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\begin{document}
\title{Supersymmetric Technicolour in Warped Spaces and Crooked
Places}
\author{B. Nobalma$^1$, N. Schlamoky$^2$, K. Weasel$^2$}
\institute{$^1$LAPTH, 9 Chemin de Bellevue, B.P. 110,
Annecy-le-Vieux 74951, France
\\$^2$Tate Gallery of Fundamental
Research, Trunka}
\maketitle
\begin{abstract}
We examine resonant techni-sleptons production at the LHC with
gravitinos in the final state. We investigate two cases: (i) where
the slepton undergoes gauge decay into neutralino and a lepton,
followed by the neutralino decay into a photon and a gravitino,
and (ii) direct decays of a slepton into a lepton and a gravitino.
We show how to accurately reconstruct both the slepton and
neutralino masses in the first case, and the slepton mass in the
second case for 300 fb$^{-1}$ of integrated luminosity at the LHC.
\end{abstract}
\section{INTRODUCTION}
This letter is devoted to the study of the signals at the Large Hadron
Collider (LHC) due to a supersymmetric generalisation of the Standard
Model (SM) which (a) violates $R$-parity, and (b) has an ultra-light
gravitino in its spectrum. The anomalous events in the CDF experiment
in the production rate of lepton-photon-${\not\!\!E}_{T}$ in $p{\bar p}$ collisions
were explained~\cite{Belanger:2001fz,Binoth:2005ff,Huston:2011ny}
in the framework of a
$R$-parity violating supersymmetric model with dominant
$L$-violating $\lambda'_{211}$ coupling,
and an ultra-light gravitino of mass $\sim10^{-3}$ eV.
The resonant production of a smuon via the $R$-violating coupling,
its decay into neutralino and a muon and, finally, the decay of the
neutralino into a gravitino and a photon
leads to the $\mu \gamma {\not\!\!E}_{T}$ final state studied in the CDF experiment.
The range of smuon and neutralino masses rel 25$ GeV on the
transverse energies of the muon, the photon and missing energy.
We have used the following cuts
on the rapidity of the photon and the muon: $|\eta_{\gamma,\mu}|<3$.
There is an isolation cut between the photon and other hard objects
$o$ in the
event of $\sqrt{(\eta_\gamma - \eta_o)^2 + (\phi_\gamma - \phi_o)^2}>0.7$.
Since the signal is hadronically quiet, we veto events with jets
reconstructed with $E_T>30$ GeV and $\eta_j<4$. Initial and final state
radiation effects, as well as fragmentation effects are included in the
background simulation.
\begin{figure}
\begin{center}
\includegraphics[width=0.5\textwidth]{sample_fig1}
\caption{Search reach for the $\mu \gamma {\not\!\!E}_{T}$ signal
(as defined in the
text) for
300 fb$^{-1}$ integrated luminosity at the LHC.
}
\label{search}
\end{center}
\end{figure}
We show the region of parameter space corresponding to
\footnote{The
statistical uncertainties
on fitted $a$ and $b$ parameters make a negligible difference to the
final numerical results.} $S/\sqrt{B}>5$
and $S\geq10$
for 300 fb$^{-1}$ luminosity option, as a function of smuon mass
and R-parity conserving coupling in Fig.~\ref{search}a.
We now turn to the decay ${\tilde l} \rightarrow {\tilde G} l$. We ignore
sneutrino production in this case because it would lead to an invisible
final state. We have calculated the production matrix element and
the branching ratio and implemented in a parton-level Monte Carlo.
We have used cuts in our analysis on the muon and missing transverse
energy identical
to the $\gamma \mu {\not\!\!E}_{T}$ analysis, i.e.
${\not\!\!E}_{T},E_T^\mu>25$ GeV and $|\eta_\mu|<3$.
\section*{CONCLUSIONS}
Resonant slepton production and its decays into $l \gamma {\tilde G}$ or $l
{\tilde G}$ can be discovered at the LHC for slepton masses into the multi-TeV
region, depending upon the $R_p$ violating coupling and provided that the gravitino is
ultra-light (with a mass less than 0.1 eV). Various $M_T$ distributions will
allow the accurate measurement of sparticle masses involved.
\section*{ACKNOWLEDGEMENTS}
K. Slane would like to thank CERN and LAPTh for hospitality offered
during which some of the work contained herein was performed.
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