%\addcontentsline{toc}{section}{Abstract}
\pagestyle{empty}
\vspace*{5cm}
\begin{abstract}
In the Minimal Supersymmetric Standard Model (MSSM), the simultaneous
appearance of lepton and baryon number
violation causes the proton to decay much faster
than the experimental bound allows. Customarily, a discrete symmetry known as
$R$-parity is imposed to forbid these dangerous interactions. This work
begins by arguing that there is no deep theoretical motivation for preferring
$R$-parity over other discrete symmetries and continues by 
adopting the MSSM with baryon number
conservation replacing $R$-parity conservation.
For the purpose of studying the influence of the 
consequent lepton number violating interactions, 1278 new decay channels of
supersymmetric particles into Standard Model particles 
have been included in the PYTHIA event generator.

%(enlarging the particle decay sector in the generator by a factor 1.5)
The augmented event generator is then used in combination with the
\atlfast\ detector simulation to study the impact of
lepton number violation (\LV) on event topologies in the ATLAS detector, and
trigger menus designed for \LV-SUSY are proposed based on very general
conclusions. The subsequent analysis uses a combination of primitive cuts and
neural networks to optimize the 
discriminating power between signal and background events. In all scenarios
studied, it is found that a $5\sigma$ discovery is possible for cross sections
down to $10^{-10}\mb$ with an integrated luminosity of 30\fb$^{-1}$, 
corresponding to one year of data taking with the LHC running 
at ``mid-luminosity'', $L=3\ttn{33}\scm$.
\end{abstract}
%\vfill
%{\begin{center}\includegraphics*[scale=0.25]{titlew_e.eps}\end{center}}
\section{Outlook and Conclusion\label{sec:conc}}
\subsection{Outlook}
Though some preliminary studies have been performed in the present work, many
important things remain to be done in this field. From my perspective, the
most important theoretical/phenomenological issues which remain are:
\begin{enumerate}
\item The inclusion of Baryon number violating processes in the \pythia\
  generator. In addition, this will require a study of the exceptional colour
  flows that are possible when baryon number is broken. Such a study has
  already been carried out for the \herwig\ generator (see \cite{dreiner00}),
  but it remains to be done in \pythia. 
\item The inclusion of resonant slepton and squark production in the \pythia\
generator. In \RV\ scenarios, the
  production of single sparticle resonances is possible and can extend 
the discovery potential of the LHC towards higher SUSY masses. 
\item The existence of \RV\ couplings of comparable magnitude to the
  gauge couplings would have a significant effect on the renormalization
  group evolution of the masses and couplings from the input scale to the
  electroweak. At present, \pythia\ can be told to call on \isasusy\ to
  perform this evolution, but the $R$-violating couplings are not yet included.
\end{enumerate}
On the experimental side, several studies would be advisable:
\begin{enumerate}
\item The present work has only dealt with lepton
  number violation, the signatures of which are most likely easier to
  identify than baryon number violating signatures (an excess of
  jets). Preliminary studies indicate a lessening of the reach of the LHC in
  these scenarios \cite{baer97}. 
  Therefore, dedicated studies which could push this reach to the limit would
  be advisable. These can be performed either with the present version of the 
  \herwig\ generator or with the \pythia\ generator when \BV\ has been
  included. Since the reach is lessened, it is advisable to wait with such a
  study until single squark production (an enhancing mechanism) has also been
  included. Studying only decays is likely to give too pessimistic
  predictions. Again, single sparticle production \emph{is} included in the
\herwig\ generator in its present form.
\item Having concentrated on signal isolation and discovery potential, no
mass reconstruction has been undertaken in this
work. Taking e.g.\ the events isolated by the current analysis as a basis,
it would be interesting to determine how well the SUSY mass spectrum can be
disentangled in the various scenarios. 
\item A systematic study of the consequences of hierarchical structure in the
\RV\ couplings. E.g.\ one sees that large 1$^{\mathrm{st}}$ generation
couplings will lead to electrons or electron-neutrinos in the final state
etc. It would be of interest to study how well we can expect to ``measure''
the individual \RV\ couplings. 
\item The mSUGRA points studied in this work were all based on the MSSM and
as such had a neutralino LSP. As mentioned, this is not required in
\RV-SUSY. It is therefore of some importance to study the effects of having
non-neutralino LSP's. A special case is if one imagines 
e.g.\ a slepton (or, less likely, a squark)
LSP, for which 
the three-body LSP decays studied here would be replaced by two-body
decays with the associated much simpler kinematics, allowing more precise
invariant mass reconstruction.
\item Re-evaluation of the trigger rates and of the trigger objects proposed
  here for both high and mid luminosities with better detector simulation,
  either a parametrization of the effects of pile-up at mid-luminosity in
  \atlfast\ or full detector simulation.
\item A study of to what extent the trigger
menus here proposed 
can be combined with trigger menus for other kinds of physics.
\end{enumerate}
\subsection{Conclusion}
In the first part of this work, it was seen that the most general space-time
symmetries possible in an interacting 
quantum field theory includes a symmetry between
bosons and fermions 
which is not present in the currently accepted theory,
the so-called Standard Model of Particle Physics. That this extra symmetry,
Supersymmetry, is not forbidden gave us our first motivation to study the
physical consequences of having such a symmetry in nature.
Disjoint from this, it was argued that the discovery of a
fundamental Higgs boson would lead, through the hierarchy problem, 
to a requirement of the existence of physics not contained within the
framework of the Standard Model itself. It was with the
realization that Supersymmetry could cure the hierarchy problem \emph{and} 
give a natural 
explanation for the size of the electroweak scale that we found our
second, more compelling 
motivation. It was then noted that supersymmetry is not without
defects in that it must be broken at low energies and some \emph{additional}
symmetry must exist to assure the experimentally observed high degree of 
proton stability. 

Basically, three choices for this symmetry exist: the
conservation of both lepton and baryon number or the conservation of only one of
them, in the supersymmetric interactions. 
The former is usually cast in the shape of a conserved, multiplicative
quantum number, $R$, and has the additional property of giving a natural dark
matter candidate, since it results in   
the Lightest Supersymmetric Particle (the LSP) being stable. 
The latter two do not have
this property in most of their parameter spaces. Moreover, 
they give rise to more free parameters and more complex phenomenologies, 
i.e.\ many additional production and decay mechanisms for the supersymmetric
particles. On these grounds, suppersymmetrized versions of the Standard Model
are most often found with $R$-parity conservation being implicitly assumed.

In section \ref{sec:lspdecays}, some effort was devoted to explain the
potential fallacies and the dangers of this assumption with the conclusion
that $R$-parity cannot assure proton stability when Supersymmetry is
embedded into more fundamental frameworks containing baryon and lepton number
violation exterior to Supersymmetry, as is the case, for example, 
in a wide range of Grand Unified Theories. The danger in focussing too much
on $R$-parity conserving scenarios in accelerator searches becomes clear when
one considers the ramifications of LSP decay on event topologies
in the detector. Particularly, the reduction of the missing transverse energy
signature associated with escaping LSP's in $R$-parity conserving
scenarios could be greatly reduced if $R$-parity is not
conserved. 

1278 decay modes of Supersymmetric particles into Standard Model
particles through lepton number violating
couplings in the Minimal Supersymmetric Standard Model
were therefore studied and implemented in the \pythia\ event
generator. Combining this augmented version of the generator with a crude
simulation of the ATLAS detector, trigger menus for mid-luminosity running of
the LHC were proposed and seen to have a high acceptance of supersymmetric
events in several $L$-violating SuperGravity scenarios while still giving
event rates in the 1Hz region. 

Taking these trigger menus as basis, the possibility for a 5$\sigma$
discovery after 30\fb$^{-1}$ data taking was estimated for each investigated
model, including also the $R$-conserving MSSM for reference. The analysis
was divided into two parts, the first of which consisted of
a series of cuts on kinematical and inclusive variables, placed so as to have
good background rejection factors
while accepting 
events from as many of the various SUSY models as possible (excepting
the MSSM scenarios used only as reference). The second part consisted of
processing the remaining events through three neural networks trained to
recognize $R$-conserving scenarios and two different variants of lepton
number violating scenarios. For cross sections down to \tn{-10}\mb\ it was
found that a $5\sigma$ discovery was possible for all scenarios with
30\fb$^{-1}$ of data. It is not estimated that uncertainties related to QCD
parameters or pile-up in the detector, both of which have not been taken into
account in the present analysis, could significantly affect this conclusion.
\vfill
\begin{center}
\textbf{Acknowledgements}
\end{center}
I am deeply grateful to my two supervisors, both for their excellent 
guidance and for having allowed me a considerable freedom in what I have
occupied myself with this last year. In many ways, the master thesis is
likely to be the only chance a student gets to
learn about and discuss within so few pages so many aspects of
his/her field, here from quantum gravity effects on
global symmetries through supersymmetric phenomenology, 
Monte Carlo simulations, and detector studies to 
brain-damaged neural networks (though of
course not one of these subjects has been treated in as much detail as it might
deserve). From my perspective, such freedom is a luxury,
and I am very happy to have found it in carrying out this work. On the same
note, I thank all the members of the HEP group at NBI for discussions, an
inspiring atmosphere, and for the $n\to\infty$ CPU hours I spent on the
farm. In addition, I would like to thank Dr.\ Alexander Khodjamirian for the depth of
physical insight he gave to me before I embarked on this work.
Lastly, I would like to thank Paula Eerola and 
the Nordic Academy for Advanced Studies for having made it possible
for me to stay in Lund on a regular basis through the spring of 2001.
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\vspace*{7cm}
\begin{center}
\parbox{0.8\textwidth}{\large \emph{
Once, this Earth was haunted 
by the flaming angels of elusive gods and by magic that seemed to move the
heavenly spheres. 
These mythic tales seem but superstitious fantasy,
despite their depth of colour, to the rational and sane of an enlightened
society. And yet this universe appears to the inquisitive mind still so
enigmatic, so full of the very mystery that breathed life and beauty into our
earliest imagination that man's greatest tragedy would be to dull his senses and
not still, despite the limits of his Earthly mind, seek to grasp the nature
of that which brought him forth.}}
\end{center}
\vspace*{-0.5cm} \begin{center}
{\sc P\!\ e\!\ t\!\ e\! r\!\ \!\ \!\ Z\!\ e\!\ i\!\ l\!\ e\!\ r\!\ \!\ \!\
S\!\ k\!\ a\!\ n\!\ d\!\ s}\\ \ \\
\textbf{\huge {\color{ddblue}{\boldmath $L$-Violating}}
{\color{ddblue}Supersymmetry\vspace*{5mm}}}\\ {\large 
\mbox{\sc implementation in pythia and study of lhc discovery 
potential}}\vspace*{5.mm}\\\normalsize \setlength{\unitlength}{0.1cm} 
\vspace{4.4cm} 
\includegraphics*[scale=2.7]{logo2.eps}\vspace*{0.04cm}\\
%\hspace*{1.2cm}
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%\hspace*{1.2cm} \includegraphics*[scale=0.25]{ptmiss.epsi}\\
%\setlength{\unitlength}{1.6mm}
%\vspace*{-9.8cm}\input{figchidecay}\\
{\normalsize\color{black}\sc thesis for the degree}
\vspace*{0.1cm}\\
{\normalsize\color{black}\sc candidatus scientiarum in physics}\vspace*{0.1cm}\\
\vfill 
%\raisebox{2cm}
%\raisebox{2cm} 
{\color{black}\sc \normalsize{July 28, 2001}} \vspace*{0.1cm}\\ 
%\raisebox{2cm}
{\normalsize{\color{black}\sc NIELS BOHR INSTITUTE}}\vspace*{0.1cm}\\ 
%\raisebox{2cm}
{\normalsize{\color{black}\sc Department for Experimental High Energy Physics}}
\end{center}
%\raisebox{12cm}{\hspace*{-2cm}\includegraphics*[scale=0.7]{ptmiss.epsi}}
\clearpage 

\noindent
This thesis is submitted for evaluation in accordance with the requirements
  for obtainment of the degree of Cand.\ Scient.\ 
in physics at the Niels Bohr Institute, University of Copenhagen. 
\vspace{0.3cm}

\noindent
I am very grateful to 
the L\o rup foundation, the Nordic Academy for Advanced
Study (NorFA), and the Niels Bohr Institute (the HEP group in particular) for
financial support. 
In addition, I would like to thank the 
University of Rostock and the Volkswagen Stiftung, the
University of Uppsala and the Nobel Comittee, the University of Oslo, 
the CTEQ/IPPP Summer School 2001, 
and the THEP group at Lund University. \vspace*{0.2cm}

\noindent \texttt{Mathematica} is a copyrighted program, trademark of Wolfram Research,
Inc. 

\noindent Version numbers for publically available programs used in this work
are -\pythia\ v.6.155, \isajet\ v.7.51, \herwig\ v.6.2, and \atlfast\ v.2.53.

\begin{center}
\vspace*{1.6cm}\setlength{\extrarowheight}{6pt}
\begin{tabular}{c} 
\textbf{Internal Supervisor (NBI):}\\ John Renner Hansen 
\\ Niels Bohr Institute (HEP), University of Copenhagen 
\\ Blegdamsvej 17 DK-2100 Copenhagen \O  
\\ renner@nbi.dk \end{tabular}\\
\vspace*{0.8cm}
\begin{tabular}{c} 
\textbf{External Supervisor (Lund):}\\
Torbj\"{o}rn Sj\"{o}strand\\
Dep.\ of Theoretical High Energy Physics, Lund University,  \\
P.O. Box 118 SE-221 00 Lund\\
Torbjorn.Sjostrand@thep.lu.se
\end{tabular}\vspace*{2.5cm}
\vfill
 \rule{2.in}{0.01in} \\ 
\mbox{Peter Z. Skands}\\
%151177-2547 \\
\end{center}

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