde \chi}^0_i &\to& f \bar{\tilde{f}_j}, \, \,  \bar{f} \tilde{f}_j \\
 {\tilde \chi}^+_k&\to&  Z^0  \, {\tilde \chi}^+_s , \, \,
                         W^+     \, {\tilde \chi}^0_j \\
 {\tilde \chi}^+_k&\to&  (h^0, H^0, A^0)   \, {\tilde \chi}^+_s , \, \,
                         H^+     \, {\tilde \chi}^0_j \\
  {\tilde \chi}^+_k&\to&  f {\tilde f}_i'
\end{eqnarray}
In case that all two body decay modes are kinematically forbidden the following
three--body decays are calculated:
\begin{eqnarray}
 {\tilde \chi}^0_i &\to& f \, \bar{f}  \, {\tilde \chi}^0_j , \, \,
                         f \, f'     \, {\tilde \chi}^\mp_k \\
 {\tilde \chi}^0_i &\to& q \, \bar{q}  \, {\tilde g}  \\
 {\tilde \chi}^+_k &\to& f \, \bar{f}  \, {\tilde \chi}^+_s , \, \,
                         f \, f'     \, {\tilde \chi}^0_j \\
 {\tilde \chi}^+_k &\to& q \, q'     \, {\tilde g}
\end{eqnarray}
In the calculation we have included all contributions from gauge bosons,
sfermions and Higgs  bosons \cite{ToBePublished,Baer:1998bj}. 
The Higgs contributions can be important in certain
regions of parameter space \cite{Bartl:1999iw}. Similarly to case
of the sleptons there exist parameter regions in GMSB models where
the lightest neutralino is the NLSP and it decays according to
\begin{eqnarray}
 {\tilde \chi}^0_1 &\to& \gamma \, \ {\tilde G} \\
 {\tilde \chi}^0_1 &\to& Z^0 \, \ {\tilde G} \\
 {\tilde \chi}^0_1 &\to& h^0 \, \ {\tilde G} 
\end{eqnarray}
Here we use the formulas given in \cite{Giudice:1998bp}.


In case of gluinos the following two--body decays are
calculated:
\begin{eqnarray}
 \tilde g \to q \, {\tilde q}_i
\end{eqnarray}
with $q=u, d, c, s, t, b$.
Again, in case that these decays are kinematically suppressed, the
three-body decay modes are calculated:
\begin{eqnarray}
\tilde g &\to& \tilde \chi^0_i \, q \, \bar{q} \\
\tilde g &\to& \tilde \chi^\pm_j \, q' \, \bar{q} \\
\tilde g &\to& \bar{b} \, W^- \, \tilde t_1,  b \, W^+ \, \tilde t_1^*
\end{eqnarray}
Here we have implemented the formulas given in
\cite{glu1}.

In case of Higgs bosons the following decays are calculated:
\begin{eqnarray}
 \phi &\to& f \, \bar{f} \\
 \phi &\to&  \tilde f_i \, \bar{\tilde f}_j \\
 \phi &\to& {\tilde \chi}^0_k \, {\tilde \chi}^0_l \\
 \phi &\to& {\tilde \chi}^+_r \, {\tilde \chi}^-_s \\
 H^0 &\to& Z^0 \, Z^0 , \, \,  W^+ \, W^-\\
 H^0 &\to& h^0 \, h^0 \\
 A^0 &\to& h^0 \, Z^0 \\
 H^+ &\to& f \, \bar{f}' \\
 H^+  &\to&  \tilde f_i \, \bar{\tilde f}_j' \\
 H^+ &\to& {\tilde \chi}^0_k \, {\tilde \chi}^-_s \\
 H^+ &\to& h^0  \, W^+
\end{eqnarray}
with $\phi=h^0, H^0, A^0$ and $f=\nu_i, e, \mu, \tau, u, d, c, s, t, b$.
It is well known, that the widths as well as the branching ratios of the 
Higgs bosons can receive large one--loop corrections 
\cite{Drees:1990dq,Eberl:2001vb,Djouadi:mr}.
In the present version only the gluonic QCD corrections for the decays into
quarks \cite{Drees:1990dq} have been implemented.
Therefore, the numbers provided by SPheno have to be taken with care
and for refined analysis other programs, such as {\sf HDECAY}
\cite{Djouadi:1997yw} should be used.

\section{Production of supersymmetric particles and Higgs bosons}
\label{sect:prod}

The program calculates the following cross sections:
\begin{eqnarray}
 e^+ \, e^- \, &\to& \tilde f_i \, \tilde f_j \hspace{1cm} (f=l, \nu, q) \\
 e^+ \, e^- \, &\to& \tilde \chi^0_k \, \tilde \chi^0_n \\
 e^+ \, e^- \, &\to& \tilde \chi^+_r \, \tilde \chi^-_s \\
  e^+ \, e^- \, &\to& h^0 \, Z , \, \, H^0 Z \\
  e^+ \, e^- \, &\to& h^0 \, A^0 , \, \, H^0 A^0 \\
  e^+ \, e^- \, &\to&  H^+ H^-
\end{eqnarray}
We haven taken the formulas of \cite{Bartl:1997yi} for sfermion
production, \cite{Moortgat-Pick:2000uz,ToBePublished} for production of
charginos and
neutralinos and \cite{Djouadi:mr} for Higgs boson production.
Initial state radiation has been included using the formula given in 
\cite{drees1}. In case
of squarks in addition QCD corrections due to gluon exchange are included
\cite{drees1,Eberl:1996wa}. Care has to be taken in case one calculates
the cross sections near threshold because then higher order corrections
are important to get reliable results \cite{Freitas:2001zh} and, thus, the
numbers obtained in the program have to be taken with care near the
threshold.
%
  All cross
sections are implemented such, that one can specify the degree of
longitudinal polarization $P_{e^-}$ of the incoming electron beam 
as well as the degree of longitudinal polarization  $P_{e^+}$ of the 
incoming positron beam.
Here $P_{e^-}$ is within the range $[-1,1]$, where $\{-1,0,1\}$
denote 100\% left-handed electrons, completely unpolarized electrons
and 100\% right-handed electrons, respectively. 
The same notation is used in case of
positrons. For example, $P_{e^-}=-0.8$ ($P_{e^+}=-0.8$) means that
80\% of the electrons (positrons) are left-polarized whereas the
remaining 20\% are unpolarized.

\section{Low Energy Constraints}
\label{sec:constraints}

The supersymmetric parameters are constrained by direct searches at
colliders and by loop-effects which supersymmetric particles induce
observables of  low energy
experiments. Provided one neglects mixing between different sfermion
generations the following quantities constrain several parameters of
the MSSM: the rare decay $b \to s \, \gamma$, the anomalous magnetic
moment of the muon $a_\mu$ and the supersymmetric contributions to the $\rho$
parameter. These constraints are implemented in the program using the
formulas given in \cite{Bertolini:1990if,Cho:1996we} for $b \to s \, \gamma$
supplemented by the QCD corrections as given in \cite{kagan},
\cite{Ibrahim:1999hh} for $a_\mu$ and \cite{Drees90} for the sfermion
contributions to the $\rho$ parameter. In call cases we use the
running couplings at $m_Z$ for the calculation of the observables.
The use of running couplings together with the correct implementation
of supersymmetric threshold corrections for the couplings
results in taking into account
the most important higher oder corrections as has been pointed out e.g.~in
\cite{Carena:2000uj,Buras:2002vd} for the case of $b \to s \, \gamma$.  The
implementation of the supersymmetric threshold corrections to the
couplings will be
discussed in the next section.

\section{Details of the Calculation}
\label{sec:calc}

\begin{figure}
\begin{center}
\begin{picture}(350,450)
\put(40,410){\makebox(280,10)[c]{\fbox{Calculate
                                    $g_i(M_Z)$, $h_{t,b,\tau}(M_Z)$ 
                                     at tree level.}}}
\put(170,400){\vector(0,-1){12}}
\put(40,365){\makebox(280,10)[c]{\fbox{Run to $M_X$ at 1-loop.
                      Apply soft SUSY breaking boundary condition}}}
\put(170,355){\vector(0,-1){12}}
\put(40,320){\makebox(280,10)[c]{\fbox{Run to $M_{EWSB}$. Calculate $|\mu|$ and
                      sparticle pole masses at tree level}}}
\put(170,310){\vector(0,-1){12}}
\put(40,275){\makebox(280,10)[c]{\fbox{SM and SUSY radiative corrections to
                                    $g_i(M_Z)$, $h_{t,b,\tau}(M_Z)$}}}
\put(170,265){\vector(0,-1){12}}
\put(40,230){\makebox(280,10)[c]{\fbox{Run to $M_X$. Apply soft SUSY breaking
                                      boundary condition}}}
\put(170,220){\vector(0,-1){12}}
\put(40,185){\makebox(280,10)[c]{\fbox{Run to $M_{EWSB}$. Calculate $|\mu|$ and
                      sparticle pole masses at loop level}}}
\put(170,175){\vector(0,-1){12}}
\put(40,140){\makebox(280,10)[c]{\fbox{Check if required precision is achieved
            }}}
\put(20,115){\makebox(280,10)[c]{yes}}
\put(170,131){\vector(0,-1){21}}
\put(180,145){\makebox(280,10)[c]{no}}
\put(293,145){\line(1,0){87}}
\put(380,145){\line(0,1){135}}
\put(380,280){\vector(-1,0){40}}
\put(40,90){\makebox(280,10)[c]{\fbox{Calculate decay widths
            and branching ratios}}}
\put(170,81){\vector(0,-1){12}}
\put(40,50){\makebox(280,10)[c]{\fbox{Calculate cross sections}}}
\put(170,42){\vector(0,-1){12}}
\put(40,10){\makebox(280,10)[c]{\fbox{Calculate low energy observables}}}
\end{picture}
\end{center}
\caption{Algorithm used to calculate the SUSY spectrum, decay widths,
production cross sections and low energy observables. Each step
(represented by a box) is explained in the text. The initial step is the
uppermost one. $M_{EWSB}$ is the scale at which the EWSB
conditions
are imposed, and $M_X$ is the scale at which the high
energy SUSY breaking boundary conditions are imposed.}
\label{fig:algorithm}
\end{figure}

In this section we describe the algorithm used. It is
schematically displayed in \fig{fig:algorithm}. The following
standard model parameters are used as input: fermion and gauge boson pole
masses, the fine structure constant $\alpha$, the Fermi constant $G_F$
and the strong coupling constant $\alpha_s(m_Z)$. It is assumed that
$\alpha(m_Z)$ and   $\alpha_s(m_Z)$ are given in the $\msbar$ scheme.

\subsection{First rough calculation of SUSY and Higgs boson masses}

In a first step, we calculate gauge and Yukawa couplings at $m_Z$
scale using tree-level formulas. These are used as input for the one--loop
RGEs to get the gauge and Yukawa couplings at the high scale where
also the boundary conditions for the high scale model under study are imposed. 
Afterwards
one--loop RGEs are used to get a first set of parameters at the electroweak
scale. These parameters are used to get a first set of supersymmetric particle
masses and Higgs masses using tree-level formulas except for the neutral
CP-even Higgs bosons where one-loop effects due to (s)quarks of the third
generation are taken into account. 
These masses are the starting point for
the iterative loop which calculates the spectrum within the required 
precision as described below.

\subsection{Main loop for the calculation of SUSY and Higgs boson masses}

In the next step the gauge couplings and $\sin^2 \theta_W$ 
are calculated at $m^2_Z$ in the $\drbar$ scheme using the formulas given
Appendix C of \cite{Pierce:1996zz}. For the calculation of the 
Yukawa couplings we use the complete formulas for the fermion masses
and the vacuum expectation values given in Appendix D of
\cite{Pierce:1996zz}. In case of third generation Yukawa couplings
we use the following improvements. In case of the  bottom quark we use 
3-loop relationship between the pole mass and the
$\overline{MS}$ mass $m_{b,\msbar}(m_b)$ 
as given in \cite{Melnikov:2000qh}. The three--loop RGEs \cite{Arason:1991ic}
are solved numerically to obtain  $m_{b,\msbar}(m_Z)$.  Afterwards
the shift from the $\msbar$ scheme to the $\drbar$ scheme arising from
massless gauge bosons is calculated using the
formula \cite{Avdeev:1997sz,Baer:2002ek}:
\begin{eqnarray}
m_{b',\drbar}(m_Z) = \left(1 - \frac{\alpha_s}{3 \pi}
        - \frac{35 \alpha_s^2}{72 \pi^2} \right)m_{b,\msbar}(m_Z)
\end{eqnarray}
where $\alpha_s$ is given in the $\drbar$ scheme which is the reason for
the different factor in front of  $\alpha_s^2$ compared to \cite{Baer:2002ek}.
We use the complete formulas given in  Appendix D of \cite{Pierce:1996zz}
to calculate the SUSY contribution denoted by $\Delta m_{b,SUSY}(m_Z)$.
For the calculation we use running gauge and Yukawa couplings at $m_Z$.
The SUSY contributions $\Delta m_{b,SUSY}(m_Z)$
are then resummed using \cite{Carena:1999py}
\begin{eqnarray}
m_{b,\drbar}(m_Z) = \frac{m_{b',\drbar}(m_Z)}
                         {1 - \frac{\Delta m_{b,SUSY}(m_Z)}{m_{b,\drbar}(m_Z)}}
\end{eqnarray}
The analogue resumation is done in case of the tau Yukawa coupling.
In case of the top quark we take the complete formulas given in 
Appendix D of  \cite{Pierce:1996zz}. We also add the 2-loop contribution
due to gluons in the $\drbar$ scheme \cite{Avdeev:1997sz} which reads as:
\begin{eqnarray}
\Delta m_t^{2-loop}(Q) = - m_t \alpha_s^2 
   \left(0.538 - \frac{43}{24 \pi^2} L + \frac{3}{8 \pi^2} L^2 \right)
\end{eqnarray}
where $m_t$ is the on--shell top mass and $L=\ln (m^2_t / Q^2)$. 
The obtained gauge and Yukawa couplings are evolved to the high scale
using two--loop RGEs \cite{Martin:1993zk}. The high scale can either
be fixed or can be calculated from the requirement  $g_1 = g_2$ at the 
high scale. The various
cases are discussed in Sect.~\ref{sec:example} and
Appendix~\ref{app:switch}. At the high scale the boundary
conditions for the soft SUSY breaking parameters are set. The implemented
models are summarized in Sect.~\ref{sect:models}; see also 
Appendix~\ref{app:model}.
The complete
set of two--loop RGEs \cite{Martin:1993zk} is used to evolve the
parameters down to the electroweak scale 
$M_{EWSB} = \sqrt{m_{\tilde t_1} m_{\tilde t_2}}$ (there exists also the
possibility to set $M_{EWSB}$ by hand as explained in 
Appendix~\ref{app:switch}). 

The parameters are used as input to calculate the sparticle pole
masses at one--loop order and in case of the neutral Higgs at
two--loop order.  Here we use the complete formulae given in the
appendices of \cite{Pierce:1996zz} for the one--loop contributions and
for the 2-loop corrections $O(\alpha_s \alpha_t + \alpha_t^2 +
\alpha_s \alpha_b)$ for the neutral Higgs boson the formulas given in
\cite{Degrassi:2001yf,Dedes:2002dy}.
  For the $O(\alpha_s \alpha_b)$ contributions
we use the complete expressions which can be obtained from the
$O(\alpha_s \alpha_t)$ contributions by appropriate replacements.  In
case of sfermions we have included in all cases left--right mixing.
All gauge and Yukawa couplings are understood as $\drbar$ quantities
at $M_{EWSB}$. Also $\tan\beta$ and the vacuum expectation values are
evaluated at $M_{EWSB}$ to get a consistent set of input parameters.
Note, that we express in all couplings the fermion masses and gauge
boson masses by their corresponding expressions due to
gauge couplings, Yukawa couplings and vacuum expectations values in
the formulas of \cite{Pierce:1996zz}. In all cases running masses are
used as input for the loop integrals.  In addition we
have implemented the $O(\alpha_s \alpha_t + \alpha_t^2 +\alpha_s
\alpha_b)$ corrections for the calculation of $|\mu|$
\cite{Dedes:2002dy}. The numerical evolution
of the one--loop integrals is based on the FF package 
\cite{vanOldenborgh:1989wn} and the
LoopTools package \cite{Hahn:1998yk}.

The masses obtained are used as input for the next iteration which starts
again by calculating the SUSY contributions to gauge and Yukawa couplings
at $m_Z$. In the case that during this iterative
process an unphysical situation occurs, e.g.~a pole mass squared being
negative, the program terminates and it provides information on the exact
reason for termination.  
 The iteration is continued until all relative differences between
the sparticle masses are smaller then the user imposed quantity $\delta$:
\begin{eqnarray}
 \delta > \frac{|m_i - m_{i-1}|}{m_i} 
\end{eqnarray}
for all sparticle masses; i denotes the i-th iteration.
% 
In most cases this achieved after three
to four iterations. 
In the case that more than the maximal allowed number of iterations
(user specified) are
necessary, the program leaves the iteration giving a warning message.

\subsection{Calculation of the other observables}

The masses and mixing angles are then used to calculate the branching
ratios and decay widths. Here two- and three body decays of supersymmetric
particles are calculate. Note that we use the couplings as input which 
are renormalized at the scale $M_{EWSB}$.
%
The user has the possibility to force the
program to calculate three body decays even if one or more of the
intermediate particles are on-shell. This possibility is useful in the
case where the 2-body decay  has only small phase because then the
calculation of the three body decay width(s) give a more reliable
result.

Afterwards the  production cross sections at an $e^+ e^-$ collider of
all supersymmetric particles as well as all Higgs bosons are
calculated. Here the user has the possibility to specify the centre 
of mass energy as well as the degree of longitudinal polarization of
the incoming beams. Moreover, the user can specify if initial state
radiation shall be included in the calculation or not.

Finally,
the low--energy constraints described in Section~\ref{sec:constraints}
are calculated: $BR(b \to s \gamma)$, 
SUSY contributions to $a_\mu$
and the sfermion contributions to $\Delta \rho$. For the the calculation 
of these quantities we evolve the gauge and Yukawa couplings from the scale 
$M_{EWSB}$ down to $m_Z$. The couplings at $m_Z$ are then used as input
for the calculation of the low energy observables.
For example in calculation of
$BR(b \to s \gamma)$ the most important contributions to 
the $C_7$ coefficients are
implemented as
\begin{eqnarray}
 C_7(W^+) &=& -\frac{K_{ts} K_{tb}x_{tW}}{4 \, m^2_W}  
\left(\frac{2}{3} F_1(x_{tW})+ F_2(x_{tW}) \right) \\
%
 C_7(H^+) &=& - \frac{K_{ts} K_{tb}}{4 \,m^2_{H^+} }
   \left[ \frac{Y_t^2 \cos^2\beta}{4}
   \left(\frac{2}{3} F_1(x_{tH^+})+ F_2(x_{tH^+}) \right)
  \right. \nonumber \\ &&\hspace{1.6cm} \left. 
    -  \frac{Y_b Y_t \cos \beta \sin \beta m_t}{m_b}
   \left(\frac{2}{3} F_3(x_{tH^+})+ F_4(x_{tH^+}) \right)
  \right]  \\
 C_7({\tilde \chi}^+) &=& \sum_{i,j=1}^2 \frac{K_{ts} K_{tb}}
                                              {4 \, m^2_{\tilde t_i}}
   \left[ C^2_{R,ij}
   \left(\frac{2}{3} F_2(x_{{\tilde \chi}^+_j \tilde t_i})
   + F_1(x_{{\tilde \chi}^+_j \tilde t_i}) \right)
  \right. \nonumber \\ &&\hspace{1.6cm} \left. 
    - C_{L,ij} C_{R,ij}
   \left(\frac{2}{3} F_4(x_{{\tilde \chi}^+_j \tilde t_i})
        + F_3(x_{{\tilde \chi}^+_j \tilde t_i}) \right)
  \right]  \\
C_{L,ij} &=& Y_b R_{\tilde t,i1} U_{j2} \\
C_{R,ij} &=& -g  R_{\tilde t,i1} V_{j1} +  Y_t R_{\tilde t,i2} V_{j2}
%  
\end{eqnarray}
Here $Y_i$ are the Yukawa couplings, $U$ and $V$ are the
chargino matrices, $K$ is the CKM matrix,
$R_{\tilde t}$ is the stop mixing matrix 
and $x_{ab} = m^2_a/m^2_b$.
The loop functions $F_i$ are given in \cite{Bertolini:1990if}.
A similar replacement
is done in the contributions to the $C_8$ coefficient.
Moreover, in the program also the contributions from the first two generation
of (s)fermions to $C_{7,8}$ are included for completeness.
We then use \cite{kagan} to obtain
\begin{eqnarray}
BR(b \to s \gamma) = 1.258 + 0.382  r7^2 + 0.015  r_8^2 
       + 1.395 r_7 + 0.161 r_8
        + 0.083 r_7 r_8
\end{eqnarray}
where $r_7 = C_7/C_7(W^+)$ and  $r_8 = C_8/C_8(W^+)$. 
%
In this way  important higher order corrections are
taken into account, in particular the large $\tan\beta$ effects in
case of $b \to s \gamma$ \cite{Buras:2002vd}.



\section{A sample example}
\label{sec:example}

In this section we discuss the executable statements of the main program
given in the file \verb+SPheno.f90+. 
%
In the first statements the required modules are loaded and the various
variables are defined.
Afterwards a series of initialization routines are called:
\begin{verbatim}
 Call InitializeControl(11,"SPheno.out","SPheno")
 Call InitializeLoopFunctions
 Call InitializeStandardModel
\end{verbatim}
The routine \verb+InitialzeControl+ opens the file \verb+Messages.out+ 
at channel 10 where
all warnings and/or debugging informations are stored. In addition 
it reads the file \verb+Control.in+ if present. For the description of
\verb+Control.in+ see Appendix~\ref{app:Control}. Moreover, it opens
the output file \verb+SPheno.out+ at channel 11. The last entry 
\verb+"SPheno"+ is the name of the calling program and is used for 
the initialization of the debugging system.
%
The routine 
\verb+InitializeLoopFunctions+ initializes the routines for the calculation of
the loop functions which are needed to calculated the loop corrected masses.
The routine \verb+InitializeStandardModel+ reads data from the file 
\verb+StandardModel.in+. In case that this file is not present, default
values are used as described in Appendix~\ref{app:SM}.

Afterwards the routine \verb+HighScaleInput+ is called:
\begin{verbatim}
 Call HighScaleInput 
\end{verbatim}
 The source code for this
routine is given in the file \verb+SPheno.f90+. This routine reads in the
data from the file \verb+HighScale.in+ which specifies the model used as
well as the high scale boundary conditions. A short description of the
implemented models is given in \sect{sect:models} and details of the 
file \verb+HighScale.in+ are given in 
Appendix~\ref{app:model}. Afterwards a first rough estimate of the
parameters and couplings is given by calling the routine \verb+FirstGuess+:
\begin{verbatim}
 Call FirstGuess(phase_mu, tanb, Mi, M2_E, M2_L, A_l, M2_D   &
          & , M2_Q, M2_U, A_d, A_u, mu, B, M2_H, gp, g, Y_l  &
          & , Y_d, Y_u, vevSM, mP02, mP0)
\end{verbatim}
%
\begin{table}
\caption{Variables for parameters and couplings.
  The parameters are explained in Section~\ref{sect:MSSM}. dp means double
  precision.}
\label{tab:parameters}
\begin{tabular}{ll}
parameter/coupling & type \& Fortran name  \\
$e^{\varphi_\mu}$ & \verb+complex(dp) :: phase_mu+ \\
$\tan \beta$  & \verb+real(dp) :: tanb+     \\
$M_1, M_2, M_3$ & \verb+complex(dp) :: Mi(3)+ \\
$M^2_E$, $M^2_L$ & \verb+complex(dp), dimension(3,3) :: M2_E, M2_L+ \\
$M^2_D$, $M^2_Q$, $M^2_U$      
  & \verb+complex(dp), dimension(3,3) :: M2_D, M2_Q, M2_U+ \\
$A_l, A_d, A_u$& \verb+complex(dp), dimension(3,3) :: A_l, A_d, A_u+ \\
$\mu$    &\verb+complex(dp) :: mu+ \\
$B \mu$    &\verb+complex(dp) :: B+ \\
$M^2_H$       & \verb+real(dp) :: M2_H(2)+ \\
$g'$, $g$   & \verb+real(dp) :: gp, g+ \\
$Y_l, Y_d, Y_u$& \verb+complex(dp), dimension(3,3) :: Y_l, Y_d, Y_u+ \\
$v_1, v_2$ & \verb+real(dp) :: vevSM(2)+ \\
$g'$, $g$, $g_s$   & \verb+real(dp) :: gauge(3)+ \\
\end{tabular}
\end{table}
%
The meaning of the various variables and their type is given in 
Table~\ref{tab:parameters} except for \verb+mP02, mP0+ which are
given in Table~\ref{tab:masses}.
The parameters obtained are used to get the initial values for the
spectrum at tree-level:
\begin{verbatim}
 Call TreeMasses(gp, g, vevSM, Mi(1), Mi(2), Mi(3), mu, B     &
      &, tanb, M2_E, M2_L, A_l, Y_l, M2_D, M2_U, M2_Q, A_d    &
      &, A_u, Y_d, Y_u, mGlu, PhaseGlu, mC, mC2, U, V, mN     &
      &, mN2, N, mSneut, mSneut2, Rsneut, mSlepton, mSlepton2 &
      &, RSlepton, mSdown, mSdown2, RSdown, mSup, mSup2, RSup &
      &, mP0, mP02, RP0, mS0, mS02, RS0, mSpm, mSpm2, RSpm, kont)
\end{verbatim}
%
\begin{table}
\caption{Variables for masses and mixing matrices as given by the routine
         {\tt Sugra}. Their connection to the parameters at tree--level 
         is explained explained in Section~\ref{sect:MSSM}. dp means
         double precision.}
\label{tab:masses}
\begin{tabular}{ll}
masses / mixing matrix & type \& Fortran name  \\
$m_{\tilde g}$ & real(dp) :: mglu \\
$e^{\varphi_{\tilde g}}$ & complex(dp) :: PhaseGlu \\
$m_{\tilde \chi^+_i}$ &  real(dp) :: mC(2)  \\
$U$, $V$ &  complex(dp) :: U(2,2), V(2,2)    \\
$m_{\tilde \chi^0_j}$ &  real(dp) :: N(4) \\
$N$ &  complex(dp) :: N(4,4)    \\
$m_{h^0}, m_{H^0}$ & real(dp) :: mS0(2) \\
$R_\alpha$ &  real(dp) :: RS0(2,2)    \\
$m_{G^0}, m_{A^0}$ &  real(dp) :: mP0(2) \\
$R_\beta$ &  real(dp) :: RP0(2,2)    \\
$m_{G^+}, m_{H^+}$ &  real(dp) :: mSpm(2) \\
$R'_\beta$ &  complex(dp) :: RSpm(2,2)    \\
$m_{\tilde \nu}$ & real(dp) :: mSneut(3) \\
$R_{\tilde \nu}$ & complex(dp) :: Rsneut(3,3) \\
$m_{\tilde l}$ & real(dp) :: mSlepton(6) \\
$R_{\tilde l}$ & complex(dp) :: Rslepton(6,6) \\
$m_{\tilde u}$ & real(dp) :: mSup(6) \\
$R_{\tilde u}$ & complex(dp) :: Rsup(6,6) \\
$m_{\tilde d}$ & real(dp) :: mSdown(6) \\
$R_{\tilde d}$ & complex(dp) :: Rsdown(6,6) \\
$U^L_u, U^R_u$ & complex(dp) :: uU\_L(3,3), uU\_L(3,3) \\
$U^L_d, U^R_d$ & complex(dp) :: uD\_L(3,3), uD\_L(3,3) \\
$U^L_l, U^R_l$ & complex(dp) :: uL\_L(3,3), uL\_L(3,3) \\
\end{tabular}
\end{table}
The variables for the masses and mixing matrices are given in 
Table~\ref{tab:masses}. Variable names ending with ``2'' indicate
masses squared. The variables for the mixing matrices are already
structured for a latter extension to include the effects of generation
mixing and/or complex phases:  the
sfermion mixing matrices are $6\times 6$ (except for sneutrions which is
a $3\times 3$ matrix). In the present release most of the entries
are zero except for the diagonal $2\times 2$ blocks which contain the
left--right mixing for every species of sfermions. For example, the
$11$, $12$, $21$ and $22$ entries in \verb+Rslepton+ specify the left--right
mixing of selectrons, and similarly the $33$, $34$, $43$ and $44$ 
($55$, $56$, $65$ and $66$) entries specifiy the left--right
mixing of smuons (staus). The squark mixing matrices have the same
generation structure.

These initial values serve as input for the more accurate calculation
of the parameters including higher oder corrections. Before calling
the  subroutine \verb+Sugra+, which performs these calculations, 
the user has the possibility to fix 
the high scale and/or the scale where the parameters and the
loop corrected masses are calculated. For this purpose one or both
of the following lines must be uncommented in the program:
\begin{verbatim}
! Call SetGUTScale(2.e16_dp)   ! please put the GUT scale
! Call SetRGEScale(1.e3_dp**2) ! please put the scale M_EWSB squared
\end{verbatim}
The default is that these scales are calculated by the program. The high
scale is computed from the requirement $g_1=g_2$ (except in GMSB where
the high scale is an input). The scale $M_{EWSB}$ is given by
$M_{EWSB}=\sqrt{m_{\tilde t_1} m_{\tilde t_2}}$.

The accurate calculation of the SUSY parameters and the spectrum is done
by the following call:
\begin{verbatim}
 delta = 1.e-3_dp
 WriteOut = .False.
 n_run = 20
 Call Sugra(delta, vevSM, mC, U, V, mN, N, mS0, mS02, RS0  &
    & , mP0, mP02, RP0, mSpm, mSpm2, RSpm, mSdown, mSdown2 &
    & , RSdown, mSup, mSup2, RSup, mSlepton, mSlepton2     &
    & , RSlepton, mSneut, mSneut2, RSneut, mGlu, PhaseGlu  &
    & , gauge, uL_L, uL_R, uD_L, uD_R, uU_L, uU_R, Y_l     &
    & , Y_d, Y_u, Mi, A_l, A_d, A_u, M2_E, M2_L, M2_D      &
    & , M2_Q, M2_U, M2_H, mu, B, m_GUT, kont, WriteOut, n_run)
\end{verbatim}
The meaning of the various variables and their type is given in 
Tables~\ref{tab:parameters} and \ref{tab:masses}. Note that
the quantities \verb+uL_L, uL_R, uD_L, uD_R, uU_L, uU_R+ are
$3 \times 3$ unit matrices in the present implementation. Also all
SUSY parameters, Yukawa couplings and the sfermion masses are flavour
diagonal. However, we have constructed the interface already in such a way
that an extension to include mixing effects between the generations is
facilitated. 
Compared to the previous calls of routines the following new variable appear:
\begin{itemize}
 \item \verb+delta+ : specifies the required relative precision on the masses.
   If the maximal relative differences between
  the physical masses obtained between two runs is smaller than  \verb+delta+,
   the routine \verb+Sugra+ leaves the iteration loop.
 \item \verb+m_GUT+ : the value of the scale where the high energy boundary
     conditions are imposed.
 \item \verb+kont+ : A variable which is 0 provided everything is o.k.
       Otherwise
     either a numerical problem has occurred and/or the parameters belong
     to an unphysical region, e.g.~a minimum of the potential where
     charge and/or colour breaking minima occur. In such a case the information
     is written to the file \verb+Messages.out+.
 \item \verb+WriteOut+ : If it is set \verb+.True.+ then 
     intermediate debugging information is written to the screen and the
     file \verb+Messages.out+. 
 \item \verb+n_run+ specifies the maximal number of iterations of the  main
     loop. A warning will be given in the case that the required precision
      \verb+delta+ has not been reached within \verb+n_run+  iterations.
\end{itemize}
Note that the parameters are running parameters at the scale $M_{EWSB}$.
The complete spectrum is calculated at 1--loop level using the formulas given
in \cite{Pierce:1996zz}. The exceptions
are the masses of the neutral Higgs bosons (scalar and pseudo-scalar),
where in addition the 2--loop corrections 
$O(\alpha_s \alpha_t + \alpha_t^2 + \alpha_s \alpha_b)$
are included \cite{Degrassi:2001yf,Dedes:2002dy}, and the $\mu$ parameter where
also the $O(\alpha_s \alpha_t + \alpha_t^2 + \alpha_s \alpha_b)$
corrections \cite{Dedes:2002dy} are included.

In the next part the branching ratios, the partial decay widths and the
total  decay widths are calculated provided that \verb+L_BR=.TRUE.+ and
\verb+kont.eq.0+:
\begin{verbatim}
 If ((L_BR).and.(kont.eq.0)) then
  epsI = 1.e-5_dp
  deltaM = 1.e-3_dp 
  CalcTBD = .False.
  ratioWoM = 1.e-4_dp
  If (HighScaleModel.Eq."GMSB")  Is_GMSB = .True.
  Call CalculateBR(gauge, mGlu, PhaseGlu, mC, U, V, mN, N   &
     & , mSneut, RSneut, mSlepton, RSlepton, mSup, RSup     &
     & , mSdown, RSdown, uL_L, uL_R, uD_L, uD_R, uU_L, uU_R &
     & , mS0, RS0, mP0, RP0, mSpm, RSpm, epsI, deltaM       &
     & , CalcTBD, kont, ratioWoM, Y_d, A_d, Y_l, A_l, Y_u   &
     & , A_u, mu, vevSM, Fgmsb, m32                         &
     & , gP_Sl, gT_Sl, BR_Sl, gP_Sn, gT_Sn, BR_Sn, gP_Sd    &
     & , gT_Sd, BR_Sd, gP_Su, gT_Su, BR_Su, gP_C2, gT_C     &
     & , BR_C2, gP_C3, BR_C3, gP_N2, gT_N, BR_N2, gP_N3     &
     & , BR_N3, gP_G2, gT_G, BR_G2, gP_G3, BR_G3, gP_P0     &
     & , gT_P0, BR_P0, gP_S0, gT_S0, BR_S0, gP_Spm, gT_Spm  &
     & , BR_Spm)
  end if
\end{verbatim}
Variables starting with \verb+gP_+, \verb+gT_+ and
\verb+BR_+ indicate partial widths, total widths and branching ratios,
respectively; they are \verb+Real(dp)+ vectors. The first index
is the index of the decaying particle whereas the second one
gives the mode.
 The correspondence between the second index and the modes
 is summarized for sfermions (variables ending
\verb+Sl+, \verb+Sn+, \verb+Sd+ and \verb+Su+ for sleptons,
sneutrino, d-squarks and u-squarks, respectively)
 in Table~\ref{tab:sfermiondecays}, for charginos in 
Table~\ref{tab:charginodecays}, for neutralinos in 
Table~\ref{tab:neutralinodecays}, for gluinos in Table~\ref{tab:gluinodecays}
and for the Higgs bosons in Tables~\ref{tab:higgsdecays} and 
\ref{tab:Hpdecays}.
%
\begin{table}
\caption{Correspondence between the indices for sfermion partial widths
(branching ratios) and the modes.}
\label{tab:sfermiondecays}
\begin{tabular}{lcccc}
mode & $\tilde l$ & $\tilde \nu$ & $\tilde d$ & $\tilde u$ \\
 $\tilde f_i \to f {\tilde \chi}^0_k$ & 1-4 & 1-4 & 1-4 & 1-4  \\ 
 $\tilde f_i \to f' {\tilde \chi}^\pm_j$ & 5-6 & 5-6 & 5-6 & 5-6 \\ 
 $\tilde f_i \to f {\tilde g}$ & - & - & 7 & 7  \\  
 $\tilde f_i \to W^\pm \tilde f_j'$ & 7 & 7-8 & 8-9 & 8-9 \\ 
 $\tilde f_i \to H^\pm \tilde f_j'$ & 8 & 9-10 & 10-11 & 10-11 \\
 $\tilde f_2 \to Z^0  \tilde f_1$ & 9 & 11 &  12 & 12 \\
 $\tilde f_2 \to A^0  \tilde f_1$ & 10 & 12 &  13 & 13 \\
 $\tilde f_2 \to h^0  \tilde f_1$ & 11 & 13 &  14 & 14 \\
 $\tilde f_2 \to H^0  \tilde f_1$ & 12 & 14 &  15 & 15 \\
 $\tilde l_1 \to l \, \tilde G$  & 13 & - & - & - \\
\end{tabular}
\end{table}
%
\begin{table}
\caption{Correspondence between the second indices for chargino partial widths
(branching ratios) and the decay modes.  In case of two body decays
the variables are gP\_C2 ( BR\_C2) and in case of three body decays
gP\_C3 (BR\_C3). }
\label{tab:charginodecays}
\begin{tabular}{lcc}
mode & index of gP\_C2 ( BR\_C2) & index of gP\_C3 (BR\_C3) \\
$\tilde \chi^+_i \to \tilde l_{m,k}^+ \, \nu_m$ & 1-6 \\ 
$\tilde \chi^+_i \to \tilde \nu_m \, l^+_m$ & 7-9 \\ 
$\tilde \chi^+_i \to \bar{\tilde d}_{m,k} \, u_m$ & 10-15 \\ 
$\tilde \chi^+_i \to \tilde u_{m,k} \, \bar{d}_m$ & 16-21 \\ 
$\tilde \chi^+_i \to \tilde \chi^0_j \, W^+$ & 22-25 \\
$\tilde \chi^+_i \to \tilde \chi^0_j \, H^+$ & 26-29 \\
$\tilde \chi^+_2 \to \tilde \chi^+_1 \, Z^0$ & 30 \\
$\tilde \chi^+_2 \to \tilde \chi^+_1 \, A^0$ & 31 \\
$\tilde \chi^+_2 \to \tilde \chi^+_1 \, h^0$ & 32 \\
$\tilde \chi^+_2 \to \tilde \chi^+_1 \, H^0$ & 33 \\
$\tilde \chi^+_i \to \tilde \chi^0_j \, u_m \, \bar{d}_m$ & & 1-12 \\
$\tilde \chi^+_i \to \tilde \chi^0_j \, l^+_m \, \nu_m$ & & 13-24 \\
$\tilde \chi^+_i \to \tilde g \, u_m \, \bar{d}_m$ & & 25-27 \\
$\tilde \chi^+_2 \to \tilde \chi^+_1 \, u_m \, \bar{u}_m$ & &  28-30 \\
$\tilde \chi^+_2 \to \tilde \chi^+_1 \, d_m \, \bar{d}_m$ & &  31-33 \\
$\tilde \chi^+_2 \to \tilde \chi^+_1 \, l_m \, l^+_m$ &  & 34-36 \\
$\tilde \chi^+_2 \to \tilde \chi^+_1 \, \sum_m \nu_m \, \bar{\nu}_m$ &  & 37 \\
\end{tabular}
\end{table}
%
\begin{table}
\caption{Correspondence between the second indices for neutralino partial 
widths
(branching ratios) and the decay modes.  In case of two body decays
the variables are gP\_C2 ( BR\_C2) and in case of three body decays
gP\_C3 (BR\_C3). }
\label{tab:neutralinodecays}
\begin{tabular}{lcc}
mode & index of gP\_C2 ( BR\_C2) & index of gP\_C3 (BR\_C3) \\
$\tilde \chi^0_i \to \tilde l_{m,k}^+ \, l_m$ & 1-6 \\ 
$\tilde \chi^0_i \to \tilde \nu_m \, l^+_m$ & 7-9 \\ 
$\tilde \chi^0_i \to \bar{\tilde u}_{m,k} \, u_m$ & 10-15 \\ 
$\tilde \chi^0_i \to \tilde d_{m,k} \, \bar{d}_m$ & 16-21 \\ 
$\tilde \chi^0_i \to \tilde \chi^-_j \, W^+$ & 22-23 \\
$\tilde \chi^0_i \to \tilde \chi^-_j \, H^+$ & 24-25 \\
$\tilde \chi^0_i \to \tilde \chi^0_j \, Z^0$ & 26-(24+i) \\
$\tilde \chi^0_i \to \tilde \chi^0_j \, A^0$ & (25+i)-(23+2 i) \\
$\tilde \chi^0_i \to \tilde \chi^0_j \, h^0$ & (26+i)-(22+3 i) \\
$\tilde \chi^0_i \to \tilde \chi^0_j \, H^0$ & (27+i)-(21+4 i) \\
$\tilde  \chi^0_1 \to \gamma \, \tilde G$ & 74 \\
$\tilde  \chi^0_1 \to  Z^0 \, \tilde G$ & 75 \\
$\tilde  \chi^0_1 \to h^0 \, \tilde G$ & 76 \\
$\tilde \chi^0_i \to \tilde \chi^0_j \, u_m \, \bar{u}_m$ & & 1-(3*i-3) \\
$\tilde \chi^0_i \to \tilde \chi^0_j \, d_m \, \bar{d}_m$ & & (3*i-2)-(6*i-6)\\
$\tilde \chi^0_i \to \tilde \chi^0_j \, l^+_m \, l^-_m$ & &  (6*i-5)-(9*i-9) \\
$\tilde \chi^0_i \to \tilde \chi^0_j \, \sum_n \nu_m \, \bar{\nu}_m$
          & & (9*i-8)-(10*i-9) \\
$\tilde \chi^0_i \to \tilde G  \, u_m \, \bar{u}_m$ & & (10*i-8) - (10*i-6) \\
$\tilde \chi^0_i \to \tilde G  \, d_m \, \bar{d}_m$ & &  (10*i-5) - (10*i-3) \\
\end{tabular}
\end{table}
%
\begin{table}
\caption{Correspondence between the indices for gluino partial widths
(branching ratios) and the decay modes.  In case of two body decays
the variables are gP\_G2 ( BR\_G2) and in case of three body decays
gP\_G3 (BR\_G3). }
\label{tab:gluinodecays}
\begin{tabular}{lcc}
mode & index of gP\_C2 ( BR\_C2) & index of gP\_C3 (BR\_C3) \\
$\tilde g \to \bar{\tilde d}_{m,k} \, d_m$ & 1-6 \\ 
$\tilde g \to \tilde u_{m,k} \, \bar{u}_m$ & 7-12 \\ 
$\tilde g \to \tilde \chi^0_j \, u_m \, \bar{u}_m$ & & 1-12 \\
$\tilde g \to \tilde \chi^0_j \, d_m \, \bar{d}_m$ & & 13-24 \\
$\tilde g \to \tilde \chi^+_i \, d_m \, \bar{u}_m$ & &  25-30 \\
$\tilde g \to \tilde t_i \, W^- \, \bar{b}$ & &  31-32 \\
$\tilde g \to \tilde t_1 \, \bar{c}$ & &  33 \\
\end{tabular}
\end{table}
%
\begin{table}
\caption{Correspondence between the indices for the partial widths
(branching ratios) of the neutral Higgs bosons 
and the decay modes. The variables are gP\_S0 ( BR\_S0) and  gP\_S0 ( BR\_S0)
for the partial decay widths (branching ratios) of the CP-even Higgs
bosons ($h^0$, $H^0$) and CP-odd Higgs boson ($A^0$). In case of
gP\_S0 ( BR\_S0) the first (second) index denotes decay modes of $h^0$ ($H^0$).
Here $\phi$ stands for $h^0$, $H^0$ and $A^0$. The index runs from 1 to 3.}
\label{tab:higgsdecays}
\begin{tabular}{lccc}
mode & $h^0$  & $H^0$  & $A^0$  \\
$\phi \to l^+_m \, l^-_m$ & 1-3 & 1-3 & 1-3 \\
$\phi \to d_m \, \bar{d}_m$ & 4-6 & 4-6 & 4-6 \\
$\phi \to u_m \, \bar{u}_m$ & 7-9 & 7-9 & 7-9 \\
$H^0 \to \tilde l^+_{m,1} \, \tilde l^-_{m,1}$ & - & 10 + 3*(m-1) & - \\
$\phi \to \tilde l^\mp_{m,1} \, \tilde l^\pm_{m,2}$ 
                     & - & 11  + 3*(m-1)& 11  + 3*(m-1)\\
$H^0 \to \tilde l^+_{m,2} \, \tilde l^-_{m,2}$ & - & 12 + 3*(m-1) & - \\
$H^0 \to \tilde \nu_{m} \, \overline{\tilde \nu}_m$ & - & 19 + m & - \\
$H^0 \to \tilde d_{m,1} \, \overline{\tilde d}_{m,1}$ & - & 22 + 3*(m-1) & - \\
$\phi \to \tilde d_{m,1} \, \overline{\tilde d}_{m,2}$ & - & 23 + 3*(m-1) 
                                                           & 20  + 3*(m-1)\\
$H^0 \to \tilde d_{m,2} \, \overline{\tilde d}_{m,2}$ & - & 24 + 3*(m-1) & - \\
$H^0 \to \tilde u_{m,1} \, \overline{\tilde u}_{m,1}$ & - & 31 + 3*(m-1) & - \\
$\phi \to \tilde u_{m,1} \, \overline{\tilde u}_{m,2}$ & - & 32 + 3*(m-1) 
                                                           & 29  + 3*(m-1)\\
$H^0 \to \tilde u_{m,2} \, \overline{\tilde u}_{m,2}$ & - & 33 + 3*(m-1) & - \\
$\phi \to \tilde \chi^0_r \, \tilde \chi^0_s$ $(r\le s)$
  & 40-49 & 40-49 &  37-46\\
$\phi \to \tilde \chi^+_k \, \tilde \chi^-_n$  $(k\le n)$
& 50-52 & 50-52 &  47-49 \\
$H^0 \to Z^0 \, Z^0$ & - & 53 & - \\
$H^0 \to W^+ \, W^-$ & - & 54 & - \\
$H^0 \to h^0 \, h^0$ & - & 59 & - \\
$A^0 \to h^0 \, Z^0$ & - & - & 52 \\
\end{tabular}
\end{table}
%
\begin{table}
\caption{Correspondence between the indices for the partial widths
(branching ratios) of the charged Higgs 
and the decay modes. The variables are gP\_Spm ( BR\_Spm) and in case 
of partial decay widths (branching ratios). }
\label{tab:Hpdecays}
\begin{tabular}{lc}
mode & index \\
$H^+ \to l^+_m \, \nu_m$ & 1-3 \\
$H^+ \to u_m \, \bar{d}_m$ & 4-6 \\
$H^+ \to \tilde e^+_{i} \, \tilde \nu_e$ & 7-8 \\
$H^+ \to \tilde \mu^+_{i} \, \tilde \nu_\mu$ & 9-10 \\
$H^+ \to \tilde \tau^+_{i} \, \tilde \nu_\tau$ & 11-12 \\
$H^+ \to \tilde u_{i} \, {\overline{\tilde d}}_j$ & 12 + 2*(i-1) + j \\
$H^+ \to \tilde c_{i} \, {\overline{\tilde s}}_j$ & 16 + 2*(i-1) + j \\
$H^+ \to \tilde t_{i} \, {\overline{\tilde b}}_j$ & 20 + 2*(i-1) + j \\
$H^+ \to \tilde \chi^+_r  \, \tilde \chi^0_s$ & 24 + 4*(r-1) + s \\
$H^+ \to h^0 \, W^+$ & 34
\end{tabular}
\end{table}
Here the following variables are new:
\begin{itemize}
  \item \verb+epsI+ : gives the accuracy to which the phase space integrals
      in three body decays are calculated.
  \item \verb+deltaM+ : this variable affects the calculation of the  phase
       space integrals in three body decays. In case that 
       $m_i / (m - \sum_i m_i) < $ \verb+deltaM+ than $m_i$ is set to zero
       in the calculation of the phase space integrals.
       $m$ denotes here mass of the decaying particle and $m_i$ (i=1,2,3)
       are the masses of the decay products. 
  \item \verb+CalcTBD+ : if this variable is set \verb+.TRUE.+ then in all
      chargino-, neutralino- and gluino decays the three body modes will be
      calculated. This option has to be taken with care, because it can 
      slow down the program considerably.
  \item \verb+ratioWoM+ : this variable is used to decide whether two body
      decays or three body decay modes are calculated in case of charginos,
      neutralino and gluino. The program tries first two-body decay modes.
      In the case that the ratio of the width $\Gamma$ over the mass $m$ of the
      decaying particle is small: $\Gamma / m <$ \verb+ratioWoM+, then 
      three body decay modes are calculated.
  \item \verb+Fgmsb+ and \verb+m32+ : the $F$ parameter and the
    gravitino mass in the GMSB model. These parameters are calculated from
    the input and are set to huge numbers in all other models. They are
    needed for the calculation of the decay width(s) of the NLSP into a 
    gravitino. 
\end{itemize}

The next statements call the routine for the calculation of the cross sections
provided \verb+L_CS = .TRUE.+ and \verb+kont = 0+:
\begin{verbatim}
 If ((L_CS).and.(kont.eq.0)) then
  Call InitializeCrossSections(Ecms, Pm, Pp, ISR)
  Call CalculateCrossSections(Ecms, Pm, Pp, ISR                &
           & , mSup, RSup, mf_u, mSdown, RSdown, mf_d, mglu    &
           & , SigSup, SigSdown, mSlepton, RSlepton            &
           & , mSneut, RSneut, SigSle, SigSn, mC, U, V, mN, N  &
           & , SigC, SigChi0, mS0, RS0, vevSM, mP0, RP0, mSpm  &
           & , RSpm, SigS0, SigSP, SigHp )
 End If
\end{verbatim}
Here the following additional input is needed:
\begin{itemize}
 \item \verb+Ecms+ : the centre of mass energy of the collider
 \item \verb+Pm+, \verb+Pp+ : degree of polarization of the incoming
    electron and positron, respectively
 \item \verb+ISR+ : logical variable, if \verb+.TRUE.+ then initial
  state radiation is taken into account using the formulas given in
  \cite{drees1}
\end{itemize}
These variables can be set in the file \verb+CrossSections.in+.
The cross sections are stored in the variables starting with \verb+Sig+
which are summarized in Table~\ref{tab:production}. Please note, that
in case of sfermions the structure of the variables is already put
such that the case of generation mixing can easily be implemented.
In the non--mixing case the cross sections are stored in the
$2\times 2$ diagonal blocks and they are sorted according to
the generations as in the case of the sfermion mixing matrices.
%
\begin{table}
\caption{Correspondence between the production cross sections
and the variables used in the program.}
\label{tab:production}
\begin{tabular}{ll}
process & Fortran name and type \\
$e^+ \, e^- \, \to \tilde u_i \, \tilde u_j$ & real(dp) :: SigSup(6,6) \\
$e^+ \, e^- \, \to \tilde d_i \, \tilde d_j$ & real(dp) :: SigSdown(6,6) \\
$e^+ \, e^- \, \to \tilde l_i \, \tilde l_j$ & real(dp) :: SigSle(6,6) \\
$e^+ \, e^- \, \to \tilde \nu_i \, \tilde \nu_j$ & real(dp) :: SigSn(6,6) \\
$e^+ \, e^- \, \to \tilde \chi^0_k \, \tilde \chi^0_n$
       & real(dp) :: SigChi0(4,4) \\
$e^+ \, e^- \, \to \tilde \chi^+_r \, \tilde \chi^-_s$
        & real(dp) :: SigN(4,4) \\
$e^+ \, e^- \, \to h^0 \, Z , \, \, H^0 Z$  & real(dp) :: SigS0(2) \\
$e^+ \, e^- \, \to h^0 \, A^0 , \, \, H^0 A^0$  & real(dp) :: SigSP(2) \\
$e^+ \, e^- \, \to  H^+ H^-$  & real(dp) :: SigHp
\end{tabular}
\end{table}

Finally the low energy constraints $b \to s \gamma$, $a_\mu$ and $\Delta \rho$
are calculated provided that calculation of the spectrum had been performed
successfully (\verb+kont.eq.0+):
\begin{verbatim}
 If (kont.eq.0) then
  Call CalculateLowEnergyConstraints(gauge, Y_l, Y_d, Y_u    &
    & , mSpm2, RSpm, mC, U, V, mN, N , mSup2, RSup, mSdown2  &
    & , RSdown, mSlepton2, RSlepton, mSneut2, RSneut         &
    & , BRbtosgamma, a_mu, Delta_Rho)
 Else
  BRbtosgamma = 0._dp
  a_mu = 0._dp
  Delta_Rho = 0._dp
 End If
\end{verbatim}
Here \verb+BRbtosgamma+, \verb+a_mu+, and \verb+Delta_Rho+ denote 
$10^4 \times \mathrm{BR}(b \to s \gamma)$, the SUSY contributions to
$a_\mu$ and the sfermion contributions to $\Delta \rho$, respectively.

Afterwards the statement 
\begin{verbatim}
 Call WriteOutPut0(11, 1.e-6_dp, 1.e-3_dp)
\end{verbatim}
is used to write all information to the file connected with unit 11
(first entry). The second entry puts a lower bound on the branching ratios
 to be written. In the case above, branching ratios smaller
than $10^{-6}$ will not be given. The third entry gives the minimum value
for the cross section in $fb$ which will be written to the output file.
In the example given above cross sections smaller than $10^{-3}$ will not
be written to the output file.

The last statement closes all open files.
\begin{verbatim}
 call closing() ! closes the files
\end{verbatim}

\section{Conclusions}

We have described \verb+SPheno+, a program calculating the spectrum,
branching ratios and cross sections of supersymmetric particle in 
$e^+ e^-$ annihilation within the MSSM. The user can choose between the
following high scale models: minimal supergravity, minimal
supergravity including right handed neutrinos, gauge mediated
supersymmetry breaking, anomaly mediated supersymmetry breaking, and
string effective field theories based on OI and OII compactification.
%
 The calculation of the spectrum are done using two-loop renormalization group
equations and the complete one-loop formulas for the SUSY masses. 
In case of the neutral
Higgs bosons and the $\mu$ parameter leading two-loop effects are included.
%
The masses and mixing angles are used to calculate the most important
two body and three body decay modes.
%
They are also used for the  calculation of the SUSY  production cross sections
in $e^+ e^-$ annihilation. Here the effects of initial state radiation and
longitudinal beam polarization is included.
% 
Finally the following low energy quantities are calculated:
$BR(b \to s \gamma)$, the supersymmetric contributions to the anomalous
magnetic moment of the muon $a_\mu$ and the sfermion contributions to
the $\rho$ parameter.

The program is set up in such a way that extensions can easily be 
included. The plans for upcoming versions are to include complex phases for
the supersymmetric parameters, to include generation mixing, to include
QCD and Yukawa corrections for various processes such as Sfermion and
Higgs production and decays. In addition beam strahlung for various
collider designs will be implemented.

\section*{Acknowledgements}
%\ack 
I would like to thank B.~Allanach, A.~Djouadi and S.~Kraml for discussions
on higher order corrections to  the Yukawa couplings. 
Special thanks go to P.~Slavich for discussions on 2-loop corrections of the 
Higgs boson masses and for providing a Fortran code performing the
2-loop corrections to the neutral Higgs boson masses and the $\mu$ parameter.
I would like to thank G.~Blair and P.~Zerwas for an enjoyable and fruitful
collaboration from which the work on this program originated.
This work is supported by the Erwin
Schr\"odinger fellowship No. J2095 of the `Fonds zur
F\"orderung der wissenschaftlichen Forschung' of Austria FWF and
partly by the Swiss `Nationalfonds'.


\begin{appendix}

\section{Switches}
\label{app:switch}

In this appendix we describe the switches for influencing the behaviour
of the program.
%
Inside the main program one can set two scales:
\begin{enumerate}
 \item The electroweak scale $M_{EWSB}$, which is the scale where 
  the loop contributions to the masses and mixing matrices are calculated.
  The default is to calculate this scale from 
   $M_{EWSB}=\sqrt{m_{\tilde t_1} m_{\tilde t_2}}$. By calling
   \begin{verbatim}
  Call SetRGEScale(1.e3_dp**2)
    \end{verbatim}
   $M_{EWSB}$ will be set to the fixed value of $10^3$~GeV in this example.
   Note that the input is the scale squared.
   In the case one uses a zero or a negative number as input for
   \verb+SetRGEScale+ then the scale will be calculated from the
   stop masses.
 \item The high energy scale, where the boundary conditions of the model
   under study are set. Except for GMSB, where the scale is fixed by default,
   the high scale is calculated from the requirement $g_1 = g_2$. By calling
   \begin{verbatim}
 Call SetGUTScale(2.e16_dp)
   \end{verbatim}
    $M_{GUT}$ will be set to $2 \cdot 10^{16}$~GeV in this example. 
   In the case one uses a zero or a negative number as input for
   \verb+SetGUTScale+ then the scale will be calculated from the requirement
   $g_1 = g_2$ except for GMSB.
\end{enumerate}
In general the strong coupling $g_s$ will be different from $g_1$ and
$g_2$ in GUT theories if one works at the two loop level 
\cite{Weinberg:1980wa}. In case someone wants to enforce strict
universality at the high scale, this can be done by using the following
statement:
\begin{verbatim}
 test = SetStrictUnification(.TRUE.)
\end{verbatim}
where \verb+test+ is a logical variable to which the old value of
SetStrictUnification is assigned. The same functions can also be used
to set this option \verb+.FALSE.+.


\section{Input files}
In this section the input files are described. Among these files only
the file \verb+HighScale.in+ has to be provided by the user. The other
files \verb+Control.in+, \verb+CrossSections.in+
 and \verb+StandardModel.in+ can be used to change
the default values which are given below in Appendices~\ref{app:Control},
\ref{app:cross} and \ref{app:SM}.

\subsection{Control.in}
\label{app:Control}

This file contains three entries as shown below:
\begin{verbatim}
0             ! ErrorLevel
.True.        ! Calculation of branching ratios
.True.        ! Calculation of cross sections
\end{verbatim}
The values given above are the default values inside the program and are
used if the the file \verb+Control.in+ is not present. Here 
\verb+ErrorLevel+ is an integer in the range [-2,2] where the numbers
correspond to the following behaviour of the program:
\begin{enumerate}
 \item[-2] do not print severe warnings
 \item[-1]  do not print warnings
 \item[0]  print every warning
 \item[1] abort in case of a severe warning
 \item[2]  abort even in case of a warning
\end{enumerate}
A warning is called severe if either a result is unphysical or if
a numerical procedure gives an unreliable result.

\subsection{CrossSections.in}
\label{app:cross}

This file contains four entries as shown below:
\begin{verbatim}
500.          ! c.m.s. energy in GeV
0.            ! degree of longitudinal polarization of electrons
0.            ! degree of longitudinal polarization of positrons
.True.        ! calculation of initial state radiation if .TRUE. 
\end{verbatim}
The values given above are the default values inside the program and are
used if the the file \verb+CrossSections.in+ is not present. 

\subsection{HighScale.in}
\label{app:model}
In this section we describe the input file for the high scale boundary
conditions. The package contains several files starting with 
\verb+Highscale.in+ and ending in the models described below. One has
to rename the model file to the name \verb+Highscale.in+ to use it as
input for \verb+SPheno+. Note that in all examples below the value
of $A_0$ given below will be multiplied by the Yukawas coupling at the
high scale and that this product enters the RGEs. For most of the
examples below we have used the so-called SPS points defined in 
\cite{Allanach:2002nj}. In Appendix~\ref{app:output} we display the output
for the point SPS1a.

\subsubsection{mSUGRA}
\label{app:mSUGRA}

The minimal SUGRA version is defined by four parameters and the sign of
the $\mu$ parameter. The parameters are the gaugino mass parameter
$M_{1/2}$, the scalar mass parameter $M_0$, the trilinear parameter
$A_0$ as well as $\tan\beta$. The file reads for example
\begin{verbatim}
mSugra
 250.                         ! M_1/2
 100.                         ! M_0
-100.                         ! A_0
  10.                         ! tan(beta)
   1.                         ! sign of mu
.TRUE.                        ! if 2-loop RGEs should be used
\end{verbatim}

\subsubsection{mSUGRA including right handed neutrinos}
\label{app:mSUGRAnuR}

In this case one needs four more input values compared to the case of
mSUGRA described above: a common right handed neutrino mass $m_{\nu_R}$
and the light neutrino masses $m_{\nu_i}$ ($i=1,2,3$).
The file reads for example
\begin{verbatim}
mSugra
 250.                         ! M_1/2
 100.                         ! M_0
-100.                         ! A_0
  10.                         ! tan(beta)
   1.                         ! sign of mu
1.e14                         ! m_nu_R
1.e-14 3.e-12 0.06e-9         ! m_nu_i 
.TRUE.                        ! if 2-loop RGEs should be used
\end{verbatim}

\subsubsection{GMSB}

The GMSB scenario is characterized by two mass parameters $M_M$ and
$\Lambda$; the multiplicity $N_5$ and $N_{10}$ of  messengers in the
$5+\overline{5}$ and $10+\overline{10}$ vector-like multiplets, respectively;
$\tan\beta$ and the sign of $\mu$  as described in \sect{sect:gmsb}.
In addition one can set a common value for the $A$ parameters at the scale
$M_M$. Note, however, that in the minimal model this value is practically
zero. The file reads for example
\begin{verbatim}
GMSB
100000.                        ! Lambda
200000.                        ! M_M
1                              ! N_5
0                              ! N_10
0.                             ! A0
15.                            ! tan(beta)
1.                             ! sign of mu
.TRUE.                         ! if 2-loop RGEs should be used
\end{verbatim}

\subsubsection{AMSB}

The implemented AMSB scenario is characterized by the gravitino mass
$m_{3/2}$, a common scalar mass $M_0$, $\tan\beta$ and the sign of $\mu$.
 The file reads for example
\begin{verbatim}
AMSB            ! model
60000.          ! M_3/2
450.            ! M_0
10.             ! tan(beta)
1.              ! sign of mu
.TRUE.          ! if 2-loop RGEs should be used
\end{verbatim}

\subsubsection{String I}

This scenario is characterized by the gravitino mass $m_{3/2}$, the
common vev $<t>$ of the moduli fields, the string coupling squared
$g^2_s$, the sine squared of the mixing angle between the dilaton fields
and moduli fields $\sin^2 \theta$, the parameter $\delta_{GS}$
 of the Green--Schwarz
counter-term, the modular weights $n_i$ characterizing
the couplings between moduli fields and matter fields, which are assumed
to be generation independent in the current implementation. Moreover,
one needs to specify $\tan\beta$ and the sign of $\mu$. The file reads for
example as
\begin{verbatim}
String_OI
180.                      ! M_3/2
14.0                      ! <t>
0.5                       ! g_s^2
0.9                       ! sin^2(theta)
 0.                       ! delta_GS
-1 -3                     ! n_E n_L
 1 -2 0                   ! n_D n_U n_Q
-1 -1                     ! n_H1 n_H2
10.                       ! tan(beta)
-1.                       ! phase(mu)
.TRUE.                    ! if 2-loop RGEs should be used
\end{verbatim}


\subsubsection{String II}

This scenario is characterized by the gravitino mass $m_{3/2}$, the
common vev of the moduli fields $<t>$, the string coupling squared
$g^2_s$, the sine squared of the mixing angle between the dilaton fields
and moduli fields $\sin^2 \theta$, the parameter of the Green--Schwarz
counter-term $\delta_{GS}$. Moreover,
one needs to specify $\tan\beta$ and the sign of $\mu$. There are two
different scenarios implemented denoted as \verb+String_OIIa+ and
 \verb+String_OIIb+ corresponding to boundary conditions $(A)$ and
$(B)$ of \cite{Binetruy:2001md}, respectively.
The files read for example as
\begin{verbatim}
String_OIIa
300.                      ! M_3/2
14.6                      ! <t>
0.5                       ! g_s^2
0.9                       ! sin^2(theta)
0.                        ! delta_GS
5.                        ! tan(beta)
1.                        ! phase(mu)
.TRUE.                    ! if 2-loop RGEs should be used
\end{verbatim}
and
\begin{verbatim}
String_OIIb
300.                      ! M_3/2
14.6                      ! <t>
0.5                       ! g_s^2
0.9                       ! sin^2(theta)
0.                        ! delta_GS
5.                        ! tan(beta)
1.                        ! phase(mu)
.TRUE.                    ! if 2-loop RGEs should be used
\end{verbatim}

\subsubsection{SUGRA}

This input files serves as interface for more general models with
gauge couplings unification. Here the user can specify non-universal
gaugino masses at the high scale $M_{1/2}[U(1)]$, $M_{1/2}[SU(2)]$,
$M_{1/2}[SU(3)]$, 15 different values of the sfermion mass parameters for 
every type of sfermions: $M^0_{\tilde E,ii}$, $ M^0_{\tilde L,ii}$, 
$ M^0_{\tilde D,ii}$,
$ M^0_{\tilde U,ii}$, $ M^0_{\tilde Q,ii}$; two Higgs mass parameters
$M^0_{H_1}$ and $M^0_{H_2}$; nine different $A$ parameters $A_{0,e,ii}$,
 $A_{0,d,ii}$ and  $A_{0,u,ii}$. Here $ii$ denotes that only the
diagonal entries can be set.

\begin{verbatim}
Sugra
480. 300. 300.       ! M_1/2_i
150. 150. 150.       ! M0_E_ii
150. 150. 150.       ! M0_L_ii
150. 150. 150.       ! M0_D_ii
150. 150. 150.       ! M0_Q_ii
150. 150. 150.       ! M0_U_ii
150. 150.            ! M0_H_i
0. 0. 0.             ! A0_u_ii
0. 0. 0.             ! A0_d_ii
0. 0. 0.             ! A0_e_ii
10.                  ! tan(beta)
1.                   ! phase(mu)
.TRUE.               ! if 2-loop RGEs should be used
\end{verbatim}


\subsection{StandardModel.in}
\label{app:SM}

This file contains the values of the Standard Model parameters and must
include all lines given below. Otherwise the default values given
in the listing below are used: 
\begin{verbatim}
91.187                    ! Z boson mass
2.490                     ! width of Z-boson
0.14 0.14 0.14 0.14 0.14  ! Br(Z -> q q) q=u,d,c,s,b
0.035 0.035 0.03          ! Br(Z -> l l) l=e, mu, tau
0.2                       ! Br(Z -> invisible)
80.41                     ! W boson mass
2.06                      ! widht of W-boson
0.35 0.35                 ! Br(W -> q q)
0.1  0.1 0.1              ! Br(W -> l nu)
0.51099906e-3             ! electron mass
0.105658                  ! muon mass 
1.7771                    ! tau mass
0.004                     ! u-quark mass
1.4                       ! c-quark mass
174.3                     ! t-quark mass
0.01                      ! d-quark mass
0.15                      ! s-quark mass
4.62                      ! b-quark mass
0.2315                    ! sin(theta_W) squared
137.0359895               ! 1 / Alpha
127.9                     ! 1 / Alpha at m_Z
0.119                     ! Alpha_s at m_Z
1.16639e-5                !  G_F, Fermi constant
0.220          ! s12 of CKM, parametrized as particle data book
0.039          ! s23 of CKM
0.0031         ! s13 of CKM
0.             ! phase of CKM
2.19709e-6     ! life time of muon
3.4e-13        ! life time of tau
\end{verbatim}
All masses are given in GeV and
$Br$ denotes ``branching ratio'' in the list above.

\section{Sample output}
\label{app:output}
Here we give the content of the file \verb+SPheno.out+ provided one
uses the content of \verb+HighScale.in+ for the mSUGRA scenario
described in Appendix~\ref{app:mSUGRA}
and the default values of the files \verb+Control.in+, \verb+CrossSections.in+
and \verb+StandardModel.in+.

\begin{verbatim}
 mSugra input at the GUT scale   1.8193751412503776E+16
 M_1/2     :    2.5000000000000000E+02
 M_0       :    1.0000000000000000E+02
 A_0       :   -1.0000000000000000E+02
 tan(beta) :   10.0000000000000000
 phase(mu) :    1.0000000000000000
  
 Parameters at the scale    4.8387163690920886E+02
  
 Gaugino mass parameters
   1.0256160300628754E+02   1.9230453743751079E+02   5.8695416971423458E+02
  
 tan(beta), mu, B
  10.0000000000000000   3.5489208425079283E+02   1.5675353981646900E+04
  
 Slepton mass parameters
 A_l
  -7.2960260902552873E-03  -1.5085451901504909 -25.2233192083639537
 M2_E
   1.8409373246520361E+04   1.8407069022083171E+04   1.7758366624396785E+04
 M2_L
   3.7890957725749206E+04   3.7889823466403272E+04   3.7570561651708413E+04
  
 Squark mass parameters
 A_d
  -0.2294422308452373  -3.4416136998921720  -1.0705947183168641E+02
 A_u
  -7.4845500397144014E-03  -2.6195690984405484  -4.4984080721097047E+02
 M2_D
   2.7694850270662527E+05   2.7694564371571731E+05   2.7392874700277165E+05
 M2_U
   2.7918011844082910E+05   2.7917785219910560E+05   1.7963017265859758E+05
 M2_Q
   2.9890503958833648E+05   2.9890250621627242E+05   2.4881821604275642E+05
  
 Higgs mass parameters
   3.2728705451079368E+04  -1.2647888724841128E+05
  
 Masses and mixing matrices
 Gluino :    5.9431308258414890E+02   1.0000000000000000
  
 Charginos
   1.8128399897496990E+02   3.7972508491362004E+02
   U
   -0.915146173   0.403122168
    0.403122168   0.915146173
   V
   -0.969411416   0.245441450
    0.245441450   0.969411416
  
 Neutralinos
  97.6301037960382843   1.8286658240938323E+02   3.6169325535757582E+02
  3.7956517886694593E+02
   N
    1   1  (  -0.985173736,   0.000000000)
    1   2  (   0.055759050,   0.000000000)
    1   3  (  -0.152169890,   0.000000000)
    1   4  (   0.056284663,   0.000000000)
    2   1  (  -0.105870636,   0.000000000)
    2   2  (  -0.939909692,   0.000000000)
    2   3  (   0.280773631,   0.000000000)
    2   4  (  -0.162872183,   0.000000000)
    3   1  (   0.000000000,   0.061494809)
    3   2  (  -0.000000000,  -0.091193095)
    3   3  (  -0.000000000,  -0.694530579)
    3   4  (  -0.000000000,  -0.711005965)
    4   1  (   0.120176983,   0.000000000)
    4   2  (  -0.324259957,   0.000000000)
    4   3  (  -0.644699749,   0.000000000)
    4   4  (   0.681744238,   0.000000000)
  
 e-sneutrino mass   :    1.9045601012611243E+02
 mu-sneutrino mass  :    1.9045285310250864E+02
 tau-sneutrino mass :    1.8956097209694545E+02
  
 selectron masses
   1.4386950800164570E+02   2.0663378686036157E+02
  R_e
    0.000088274   0.999999996
   -0.999999996   0.000088274
  
 smuon masses
   1.4383537094841918E+02   2.0664861475069350E+02
  R_mu
    0.018241899   0.999833603
   -0.999833603   0.018241899
  
 stau masses
   1.3457995016660027E+02   2.1033431394260100E+02
  R_tau
    0.268468657   0.963288420
   -0.963288420   0.268468657
  
 u-squark masses
   5.4780614315239006E+02   5.6490633570208024E+02
  R_u
    0.000077527   0.999999997
   -0.999999997   0.000077527
  
 c-squark masses
   5.4779164376198435E+02   5.6491659043591176E+02
  R_c
    0.027104541   0.999632604
   -0.999632604   0.027104541
  
 t-squark masses
   3.9757274604952244E+02   5.8855899352335769E+02
  R_t
    0.554536381   0.832159481
   -0.832159481   0.554536381
  
 d-squark masses
   5.4761741237742456E+02   5.6953755385412876E+02
  R_d
    0.000836413   0.999999650
   -0.999999650   0.000836413
  
 s-squark masses
   5.4761111206790952E+02   5.6953840728628120E+02
  R_s
    0.012543035   0.999921333
   -0.999921333   0.012543035
  
 b-squark masses
   5.1664747823588539E+02   5.4745980835840328E+02
  R_b
    0.951026325   0.309109898
   -0.309109898   0.951026325
  
 m_A0, m_H+
   3.9716087636273568E+02   4.0654002309066368E+02
  
 m_h0, m_H0
   1.1166181009637616E+02   3.9789685848133115E+02
  R_S0
    0.113896390   0.993492633
   -0.993492633   0.113896390
  
  
 Low energy constraints 
  10^4 Br(b -> s gamma) :   0.3838177E+01
  Delta(a_mu)           :   0.5447498E-08
  Delta(rho)            :   0.1829291E-03
  
  
                     Decay widths (GeV) and branching ratios
  
  Selectron_1
   Neutralino_1 e               0.21131224  100.00000000
  Total width :                 0.21131224
  
  
  Selectron_2
   Neutralino_1 e               0.12712238   52.26317145
   Neutralino_2 e               0.04013733   16.50145248
   Chargino_1 neutrino          0.07597540   31.23537607
  Total width :                 0.24323511
  
  
  Smuon_1
   Neutralino_1 mu              0.21104744  100.00000000
  Total width :                 0.21104744
  
  
  Smuon_2
   Neutralino_1 mu              0.12728238   52.28029028
   Neutralino_2 mu              0.04016202   16.49625242
   Chargino_1 neutrino          0.07601710   31.22345730
  Total width :                 0.24346150
  
  
  Stau_1
   Neutralino_1 tau             0.14597684  100.00000000
  Total width :                 0.14597684
  
  
  Stau_2
   Neutralino_1 tau             0.16310412   55.22030445
   Neutralino_2 tau             0.04619971   15.64130946
   Chargino_1 neutrino          0.08606600   29.13838609
  Total width :                 0.29536983
  
  
  e-Sneutrino
   Neutralino_1 neutrino        0.15829938   90.39621196
   Neutralino_2 neutrino        0.00372885    2.12934196
   Chargino_1 e                 0.01308905    7.47444608
  Total width :                 0.17511727
  
  
  mu-Sneutrino
   Neutralino_1 neutrino        0.15829302   90.40278693
   Neutralino_2 neutrino        0.00372587    2.12788095
   Chargino_1 mu                0.01307861    7.46933212
  Total width :                 0.17509749
  
  
  tau-Sneutrino
   Neutralino_1 neutrino        0.15649412   92.23051574
   Neutralino_2 neutrino        0.00292840    1.72586668
   Chargino_1 tau               0.01025464    6.04361757
  Total width :                 0.16967717
  
  
  Sdown_1
   Neutralino_1 d-quark         0.28784101   98.48847777
   Neutralino_2 d-quark         0.00280074    0.95830889
   Neutralino_3 d-quark         0.00038028    0.13011842
   Neutralino_4 d-quark         0.00123347    0.42204919
   Chargino_1 u-quark           0.00000306    0.00104559
  Total width :                 0.29225857
  
  
  Sdown_2
   Neutralino_1 d-quark         0.12768972    2.43021937
   Neutralino_2 d-quark         1.60529969   30.55242392
   Neutralino_3 d-quark         0.00884812    0.16839948
   Neutralino_4 d-quark         0.08754132    1.66610595
   Chargino_1 u-quark           3.18849528   60.68415751
   Chargino_2 u-quark           0.23637246    4.49869376
  Total width :                 5.25424660
  
  
  S-strange_1
   Neutralino_1 s-quark         0.28785440   98.14255868
   Neutralino_2 s-quark         0.00313853    1.07006608
   Neutralino_3 s-quark         0.00039188    0.13360864
   Neutralino_4 s-quark         0.00123018    0.41942337
   Chargino_1 c-quark           0.00068723    0.23430866
   Chargino_2 c-quark           0.00000010    0.00003458
  Total width :                 0.29330232
  
  
  S-strange_2
   Neutralino_1 s-quark         0.12767855    2.43041977
   Neutralino_2 s-quark         1.60496370   30.55122040
   Neutralino_3 s-quark         0.00888876    0.16920168
   Neutralino_4 s-quark         0.08758857    1.66728859
   Chargino_1 c-quark           3.18774099   60.68011250
   Chargino_2 c-quark           0.23649323    4.50175707
  Total width :                 5.25335380
  
  
  Sbottom_1
   Neutralino_1 b-quark         0.16184398    4.11945668
   Neutralino_2 b-quark         1.32661019   33.76655332
   Neutralino_3 b-quark         0.01759582    0.44787087
   Neutralino_4 b-quark         0.04615410    1.17477226
   Chargino_1 t-quark           1.71616072   43.68188400
   Stop_1 W-                    0.66040512   16.80946286
  Total width :                 3.92876992
  
  
  Sbottom_2
   Neutralino_1 b-quark         0.24397318   33.44230042
   Neutralino_2 b-quark         0.08601743   11.79072502
   Neutralino_3 b-quark         0.03700740    5.07274017
   Neutralino_4 b-quark         0.05304386    7.27091758
   Chargino_1 t-quark           0.11582889   15.87709181
   Stop_1 W-                    0.19366391   26.54622500
  Total width :                 0.72953467
  
  
  Sup_1
   Neutralino_1 u-quark         1.15181264   98.48926332
   Neutralino_2 u-quark         0.01120273    0.95792374
   Neutralino_3 u-quark         0.00152307    0.13023466
   Neutralino_4 u-quark         0.00494195    0.42257635
   Chargino_1 d-quark           0.00000002    0.00000193
  Total width :                 1.16948041
  
  
  Sup_2
   Neutralino_1 u-quark         0.03620866    0.66423008
   Neutralino_2 u-quark         1.72553982   31.65418423
   Neutralino_3 u-quark         0.00517093    0.09485826
   Neutralino_4 u-quark         0.06407609    1.17544453
   Chargino_1 d-quark           3.53559056   64.85867992
   Chargino_2 d-quark           0.08463583    1.55260297
  Total width :                 5.45122190
  
  
  S-charm_1
   Neutralino_1 c-quark         1.15098392   98.14036844
   Neutralino_2 c-quark         0.01253940    1.06919075
   Neutralino_3 c-quark         0.00158298    0.13497525
   Neutralino_4 c-quark         0.00492241    0.41971639
   Chargino_1 s-quark           0.00276378    0.23565786
   Chargino_2 s-quark           0.00000107    0.00009130
  Total width :                 1.17279356
  
  
  S-charm_2
   Neutralino_1 c-quark         0.03701501    0.67941726
   Neutralino_2 c-quark         1.72415946   31.64725980
   Neutralino_3 c-quark         0.00516765    0.09485322
   Neutralino_4 c-quark         0.06416446    1.17775023
   Chargino_1 s-quark           3.53281680   64.84549368
   Chargino_2 s-quark           0.08472953    1.55522582
  Total width :                 5.44805290
  
  
  Stop_1
   Neutralino_1 t-quark         0.39250239   19.40691906
   Neutralino_2 t-quark         0.22674584   11.21123908
   Chargino_1 b-quark           1.38120247   68.29228464
   Chargino_2 b-quark           0.02203615    1.08955722
  Total width :                 2.02248685
  
  
  Stop_2
   Neutralino_1 t-quark         0.22161960    2.91852834
   Neutralino_2 t-quark         0.62619038    8.24635720
   Neutralino_3 t-quark         0.34624563    4.55973974
   Neutralino_4 t-quark         1.54482109   20.34388720
   Chargino_1 b-quark           1.54991244   20.41093566
   Chargino_2 b-quark           1.51409588   19.93926416
   Stop_1  Z                    1.51313204   19.92657136
   Stop_1  h0                   0.27752232    3.65471634
  Total width :                 7.59353939
  
  
  Chargino_1
   neutralino_1 d u             0.00033235    1.99860842
   neutralino_1 s c             0.00033232    1.99844982
   neutralino_1 e nu            0.00058806    3.53637657
   neutralino_1 mu nu           0.00063093    3.79415091
   neutralino_1 tau nu          0.01474527   88.67241428
  Total width :                 0.01662893
  
  Chargino_2
   Selectron_2 neutrino         0.12652636    5.19161956
   Smuon_1 neutrino             0.00000150    0.00006154
   Smuon_2 neutrino             0.12656625    5.19325658
   Stau_1 neutrino              0.00104893    0.04303979
   Stau_2 neutrino              0.13749520    5.64169248
   e-sneutrino e                0.05302870    2.17586926
   mu-sneutrino mu              0.05309068    2.17841255
   tau-sneutrino tau            0.07070699    2.90124380
   Neutralino_1 W               0.17302320    7.09947452
   Neutralino_2 W               0.67940247   27.87718885
   Chargino_1 Z                 0.58927646   24.17914547
   Chargino_1 h0                0.42696015   17.51899560
  Total width :                 2.43712690
  
  Neutralino_1 : stable
  
  Neutralino_2
   Selectron_1 e                0.00154723    7.10543425
   Smuon_1 mu                   0.00160018    7.34859632
   Stau_1 tau                   0.01862788   85.54596943
  Total width :                 0.02177529
  
  
  Neutralino_3
   Selectron_1 e                0.00503923    0.26009421
   Selectron_2 e                0.00218588    0.11282149
   Smuon_1 mu                   0.00508346    0.26237682
   Smuon_2 mu                   0.00227146    0.11723867
   Stau_1 tau                   0.02025229    1.04529883
   Stau_2 tau                   0.02419151    1.24861727
   e-sneutrino neutrino         0.01234523    0.63718479
   mu-sneutrino neutrino        0.01234554    0.63720099
   tau-sneutrino neutrino       0.01243421    0.64177746
   Chargino_1 W                 1.14827835   59.26707890
   Neutralino_1 Z               0.22657242   11.69427718
   Neutralino_2 Z               0.40462398   20.88420588
   Neutralino_1 h0              0.04071375    2.10139378
   Neutralino_2 h0              0.02112676    1.09043373
  Total width :                 1.93746405
  
  
  Neutralino_4
   Selectron_1 e                0.02090064    0.79655160
   Selectron_2 e                0.05133031    1.95626710
   Smuon_1 mu                   0.02086555    0.79521429
   Smuon_2 mu                   0.05145801    1.96113393
   Stau_1 tau                   0.01565228    0.59652937
   Stau_2 tau                   0.08419943    3.20895348
   e-sneutrino neutrino         0.13486416    5.13985427
   mu-sneutrino neutrino        0.13486717    5.13996895
   tau-sneutrino neutrino       0.13571657    5.17234103
   Chargino_1 W                 1.34016810   51.07560769
   Neutralino_1 Z               0.05567616    2.12189348
   Neutralino_2 Z               0.04779240    1.82143249
   Neutralino_1 h0              0.17892991    6.81925922
   Neutralino_2 h0              0.35146997   13.39499312
  Total width :                 2.62389066
  
  
  Gluino
   Sup_1 u-quark                0.32555602    9.88307192
   Sup_2 u-quark                0.13408883    4.07060373
   S-charm_1 c-quark            0.32506240    9.86808701
   S-charm_2 c-quark            0.13420743    4.07420414
   Stop_1 t-quark               0.35279908   10.71010362
   Sdown_1 d-quark              0.32809509    9.96015176
   Sdown_2 d-quark              0.09594182    2.91255533
   S-strange_1 s-quark          0.32815106    9.96185087
   S-strange_2 s-quark          0.09594849    2.91275775
   Sbottom_1 b-quark            0.82565254   25.06475973
   Sbottom_2 b-quark            0.34857445   10.58185414
  Total width :                 3.29407721
  
 h0 
   electrons                    0.00000000    0.00000125
   muons                        0.00000103    0.05351444
   taus                         0.00029239   15.14367767
   d-quark                      0.00000001    0.00031725
   s-quark                      0.00000138    0.07138010
   b-quark                      0.00152831   79.15466880
   u-quark                      0.00000000    0.00004556
   c-quark                      0.00010767    5.57639494
  Total width :                 0.00193079
  
  
 H0 
   muons                        0.00028014    0.04201232
   taus                         0.07938694   11.90538074
   d-quark                      0.00000168    0.00025219
   s-quark                      0.00037836    0.05674169
   b-quark                      0.42140146   63.19609693
   c-quark                      0.00000511    0.00076636
   t-quark                      0.03081125    4.62065503
   Selectron 1 1                0.00039974    0.05994791
   Smuon 1 1                    0.00040732    0.06108426
   Smuon 1 2                    0.00003734    0.00559954
   Stau 1 1                     0.00433734    0.65045550
   Stau 1 2                     0.00799437    1.19888731
   e-Sneutrino                  0.00073208    0.10978775
   mu-Sneutrino                 0.00073222    0.10980771
   tau-Sneutrino                0.00076881    0.11529554
   neutralino_1 neutralino_1    0.01687144    2.53015073
   neutralino_1 neutralino_2    0.04686601    7.02833048
   neutralino_2 neutralino_2    0.01058042    1.58670780
   chargino_1 chargino_1        0.03027976    4.54094909
   Z Z                          0.00153237    0.22980460
   W W                          0.00320663    0.48088662
   h0 h0                        0.00980485    1.47039879
  Total width :                 0.66681564
  
  
  
 A0 
   muons                        0.00028050    0.02631577
   taus                         0.07949301    7.45791191
   d-quark                      0.00000168    0.00015796
   s-quark                      0.00037883    0.03554126
   b-quark                      0.42198287   39.58978482
   c-quark                      0.00000389    0.00036525
   t-quark                      0.10032310    9.41215930
   Smuon 1 2                    0.00003869    0.00362993
   Stau 1 2                     0.01130912    1.06100403
   neutralino_1 neutralino_1    0.02607822    2.44661842
   neutralino_1 neutralino_2    0.10959778   10.28229529
   neutralino_2 neutralino_2    0.08682800    8.14606947
   chargino_1 chargino_1        0.22688237   21.28575532
   h0 Z                         0.00269020    0.25239056
  Total width :                 1.06588826
  
  
  
  H^+
   electron neutrino            0.00000001    0.00000109
   muon neutrino                0.00028712    0.04644904
   tau neutrino                 0.08137042   13.16371935
   d-quark u-quark              0.00000151    0.00024435
   s-quark c-quark              0.00034333    0.05554153
   b-quark t-quark              0.37287242   60.32152442
   Selectron_2 Sneutrino        0.00053557    0.08664129
   Smuon_1 Sneutrino            0.00005577    0.00902161
   Smuon_2 Sneutrino            0.00053145    0.08597568
   Stau_1 Sneutrino             0.01497337    2.42231984
   Stau_2 Sneutrino             0.00000770    0.00124494
   chargino_1 neutralino_1      0.14336239   23.19248520
   chargino_1 neutralino_2      0.00074334    0.12025399
   h0 W                         0.00305719    0.49457746
  Total width :                 0.61814157
  
  
 Total cross sections in fb for:
  E_cms :     500.0000000  GeV
  Degree of polarization: P_e- = 0.000000 P_e+ = 0.000000
  Intial state radiation is included
  
  u-squarks : kinematically not possible
  
  c-squarks : kinematically not possible
  
  t-squarks : kinematically not possible
  
  
  d-squarks : kinematically not possible
  
  s-squarks : kinematically not possible
  
  b-squarks : kinematically not possible
  
  
  selectrons
   1   1     290.9786253 fb
   1   2      81.1156881 fb
   2   2      43.5380487 fb
  
  smuons
   1   1      57.2730680 fb
   1   2       0.0058106 fb
   2   2      18.4801616 fb
  
  staus
   1   1      62.1659720 fb
   1   2       1.2151999 fb
   2   2      15.5585302 fb
  
  
  e-sneutrino
             412.6967832 fb
  
  mu-sneutrino
              12.9553932 fb
  
  tau-sneutrino
              13.2367076 fb
  
  
  neutralinos
   1   1     284.9858436 fb
   1   2      64.4974860 fb
   1   3       8.0550495 fb
   1   4       1.0888651 fb
   2   2      61.0982614 fb
  
  
  charginos
   1   1     142.6642433 fb
  
  
  h^0 Z
              23.1467991 fb
  
  H^0 Z : cross section below   1.0000000E-03 fb
  
  h^0 A^0 : kinematically not possible
  
  H^0 A^0 : kinematically not possible
  
  H^+ H^- : kinematically not possible
  
\end{verbatim}

\end{appendix}

\begin{thebibliography}{99}

%\cite{Wess:tw}
\bibitem{Wess:tw}
J.~Wess and B.~Zumino,
%``Supergauge Transformations In Four-Dimensions,''
Nucl.\ Phys.\  {\bf B~70} (1974) 39;
%%CITATION = NUPHA,B70,39;%%
P.~Fayet and S.~Ferrara,
%``Supersymmetry,''
Phys.\ Rept.\  {\bf 32} (1977) 249.
%%CITATION = PRPLC,32,249;%%



%\cite{Nilles:1983ge}
\bibitem{Nilles:1983ge}
H.P.~Nilles,
%``Supersymmetry, Supergravity And Particle Physics,''
Phys.\ Rept.\  {\bf 110} (1984) 1.
%%CITATION = PRPLC,110,1;%%

\bibitem{habkan}
H.E.~Haber and G.L.~Kane,
%``The Search For Supersymmetry: Probing Physics Beyond The Standard Model,''
Phys.\ Rept.\  {\bf 117} (1985) 75.
%%CITATION = PRPLC,117,75;%%


%\cite{Witten:nf}
\bibitem{Witten:nf}
E.~Witten,
%``Dynamical Breaking Of Supersymmetry,''
Nucl.\ Phys.\ {\bf B~188} (1981) 513.
%%CITATION = NUPHA,B188,513;%%

\bibitem{GUT} S.~Dimopoulos, S.~Raby, and F.~Wilczek, 
Phys. Rev.~{\bf D~24} (1981) 1681;
%%CITATION = PHRVA,D24,1681;%%
L.E.~Ib\'a\~nez and G.G.~Ross, Phys.~Lett.~{\bf B~105} (1981) 439;
%%CITATION = PHLTA,B105,439;%%
U.~Amaldi, W.~de Boer, and H.~F\"urstenau, Phys.~Lett.~{\bf B~260} 
           (1991) 447;
%%CITATION = PHLTA,B260,447;%%
P.~Langacker and M.~Luo, Phys.~Rev.~{\bf D~44} (1991) 817;
%%CITATION = PHRVA,D44,817;%%
J.~Ellis, S.~Kelley, and D.V.~Nanopoulos, Phys.~Lett.~{\bf B~260} (1991) 161.
%%CITATION = PHLTA,B260,131;%%

\bibitem{Ibanez:fr}
L.E.~Ib\'a\~nez and G.G.~Ross,
%``SU(2)-L X U(1) Symmetry Breaking As A Radiative Effect Of Supersymmetry Breaking In Guts,''
Phys.\ Lett.\ {\bf B~110} (1982) 215.
%%CITATION = PHLTA,B110,215;%%

%\cite{Ellis:1983ew}
\bibitem{Ellis:1983ew}
J.R.~Ellis et al.,
%``Supersymmetric Relics From The Big Bang,''
Nucl.\ Phys.\ {\bf B~238} (1984) 453.
%%CITATION = NUPHA,B238,453;%%


%\cite{Carena:1997mb}
\bibitem{Carena:1997mb}
M.~Carena et al.,
%``The search for supersymmetry at the Tevatron collider,''
Rev.\ Mod.\ Phys.\  {\bf 71} (1999) 937; 
%%CITATION = ;%%
%\cite{Allanach:1999bf}
B.~Allanach et al.,
%``Searching for R-parity violation at Run-II of the Tevatron,''
;
%%CITATION = ;%%
S.~Ambrosanio et al.,
%``Report of the Beyond the MSSM subgroup for the Tevatron Run II SUSY /  Higgs workshop,''
.
%%CITATION = ;%%

\bibitem{LHC} 
 Atlas Collaboration, Technical Design Report 1999, Vol.~II,
 CERN/LHC/99-15, ATLAS TDR 15;
S.~Abdullin et al.  [CMS Collaboration],
%``Discovery potential for supersymmetry in CMS,''
J.\ Phys.\ G {\bf 28} (2002) 469.
%%CITATION = ;%%

\bibitem{LC}  P.M.~Zerwas, 
             Proceedings, 1999 Carg\`{e}se Institute for High-Energy Physics,
             ; 
%%CITATION = ;%%
H.~Murayama and M.E.~Peskin, Ann. Rev. Nucl. Part. Sci. {\bf 46},
             (1996) 533;
%%CITATION = ;%%
E.~Accomando et al., ECFA/DESY LC Working
             Group, Phys. Rep. {\bf 299} (1998) 1;
%%CITATION = ;%%
``TESLA Technical Design Report, Part III: Physics at an $e^+e^-$ 
Linear Collider,''
{\it ed.} R.Heuer, D.J.~Miller, F.~Richard and P.M.~Zerwas,
 [ECFA/DESY LC Physics Working Group Collaboration],  DESY 01--110 and
.
%%CITATION = ;%%


%\cite{Abdullin:1999zp}
\bibitem{Abdullin:1999zp}
S.~Abdullin et al.,
%``The SUSY working group: Summary report,''
.
%%CITATION = ;%%

\bibitem{Haber:1997if}
H.~E.~Haber,
%``The status of the minimal supersymmetric standard model and beyond,''
Nucl.\ Phys.\ Proc.\ Suppl.\  {\bf 62} (1998) 469;
%%CITATION = ;%%
G.~L.~Kane,
%``The supersymmetry soft-breaking Lagrangian: Where experiment and string  theory meet,''
.
%%CITATION = ;%%

\bibitem{sugra} A.H.~Chamseddine, R.~Arnowitt, and P.~Nath,
Phys.~Rev.~Lett.~{\bf 49} (1982) 970.
%%CITATION = PRLTA,49,970;%%


\bibitem{gmsb} M.~Dine and A.E.~Nelson,
Phys.~Rev.~{\bf D~48} (1993) 1277.
%%CITATION = ;%%

\bibitem{Giudice:1998xp}
L.~Randall and R.~Sundrum,
%``Out of this world supersymmetry breaking,''
Nucl.\ Phys.\ {\bf B~557} (1999) 79;
%.
%%CITATION = ;%%
%
G.F.~Giudice, M.A.~Luty, H.~Murayama and R.~Rattazzi,
%``Gaugino mass without singlets,''
JHEP {\bf 9812} (1998) 027.
%%CITATION = ;%%


%\cite{Blair:2000gy}
\bibitem{Blair:2000gy}
G.~A.~Blair, W.~Porod and P.~M.~Zerwas,
%``Reconstructing supersymmetric theories at high energy scales,''
Phys.\ Rev.\ D {\bf 63} (2001) 017703; 
%%CITATION = ;%%
 to be published in Eur.\ Phys.\ J.\ C.
%%CITATION = ;%%


%\cite{Baer:1999sp}
\bibitem{Baer:1999sp}
H.~Baer, F.~E.~Paige, S.~D.~Protopopescu and X.~Tata,
%``ISAJET 7.48: A Monte Carlo event generator for p p, anti-p p, and  e+ e- reactions,''
.
%%CITATION = ;%%


%\cite{Allanach:2001kg}
\bibitem{Allanach:2001kg}
B.~C.~Allanach,
%``SOFTSUSY: A C++ program for calculating supersymmetric spectra,''
Comput.\ Phys.\ Commun.\  {\bf 143} (2002) 305.
%%CITATION = ;%%

\bibitem{suspect} 
A.~Djouadi, J.~L.~Kneur and G.~Moultaka,
%``SuSpect: A Fortran code for the supersymmetric and Higgs particle  spectrum in the MSSM,''
.
%%CITATION = ;%%

%\cite{Allanach:2002pz}
\bibitem{Allanach:2002pz}
B.~Allanach, S.~Kraml and W.~Porod,
%``Comparison of SUSY mass spectrum calculations,''
; B.~Allanach, S.~Kraml and W.~Porod, in preparation.
%%CITATION = ;%%

%\cite{Mrenna:1996hu}
\bibitem{Mrenna:1996hu}
S.~Mrenna,
%``SPYTHIA, a supersymmetric extension of PYTHIA 5.7,''
Comput.\ Phys.\ Commun.\  {\bf 101} (1997) 232.
%%CITATION = ;%%


%\cite{Ghodbane:1999va}
\bibitem{Ghodbane:1999va}
N.~Ghodbane,
%``SUSYGEN3: An event generator for linear colliders,''
.
%%CITATION = ;%%


\bibitem{Martin:1993zk}
 S.~Martin and M.~Vaughn, Phys.~Rev.~{\bf D50}, 2282 (1994);
%%CITATION = ;%%
Y.~Yamada,  Phys.~Rev.~{\bf D~50}, 3537 (1994);
%%CITATION = ;%%
I.~Jack, D.R.T.~Jones, Phys.~Lett.~{\bf B333} (1994) 372.
%%CITATION = ;%%


\bibitem{Pierce:1996zz}
D.~M.~Pierce et al.,
%``Precision corrections in the minimal supersymmetric standard model,''
Nucl.\ Phys.\ B {\bf 491} (1997) 3.
%%CITATION = ;%%


%\cite{Degrassi:2001yf}
\bibitem{Degrassi:2001yf}
G.~Degrassi, P.~Slavich and F.~Zwirner,
%``On the neutral Higgs boson masses in the MSSM for arbitrary stop  mixing,''
Nucl.\ Phys.\ B {\bf 611} (2001) 403;
%%CITATION = ;%%
A.~Brignole, G.~Degrassi, P.~Slavich and F.~Zwirner,
%``On the O(alpha**2(t)) two-loop corrections to the neutral Higgs boson  masses in the MSSM,''
Nucl.\ Phys.\ B {\bf 631} (2002) 195;
%%CITATION = ;%%
%\cite{Brignole:2002bz}
%A.~Brignole, G.~Degrassi, P.~Slavich and F.~Zwirner,
%``On the two-loop sbottom corrections to the neutral Higgs boson masses  in the MSSM,''
Nucl.\ Phys.\ B {\bf 643} (2002) 79.
%%CITATION = ;%%

%\cite{Dedes:2002dy}
\bibitem{Dedes:2002dy}
A.~Dedes and P.~Slavich,
%``Two-loop corrections to radiative electroweak symmetry breaking in the  MSSM,''
.
%%CITATION = ;%%


%\cite{Giudice:1998bp}
\bibitem{Giudice:1998bp}
G.~F.~Giudice and R.~Rattazzi,
%``Theories with gauge-mediated supersymmetry breaking,''
Phys.\ Rept.\  {\bf 322} (1999) 419.
%%CITATION = ;%%

\bibitem{Martin}
S.P. Martin, 
%``Generalized messengers of supersymmetry breaking and the sparticle mass  spectrum,''
Phys.\ Rev.\ {\bf D~55} (1997) 3177;
%%CITATION = ;%%
%
S.~Dimopoulos, G.F.~Giudice and A.~Pomarol,
%``Dark matter in theories of gauge-mediated supersymmetry breaking,''
Phys.\ Lett.\ {\bf B~389} (1996) 37.
%%CITATION = ;%%



\bibitem{AMSBmodels}
T.~Gherghetta, G.~F.~Giudice and J.~D.~Wells,
%``Phenomenological consequences of supersymmetry with anomaly-induced  masses,''
Nucl.\ Phys.\ B {\bf 559} (1999) 27;
%%CITATION = ;%%
M.~Carena, K.~Huitu and T.~Kobayashi,
%``RG-invariant sum rule in a generalization of anomaly mediated SUSY  breaking models,''
Nucl.\ Phys.\ B {\bf 592} (2001) 164;
%%CITATION = ;%%
B.~C.~Allanach and A.~Dedes,
%``R-parity violating anomaly mediated supersymmetry breaking,''
JHEP {\bf 0006} (2000) 017;
%%CITATION = ;%%
D.~E.~Kaplan and G.~D.~Kribs,
%``Gaugino-assisted anomaly mediation,''
JHEP {\bf 0009} (2000) 048;
%%CITATION = ;%%
F.~De Campos et al.,
%``Anomaly mediated supersymmetry breaking without R-parity,''
Nucl.\ Phys.\ B {\bf 623} (2002) 47;
%%CITATION = ;%%
K.~Huitu, J.~Laamanen and P.~N.~Pandita,
%``Sparticle spectrum and constraints in anomaly mediated supersymmetry  breaking models,''
Phys.\ Rev.\ D {\bf 65} (2002) 115003.
%%CITATION = ;%%



\bibitem{cvetic}
M.~Cveti\v c et al.,
%``Target space duality, supersymmetry breaking and the stability of classical string vacua,''
Nucl.\ Phys.\ {\bf B~361} (1991) 194;
%%CITATION = NUPHA,B361,194;%%
A.~Brignole, L.E.~Ib\'a\~nez and C.~Mu\~noz,
%``Towards a theory of soft terms for the supersymmetric Standard Model,''
Nucl.\ Phys.\ {\bf B~422} (1994) 125
[Erratum-ibid.\ {\bf B~436} (1995) 747];
%%CITATION = ;%%
A.~Love and P.~Stadler,
%``The supersymmetric particle spectrum in orbifold compactifications of  string theory,''
Nucl.\ Phys.\ {\bf B~515} (1998) 34.
%%CITATION = ;%%

\bibitem{Binetruy:2001md}
%%CITATION = ;%%
P.~Binetruy, M.K.~Gaillard and B.D.~Nelson,
%``One loop soft supersymmetry breaking terms in superstring effective  theories,''
Nucl.\ Phys.\ {\bf B~604} (2001) 32.
%%CITATION = ;%%


%\cite{Bartl:2001wc}
\bibitem{Bartl:2001wc}
A.~Bartl et al.,
 and O.~Vives,
%``General flavor blind MSSM and CP violation,''
Phys.\ Rev.\ D {\bf 64} (2001) 076009.
%%CITATION = ;%%

%\cite{Kaplan:1999ac}
\bibitem{Kaplan:1999ac}
D.E.~Kaplan, G.D.~Kribs and M.~Schmaltz,
%``Supersymmetry breaking through transparent extra dimensions,''
Phys.\ Rev.\ {\bf D~62} (2000) 035010;
%%CITATION = ;%%
Z.~Chacko, M.A.~Luty, A.E.~Nelson and E.~Ponton,
%``Gaugino mediated supersymmetry breaking,''
JHEP {\bf 0001} (2000) 003.
%%CITATION = ;%%

\bibitem{ToBePublished}
W.~Porod, in preparation.


\bibitem{Hikasa:1987db}
K.~I.~Hikasa and M.~Kobayashi,
%``Light Scalar Top At E+ E- Colliders,''
Phys.\ Rev.\ D {\bf 36} (1987) 724.
%%CITATION = PHRVA,D36,724;%%

%\cite{Porod:1996at}
\bibitem{Porod:1996at}
%
W.~Porod and T.~W\"ohrmann,
%``Higher order top squark decays,''
Phys.\ Rev.\ D {\bf 55} (1997) 2907;
%%CITATION = ;%%
%
W.~Porod,
%``More on higher order decays of the lighter top squark,''
Phys.\ Rev.\ D {\bf 59} (1999) 095009;
%%CITATION = ;%%

\bibitem{djouadi3}
A.~Djouadi and Y.~Mambrini,
%``Three-body decays of top and bottom squarks,''
Phys.\ Rev.\ D {\bf 63} (2001) 115005.
%%CITATION = ;%%


%\cite{Kraml:1996kz}
\bibitem{Kraml:1996kz}
K.~I.~Hikasa and Y.~Nakamura,
%``Soft breaking correction to hard supersymmetric relations: QCD corrections to squark decay,''
Z.\ Phys.\ C {\bf 70} (1996) 139
[Erratum-ibid.\ C {\bf 71} (1996) 356];
%%CITATION = ;%%
W.~Beenakker, R.~Hopker and P.~M.~Zerwas,
%``SUSY-QCD Decays of Squarks and Gluinos,''
Phys.\ Lett.\ B {\bf 378} (1996) 159;
%%CITATION = ;%%
S.~Kraml et al.,
%``SUSY-QCD corrections to scalar quark decays into charginos and  neutralinos,''
Phys.\ Lett.\ B {\bf 386} (1996) 175;
%%CITATION = ;%%
A.~Djouadi, W.~Hollik and C.~Junger,
%``QCD corrections to scalar quark decays,''
Phys.\ Rev.\ D {\bf 55} (1997) 6975;
%%CITATION = ;%%
W.~Beenakker et al.,
%``Stop decays in SUSY-QCD,''
Z.\ Phys.\ C {\bf 75} (1997) 349;
%%CITATION = ;%%
A.~Bartl et al.,
%``SUSY-QCD corrections to stop and sbottom decays into W+- and Z0 bosons,''
Phys.\ Lett.\ B {\bf 419} (1998) 243;
%%CITATION = ;%%
J.~Guasch, J.~Sola and W.~Hollik,
%``Yukawa-coupling corrections to scalar quark decays,''
Phys.\ Lett.\ B {\bf 437} (1998) 88;
%%CITATION = ;%%
%\bibitem{Bartl:1998xp}
A.~Bartl et al.,
%``SUSY-{QCD} corrections to stop and sbottom decays into Higgs bosons,''
Phys.\ Rev.\ D {\bf 59} (1999) 115007;
%%CITATION = ;%%
J.~Guasch, W.~Hollik and J.~Sola,
%``Full electroweak one-loop radiative corrections to squark decays in the  MSSM,''
Phys.\ Lett.\ B {\bf 510} (2001) 211;
%%CITATION = ;%%
L.~G.~Jin and C.~S.~Li,
%``Supersymmetric electroweak corrections to sbottom decay into lighter  stop and charged Higgs boson,''
Phys.\ Rev.\ D {\bf 65} (2002) 035007;
%%CITATION = ;%%
H.~S.~Hou et al.,
%``Electroweak corrections to the decays of stop and gluino,''
Phys.\ Rev.\ D {\bf 65} (2002) 075019;
%%CITATION = ;%%
Q.~Li, L.~G.~Jin and C.~S.~Li,
%``Supersymmetric electroweak corrections to heavier top squark decay into  lighter top squark and neutral Higgs boson,''
.
%%CITATION = ;%%

%\cite{Bartl:2000kw}
\bibitem{Bartl:2000kw}
A.~Bartl et al.,
%``Phenomenology of stops, sbottoms, tau sneutrinos, and staus at an e+ e-  linear collider,''
Eur.\ Phys.\ J.\ directC {\bf 2} (2000) 6.
%%CITATION = ;%%


%\cite{Baer:1998bj}
\bibitem{Baer:1998bj}
H.~Baer et al.,
%``Supersymmetry reach of Tevatron upgrades: The large tan(beta) case,''
Phys.\ Rev.\ D {\bf 58} (1998) 075008;
%%CITATION = ;%%
A.~Djouadi, Y.~Mambrini and M.~M\"uhlleitner,
%``Chargino and neutralino decays revisited,''
Eur.\ Phys.\ J.\ C {\bf 20} (2001) 563.
%%CITATION = ;%%


%\cite{Bartl:1999iw}
\bibitem{Bartl:1999iw}
A.~Bartl, W.~Majerotto and W.~Porod,
%``Large Higgs boson exchange contribution in three-body neutralino  decays,''
Phys.\ Lett.\ B {\bf 465} (1999) 187.
%%CITATION = ;%%

\bibitem{glu1}
A.~Bartl, W.~Majerotto and W.~Porod,
%``Squark And Gluino Decays For Large Tan Beta,''
Z.\ Phys.\ C {\bf 64} (1994) 499
[Erratum-ibid.\ C {\bf 68} (1995) 518];
%%CITATION = ZEPYA,C64,499;%%
W.~Porod,
%``The decays gluino $\to$ stop(1) anti-b W- and gluino $\to$ stau(1) anti-c  and phenomenological implications in supersymmetric theories,''
JHEP {\bf 0205} (2002) 030.
%%CITATION = ;%%

\bibitem{Drees:1990dq}
M.~Drees and K.~I.~Hikasa,
%``Note On QCD Corrections To Hadronic Higgs Decay,''
Phys.\ Lett.\ B {\bf 240} (1990) 455
[Erratum-ibid.\ B {\bf 262} (1991) 497];
%%CITATION = PHLTA,B240,455;%%
A.~Djouadi, M.~Spira and P.~M.~Zerwas,
%``QCD Corrections to Hadronic Higgs Decays,''
Z.\ Phys.\ C {\bf 70} (1996) 427.
%%CITATION = ;%%


\bibitem{Eberl:2001vb}
%\cite{Dabelstein:1995js}
A.~Dabelstein,
%``Fermionic decays of neutral MSSM Higgs bosons at the one loop level,''
Nucl.\ Phys.\ B {\bf 456} (1995) 25;
%%CITATION = ;%%
A.~Bartl et al.,
%``QCD corrections to the decay H+ $\to$ scalar t scalar anti-b in the minimal supersymmetric Standard Model,''
Phys.\ Lett.\ B {\bf 373} (1996) 117;
%%CITATION = ;%%
%\cite{Jimenez:1995wf}
R.~A.~Jimenez and J.~Sola,
%``Supersymmetric QCD corrections to the top quark decay of a heavy charged higgs boson,''
Phys.\ Lett.\ B {\bf 389} (1996) 53;
%%CITATION = ;%%
A.~Bartl et al.,
%``QCD corrections to the decay $H~+ \to t \bar{b}$ in the Minimal Supersymmetric Standard Model,''
Phys.\ Lett.\ B {\bf 378} (1996) 167;
%%CITATION = ;%%
J.~A.~Coarasa, R.~A.~Jimenez and J.~Sola,
%``Strong effects on the hadronic widths of the neutral Higgs Bosons in the MSSM,''
Phys.\ Lett.\ B {\bf 389} (1996) 312;
%%CITATION = ;%%
A.~Bartl et al.,
%``QCD corrections to Higgs boson decays into squarks in the minimal  supersymmetric standard model,''
Phys.\ Lett.\ B {\bf 402} (1997) 303;
%%CITATION = ;%%
%\cite{Arhrib:1997nf}
A.~Arhrib et al.,
%``SUSY Higgs boson decays into scalar quarks: QCD corrections,''
Phys.\ Rev.\ D {\bf 57} (1998) 5860;
%%CITATION = ;%%
H.~Eberl et al.,
%``Improved SUSY QCD corrections to Higgs boson decays into quarks and  squarks,''
Phys.\ Rev.\ D {\bf 62} (2000) 055006;
%%CITATION = ;%%
Y.~S.~Yang and C.~S.~Li,
%``Electroweak corrections to the deacy H+ $\to$ W+ h in the minimal  supersymmetric model,''
Phys.\ Lett.\ B {\bf 497} (2001) 101;
%%CITATION = ;%%
L.~H.~Wan et al.,
%``Electroweak corrections to the charged Higgs boson decay into chargino  and neutralino,''
Phys.\ Rev.\ D {\bf 64} (2001) 115004;
%%CITATION = ;%%
H.~Eberl et al.,
%``One-loop corrections to neutral Higgs boson decays into neutralinos,''
Nucl.\ Phys.\ B {\bf 625} (2002) 372;
%%CITATION = ;%%
R.~Y.~Zhang et al.,
%``Supersymmetric electroweak corrections to the Higgs boson decays into  chargino or neutralino pair,''
Phys.\ Rev.\ D {\bf 65} (2002) 075018.
%%CITATION = ;%%

%\cite{Djouadi:mr}
\bibitem{Djouadi:mr}
A.~Djouadi,
%``Higgs Particles At Future Hadron And Electron - Positron Colliders,''
Int.\ J.\ Mod.\ Phys.\ A {\bf 10} (1995) 1;
%%CITATION = ;%%
M.~Spira,
%``QCD effects in Higgs physics,''
Fortsch.\ Phys.\  {\bf 46} (1998) 203.
%%CITATION = ;%%


%\cite{Djouadi:1997yw}
\bibitem{Djouadi:1997yw}
A.~Djouadi, J.~Kalinowski and M.~Spira,
%``HDECAY: A program for Higgs boson decays in the standard model and its  supersymmetric extension,''
Comput.\ Phys.\ Commun.\  {\bf 108} (1998) 56.
%%CITATION = ;%%

%\cite{Bartl:1997yi}
\bibitem{Bartl:1997yi}
A.~Bartl, H.~Fraas and W.~Majerotto,
%``Gaugino - Higgsino Mixing In Selectron And Sneutrino Pair Production,''
Z.\ Phys.\ C {\bf 34} (1987) 411.
%%CITATION = ZEPYA,C34,411;%%
A.~Bartl et al.,
%``Search of stop, sbottom, tau-sneutrino, and stau at an e+ e- linear  collider with s**(1/2) = 0.5-TeV to 2-TeV,''
Z.\ Phys.\ C {\bf 76} (1997) 549;
%%CITATION = ;%%
%\cite{Kraml:1999qd}
S.~Kraml,
%``Stop and sbottom phenomenology in the MSSM,''
;
%%CITATION = ;%%
%\cite{Blochinger:2002zw}
C.~Bl\"ochinger et al.,
%``Selectron pair production at e- e- and e+ e- colliders with polarized  beams,''
Eur.\ Phys.\ J.\ C {\bf 24} (2002) 297.
%%CITATION = ;%%

%\cite{Moortgat-Pick:2000uz}
\bibitem{Moortgat-Pick:2000uz}
G.~Moortgat-Pick et al.,
%``Impact of e+ and e- beam polarization on chargino and neutralino  production at a linear collider,''
Eur.\ Phys.\ J.\ C {\bf 18} (2000) 379.
%%CITATION = ;%%


\bibitem{drees1}
M.~Drees and K.~Hikasa, Phys.~Lett.~B{\bf 252} (1990) 127.
%``Scalar Top Production In E+ E- Annihilation,''
%%CITATION = PHLTA,B252,127;%%

%\cite{Eberl:1996wa}
\bibitem{Eberl:1996wa}
H.~Eberl, A.~Bartl and W.~Majerotto,
%``SUSY--QCD corrections to scalar quark pair production in $e~+ e~-$ annihilation,''
Nucl.\ Phys.\ B {\bf 472} (1996) 481.
%%CITATION = ;%%

%\cite{Freitas:2001zh}
\bibitem{Freitas:2001zh}
I.~I.~Bigi, V.~S.~Fadin and V.~A.~Khoze,
%``Stop near threshold,''
Nucl.\ Phys.\ B {\bf 377} (1992) 461;
%%CITATION = NUPHA,B377,461;%%
N.~Fabiano,
%``Estimates of threshold cross section for stoponium production at e+ e-  colliders,''
Eur.\ Phys.\ J.\ C {\bf 19} (2001) 54;
%%CITATION = ;%%
A.~Freitas, D.~J.~Miller and P.~M.~Zerwas,
%``Pair production of smuons and selectrons near threshold in e+ e-  collisions,''
Eur.\ Phys.\ J.\ C {\bf 21} (2001) 361.
%%CITATION = ;%%

%\cite{Bertolini:1990if}
\bibitem{Bertolini:1990if}
S.~Bertolini, F.~Borzumati, A.~Masiero and G.~Ridolfi,
%``Effects Of Supergravity Induced Electroweak Breaking On Rare B Decays And Mixings,''
Nucl.\ Phys.\ B {\bf 353} (1991) 591.
%%CITATION = NUPHA,B353,591;%%


\bibitem{Cho:1996we}
P.~L.~Cho, M.~Misiak and D.~Wyler,
%``$K_L \to \pi~0 e~+ e~-$ and $B \to X_s \ell~+ \ell~-$ Decay in the MSSM,''
Phys.\ Rev.\ D {\bf 54} (1996) 3329.
%%CITATION = ;%%

\bibitem{kagan}
 A.L.~Kagan and M.~Neubert, Eur.~Phys.~J.~{\bf C~7}, 5 (1999).
%%CITATION = ;%%

%\cite{Ibrahim:1999hh}
\bibitem{Ibrahim:1999hh}
T.~Ibrahim and P.~Nath,
%``CP violation and the muon anomaly in N = 1 supergravity,''
Phys.\ Rev.\ {\bf D~61} (2000) 095008.
%%CITATION = ;%%

\bibitem{Drees90} M.~Drees and K.~Hagiwara, Phys.~Rev.~{\bf D~42}, 1709 (1990).
%%CITATION = PHRVA,D42,1709;%%

%\cite{Carena:2000uj}
\bibitem{Carena:2000uj}
M.~Carena, D.~Garcia, U.~Nierste and C.~E.~Wagner,
%``b $\to$ s gamma and supersymmetry with large tan(beta),''
Phys.\ Lett.\ B {\bf 499} (2001) 141.
%%CITATION = ;%%


%\cite{Buras:2002vd}
\bibitem{Buras:2002vd}
A.~J.~Buras et al.,
%``Delta(M(d,s)), B/(d,s)0 $\to$ mu+ mu- and B $\to$ X/s gamma in  supersymmetry at large tan beta,''
.
%%CITATION = ;%%

\bibitem{Melnikov:2000qh}
K.~Melnikov and T.~V.~Ritbergen,
%``The three-loop relation between the MS-bar and the pole quark masses,''
Phys.\ Lett.\ B {\bf 482} (2000) 99;
%%CITATION = ;%%
K.~G.~Chetyrkin and M.~Steinhauser,
%``The relation between the MS-bar and the on-shell quark mass at order  alpha(s)**3,''
Nucl.\ Phys.\ B {\bf 573} (2000) 617.
%%CITATION = ;%%

%\cite{Arason:1991ic}
\bibitem{Arason:1991ic}
H.~Arason et al.,
%``Renormalization group study of the standard model and its extensions. 1. The Standard model,''
Phys.\ Rev.\ D {\bf 46} (1992) 3945.
%%CITATION = PHRVA,D46,3945;%%

%\cite{Avdeev:1997sz}
\bibitem{Avdeev:1997sz}
L.~V.~Avdeev and M.~Y.~Kalmykov,
%``Pole masses of quarks in dimensional reduction,''
Nucl.\ Phys.\ B {\bf 502} (1997) 419.
%%CITATION = ;%%

%\cite{Baer:2002ek}
\bibitem{Baer:2002ek}
H.~Baer et al.,
%``Relating bottom quark mass in DR-bar and MS-bar regularization schemes,''
Phys.\ Rev.\ D {\bf 66} (2002) 074007.
%%CITATION = ;%%

\bibitem{Carena:1999py}
M.~Carena et al.,
%``Effective Lagrangian for the anti-t b H+ interaction in the MSSM and  charged Higgs phenomenology,''
Nucl.\ Phys.\ B {\bf 577} (2000) 88.
%%CITATION = ;%%

%\cite{vanOldenborgh:1989wn}
\bibitem{vanOldenborgh:1989wn}
G.~J.~van Oldenborgh and J.~A.~Vermaseren,
%``New Algorithms For One Loop Integrals,''
Z.\ Phys.\ C {\bf 46} (1990) 425.
%%CITATION = ZEPYA,C46,425;%%


%\cite{Hahn:1998yk}
\bibitem{Hahn:1998yk}
T.~Hahn and M.~Perez-Victoria,
%``Automatized one-loop calculations in four and D dimensions,''
Comput.\ Phys.\ Commun.\  {\bf 118} (1999) 153.
%%CITATION = ;%%


%\cite{Weinberg:1980wa}
\bibitem{Weinberg:1980wa}
S.~Weinberg,
%``Effective Gauge Theories,''
Phys.\ Lett.\ {\bf B~91} (1980) 51;
%%CITATION = PHLTA,B91,51;%%
L.J.~Hall,
%``Grand Unification Of Effective Gauge Theories,''
Nucl.\ Phys.\ {\bf B~178} (1981) 75.
%%CITATION = NUPHA,B178,75;%%

%\cite{Allanach:2002nj}
\bibitem{Allanach:2002nj}
B.~C.~Allanach et al.,
Eur.\ Phys.\ J.\ C {\bf 25} (2002) 113.
%%CITATION = ;%%


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