\documentstyle{cmspaper} \RequirePackage{graphicx} \RequirePackage{multirow} \RequirePackage{axodraw} \begin{document} \begin{titlepage} \analysisnote{2006/003} \date{23 March 2006} \title{ Trilepton final state from neutralino-chargino production in mSUGRA.} \begin{Authlist} ~W.~de Boer, ~M.~Niegel, ~C.~Sander, ~V.~Zhukov\Aref{*}\Aref{b} \\ \vspace{0.5cm} { \sl IEKP, University Karlsruhe, Germany} \\ \vspace{0.5cm} ~K.~Mazumdar \\ \vspace{0.5cm} {\sl Tata Institute of Fundamental Research, Mumbai, India} \Anotfoot{*}{Valery.Joukov@cern.ch} \Anotfoot{b}{On leave from SINP MSU} \end{Authlist} \begin{abstract} The direct production of neutralino-chargino $\chi^0_2 \chi^\pm_1$ pairs in the mSUGRA scenario with decays into pure trilepton final states has a significant cross section for low neutralino masses. The trilepton signature was studied with the full and fast CMS detector simulations. The 5$\sigma$ signal can be observed in the dilepton invariant mass distribution at the integrated luminosity of 30 fb$^{-1}$ for $m_{1/2}<180$ GeV/c$^2$. \end{abstract} \end{titlepage} \setcounter{page}{2}%JPP \section{Introduction} % mSUGRA discovery channels The decays of neutralino $\chi^0_2$ into an Opposite Sign Same Flavor (OSSF) lepton pair is one of the possible mSUGRA discovery signatures at the LHC. The neutralinos are abundantly produced in gluino and squark cascade decays with a multijet and large missing transverse energy final state. However for low neutralino masses, corresponding to low values of $m_{1/2}<300$ GeV, the neutralinos can be produced directly, together with charginos: $pp\rightarrow \chi_2^0\chi_1^{\pm}$. This is a weak process and corresponds to the Standard Model (SM) reaction ${\rm pp \rightarrow WZ}$ where the trilepton final state results from the leptonic decays. In case of SUSY the final state has in addition the lightest neutralino either in three body decays: $\chi_2^0\rightarrow \chi_1^0 \ell^+\ell^-$ and chargino; ~$\chi_1^\pm\rightarrow \chi_1^0 \ell^{\pm}\nu$ or in two body decays; $\chi_2^0\rightarrow \ell\tilde \ell\rightarrow \ell\chi_1^0 \ell$ and ~$\chi_1^\pm\rightarrow \ell\tilde\nu\rightarrow \ell\chi_1^0\nu$, ~$\chi_1^\pm\rightarrow\nu\tilde \ell\rightarrow \nu\chi_1^0 \ell$ ~\cite{cmsin039}. The main signature of this reaction is two OSSF isolated leptons plus one of any flavor along with the absence of hard jets in the final state. The invariant mass of the OSSF dileptons exhibits a particular triangular shape with the kinematic end point depending upon the event topology: either $M_{\ell\ell}^{max}$=$m_{\chi_2^0}-m_{\chi_1^0}$ for three body or $M_{\ell\ell}^{max}$=$\sqrt{(m^2_{\chi_2^0}-m^2_{\tilde \ell})(m^2_{\tilde \ell}-m^2_{\chi_1^0})/m^2_{\tilde \ell}}$ for two body decays. \par The trilepton channel has been intensively searched for at the Tevatron ~\cite{fnal} with a negative result for $L_{int} \sim 300$ pb$^{-1}$. During the coming years the Tevatron will be able to investigate this channel with higher luminosity, thus probing high cross section region at low $m_0,m_{1/2}$ region further. The interest in the low $m_{1/2}$ region has been boosted by the recent observation, that the observed excess of diffuse Galactic gamma rays can be explained by the annihilation of the relic neutralino with $m_{\chi^0_1}<100$ GeV/c$^2$ \cite{dmegret}. \par In this paper a study of the CMS discovery potential for the mSUGRA pure trilepton final state at low value of $m_{1/2}$ is presented using full and fast detector simulation. In Section 2 the cross sections and event generation are discussed. Section 3 is dedicated to the detector simulation and event reconstruction framework. The event selection and background suppression is described in the Sections 4 and 5. Section 6 discusses the signal significance and the uncertainties. The CMS discovery reach for a luminosity of 30 fb$^{-1}$ is presented in Section 7. \section{Cross sections and data samples} The signal and background cross sections were calculated with {\tt ISASUGRA~7.69} and {\tt PYTHIA~6.225}(CTEQ5L) at leading order(LO). The NLO corrections have been taken into account by multiplying with the K factor. Full MC signal and background data samples for an integrated luminosity of $L_{int}=30$ fb$^{-1}$ have been generated with CMKIN~4.0.0 . The detector performance was simulated with the full GEANT model (OSCAR~3.7.0+ORCA~8.7.3) and with the fast simulation (FAMOS~1.3.2). The low luminosity pile-up events have been added to the samples. Most of the data samples have been accessed or produced via GRID. In total $\sim$ 10$^7$ events have been analyzed. \subsection{Signal} The neutralino-chargino mass spectrum and their production rates are defined in mSUGRA by the mass parameters $m_0, m_{1/2}$. The neutralino and chargino masses are approximately given by: $m_{\chi^0_1} \sim 0.4 m_{1/2}$, ~ $m_{\chi^0_2}\sim m_{\chi_1^\pm}\sim 0.8 m_{1/2}$ and the production cross section $\sigma(\chi^0_2\chi_1^{\pm})\propto m_{1/2}^{-4}$. Here only the $\chi^0_2 \chi^\pm_1$ pairs were studied, the cross section for heavier neutralinos and charginos ($\chi^0_3,\chi^0_4,\chi_2^\pm $) is an order of magnitude smaller and was not considered. For the trilepton final state the $\chi_2^0$ and $\chi_1^{\pm}$ have been forced to decay to electrons or muons without any kinematic preselection. The decays into $\tau$'s produces soft leptons and would require a separate study. At relatively large $m_0>$100 GeV/c$^2$ the neutralino $\chi_2^0$ decays via off-shell Z$^*$ with subsequent decay into leptons~($e$, $\mu$) with a typical branching Br$(\chi_2^0\rightarrow ll\chi_1^0)\sim3\% \times2$. The chargino $\chi_1^{\pm}$ decays to leptons with Br$(\chi_1^{\pm} \rightarrow \ell\nu\chi_1^0)\sim11\% \times2$ via W$^*$. The rest of decays is going into quarks. For two body decays, at $m_0<100$ GeV/c$^2$, the total branching to sleptons ($\tilde e^\pm$, $\tilde \mu^\pm$) and further to leptons is Br$(\chi_2^0\rightarrow \ell \tilde \ell)\sim2.7\% \times 4$. The rest of decays are mostly to staus. The neutralino with $m_{\chi^0_2}>m_{\chi^0_1}+m_h$ ($m_{1/2}> $300 GeV/c$^2$) can decay into a light Higgs boson $\chi_2^0 \rightarrow \chi_1^0 h$, however the production cross section is small and this channel was not analyzed. \par Figure ~\ref{fig:cs3l} shows the trilepton cross section (LO) in the $m_0$, $m_{1/2}$ plane for the tan$\beta$= 10 and 50. The trilepton cross section can be a substantial part of the total SUSY cross section at large $m_0$ values. The three body decays are dominant over most of the $m_0$, $m_{1/2}$ plane except for tan$\beta \le 20$ and $m_0<$100 GeV. The kinematic end point in the invariant mass is $M^{max}_{\ell\ell}\sim 0.42*m_{1/2}-18.4$ GeV/c$^2$~ (for $m_0\sim 1000$), thus moving into the Z-peak for $m_{1/2}>$250 GeV/c$^2$. For larger $m_{1/2}>300$GeV/ c after the Z-peak, the trilepton production cross section is below 1fb$^{-1}$ and would require $L_{int}>1000$ fb$^{-1}$. The $m_0$, $m_{1/2}$ plane is constrained for the low $m_{1/2}$ and $m_{0}$ by the mass limits on the light Higgs boson ($m_h>114.3$ GeV/c$^2$ ) from LEP and the limit on $b\rightarrow s\gamma$ ([3.43$\pm$0.36] 10$^{-4}$) branching ratio from BaBar, CLOE and BELL. The constraints on the chargino mass ($m_{\chi_1^{\pm}}>103$ GeV/c$^2$) limits $m_{1/2}$ from below for all $m_0$. The region excluded by the electroweak symmetry breaking (EWSB) requirements is indicated on Fig. ~\ref{fig:cs3l} as well. \begin{figure}[hbtp] \begin{center} \includegraphics[width=0.48\textwidth]{Plots/tb10_cs.eps} \includegraphics[width=0.48\textwidth]{Plots/tb50_cs.eps} \caption[]{ Trilepton cross section(LO) from direct neutralino-chargino production for two values of tan$\beta$=10(left) and 50(right). } \label{fig:cs3l} \end{center} \end{figure} % also maybe all total by PROSPINO % correct numbers \begin{table}[htb] \caption[]{Trilepton cross sections for the CMS benchmark points} \label{tab:cslm} \begin{center} \begin{tabular}{|l|l|l|l|l|c|c|c|} \hline &$m_{1/2}$ & $m_0$ & tan$\beta$ & $\sigma^{LO}_{tot}$ & $\sigma^{LO}\times BR3l(e,\mu) $ & $\sigma^{NLO}\times BR3l(e,\mu)$ & M$_{ll}^{max}$ \\ & [GeV/c$^2$]&[GeV/c$^2$]& & [pb] & [pb] & [pb] & [GeV/c$^2$] \\ \hline LM1 & 250 & 60 & 10 & 42 & 0.062 & 0.088 & 81 \\ LM2 & 350 & 175 & 35 & 7.3 & 1.8 10$^{-4}$ & 2.2 10$^{-4}$ & - \\ LM3 & 240 & 330 & 20 & 3.1 & 0.0094 & 0.012 & 82.3 \\ LM4 & 285 & 210 & 10 & 18.8 & 0.009 & 0.012 & 91.2 (Z) \\ LM5 & 360 & 230 & 10 & 6.0 & 0.8 10$^{-3}$ & 1.0 10$^{-3}$ & 91.2 (Z) \\ LM6 & 400 & 85 & 10 & 4.0 & 0.022 & 0.028 & 76.7 \\ LM7 & 230 & 3000 & 10 & 8.4 & 0.039 & 0.051 & 55.3 \\ LM8 & 300 & 500 & 10 & 8.9 & 0.008 & 0.01 & 91.2 (Z) \\ LM9 & 175 & 1450 & 50 & 24.6 & 0.095 & 0.125 & 52.2 \\ \hline \end{tabular} \end{center} \end{table} Table ~\ref{tab:cslm} presents cross sections for the Low Mass (LM) CMS benchmark points and values for the kinematic end point of the dilepton invariant mass M$_{\ell\ell}$. The NLO K factor was calculated with PROSPINO~\cite{prospino} and is decreasing from 1.30 at $m_{\chi^0_2}=150$ GeV/c$^2$ to 1.25 at $m_{\chi^0_2}=300$ GeV/c$^2$. The trilepton signal has non negligible cross section for the LM9, LM7, LM3 (three body) and the LM1, LM6 (two body) points. For the LM4, LM5 and LM8 the neutralino decays via on-shell Z and cannot be distinguished from the background or decays to the light Higgs boson $h_0$. For LM2 the neutralinos and charginos decay mostly into staus and $h_0$ and this point was not analyzed. Figure ~\ref{fig:invmasslm} shows the expected invariant mass of the OSSF leptons for different points at $L_{int}=30$fb$^{-1}$. The OSSF leptons required to be inside the acceptance of $|\eta | <2.4$ and to have a transverse momentum of P$_T>3(5)$GeV/c for muons(electrons) pairs. The LM9 point has the largest cross section and was used as a reference in this analysis (called signal thereafter), for the 30fb$^{-1}$ $\sim$3700 events are expected. The selection criteria have been tuned to this point, the 2 body region at low $m_0$ may require another optimization. The LM9 data sample was generated using both, full and fast simulations. Other benchmark points and the SUSY scan over the $m_0$, $m_{1/2}$ plane have been done with the FAMOS. \begin{figure}[hbtp] \begin{center} \includegraphics[width=0.5\textwidth]{Plots/complm.eps} \caption[]{ Invariant mass of OSSF leptons from $\chi^0_2$ decay at generator level for different benchmark points at $\int L=30$ fb$^{-1}$. } \label{fig:invmasslm} \end{center} \end{figure} \subsection{Backgrounds} Any reaction which can produce the OSSF lepton pair with sufficiently high P$_T$ can be a potential background for the trilepton final state. The background channels can be divided into a few groups: \begin{itemize} \item Direct production of vector bosons ${\rm ZW}$ and ${\rm ZZ}$ with leptonic decay of Z and W bosons. These channels can be suppressed by excluding the ${\rm Z}$ boson invariant mass for the OSSF leptons. \item ${\rm t \bar t}$, ${\rm Wt}$+jets , ${\rm WW}$+jets channels. The OSSF leptons originate from different decays and the third lepton appears from a jet not vetoed by the jet veto and having either an isolated lepton or a large electromagnetic component. The central jet veto removes part of these backgrounds. \item SUSY background is coming from the cascade decays with leptons not from the neutralino decays. In this study the inclusive mSUGRA channel for LM9 point except the direct neutralino-chargino production have been considered as the SUSY background. \item Drell Yan(DY) and ${\rm Z+}$jets, $\rm Z\rm b \bar b$ produces a high P$_T$ OSSF lepton pair from Z or gamma decays. The ${\rm Z+}$jets are acquiring the third lepton from jets. For the DY the third lepton is coming from the jets produced from the initial state radiation (ISR) gluon splitting into the ${\rm q \bar q}$ pair. Most of isolated leptons($\sim75\%$) are produced from ${\rm b \bar b}$ with $b\rightarrow l+jets$. The lepton's isolation and the veto on the Z peak reduce part of this background but due to large cross sections ($\sigma_{\rm Z+jets, DY}\sim$ 10 nb) , the DY and Z+jets channels can be the most important. Since it is diffiuclt to simulate the full samples, the generator level preselection is required. \item W+jets and QCD acquire missing leptons from jets. The large cross section prevents the detailed analysis of these channels. In this study only estimation is presented. \end{itemize} The background cross sections have been calculated at LO with PYTHIA plus TopReX(${\rm t\bar t}$, ${\rm W t}$) or ALPGEN($\rm Z\rm b \bar b$) and corrected to NLO with the K factors~\cite{nlo}. For all backgrounds the $\rm Z$ and $\rm W$ bosons were forced to decay leptonically to $e,\mu$ and $\tau \rightarrow e,\mu $. No kinematic cuts have been used except for the ${\rm Z}$+jets, DY and $\rm Z\rm b \bar b$, where three leptons were preselected at the generator level to have P$_T>$5 GeV/c and $|\eta|<$2.4. The ${\rm ZZ}$, ${\rm ZW}$ and partially the ${\rm t\bar t}$ channels have been analyzed using the existing DST data samples from the full CMS simulations ($jm03\_ZWjets\_leptonic, jm03\_ZZ, jm03\_TTbar\_leptonic, jm03\_qcd, jm03\_Wjets$ ). Larger statistics was simulated for all backgrounds using FAMOS. The FAMOS samples have been verified with the smaller ($\sim10^4$ events) ORCA DST samples available from CMS ($jm03\_Zjets\_, jm03\_WWjets\_leptonic, mu03\_dy\_2m$) or produced locally. A summary of the background cross sections and used statistics is presented in Table ~\ref{tab:bkgdata}. After reconstruction the fake leptons can appear which can increase both, number of background channels and,in case of preselections, number of background events in each channel. For example in case of the large fake rate the W+jets and QCD can be not negligible. In this case the generator level preselection will underestimate the background for the DY, Z+jets channels. The detailed study of fakes would require simulation of large data samples in full simulation and is out of the scope of the current paper, here only estimations are presented based on the FAMOS reconstruction. In the other hand the fake rates depend on the simulation model and the reconstruction algorithms which are expected to be significantly improved after beginning of the LHC operation and the estimation may be considered as an upper limits. \begin{table}[htb] \caption[]{Background cross sections and list of data samples used in the analysis.} \label{tab:bkgdata} \begin{center} \begin{tabular}{|l|c|c|c|c|} \hline channel & $\sigma \times BR (e,\mu,\tau)$ [pb] & Nev, 30$$fb$^{-1}$ & DST & FAMOS \\ \hline ZW & 1.68$^{NLO}$ & 5 10$^4$ & 5.~10$^4$ & 2.~10$^5$ \\ ZZ & 0.16$^{NLO}$ & 4800 & 10$^4$ & 2.~10$^5$ \\ ${\rm t\bar t}$ & 88 $^{NLO}$ & 2.6 ~10$^6$ & 3.~10$^5$ & 2.6~10$^6$ \\ ${\rm Wt+}$ jets & 10$^{NLO}$ & 3 10$^5$ & 1.~10$^5$ & 1.~10$^6$ \\ SUSY(LM9) & 13.1$^{NLO}$ & 4 10$^5$ & 10$^4$ & 5.~10$^5$ \\ WW+jets & 19.8$^{LO}$ & 6 10$^5$ & 10$^4$ & 4.~10$^5$ \\ $Z b \bar b$ 3lept. & 2.8 $^{LO}$ & 8.4 10$^4$ & - & 7.1 10$^4$ \\ ${\rm Z+}$jets 3lept. & 15.4 $^{LO}$ & 4.6~10$^5$ & 10$^4$ & 9.2~10$^5$ \\ DY 3lept. & 15.1 $^{LO}$ & 4.5~10$^5$ & 10$^4$ & 8.5~10$^5$ \\ W+jets($>30GeV/c$) & 1.8~ 10$^{4}$ $^{LO}$ & 5.4~10$^8$ & 10$^5$ & 5 10$^5$ \\ QCD($>50GeV/c$) & 2.4~10$^{7}$ $^{LO}$ & 7.4~10$^{11}$ & 5 10$^4$ & 10$^6$ \\ \hline \end{tabular} \end{center} \end{table} \section{Event reconstruction} The simulated signal and background events have been reconstructed with the CMS software ORCA 8.7.3 and FAMOS 1.3.2 using a similar code and the standard reconstruction algorithms. \subsection{Trigger} All events have required to pass L1 and HLT triggers. Table ~\ref{tab:L1trigger} shows how the trilepton signal events (LM9) are distributed among different L1 streams before and after offline selection, which will be discussed in the following sections. The dimuons and the single muons are the main L1 trigger channels where the trilepton state is expected. The single electron and dielectrons streams are less populated due to higher thresholds. Some of the electrons can also be identified as $\tau$s, populating the $\tau$ streams. The increase of the muons channels after offline selection is due to the higher threshold used in the offline selection. The presented rates are inclusive, the exclusive rates are shown for some channels in brackets. \begin{table}[htb] \caption[]{L1 trigger streams for the LM9 mSUGRA point before and after offline selection.} \label{tab:L1trigger} \begin{center} \begin{tabular}{|c|c|c|c|c|} \hline bit & L1 stream & threshold(LL) GeV/c or GeV & $\%$ before selection & $\%$ offline selected (excl.) \\ \hline 0 & single $\mu$ & 14 & 64 & 90 (0.2) \\ 1 & 2 $\mu$ & 3 & 41 & 74 (0.8) \\ 2 & single $e/\gamma$ & 20 & 50 & 45 (0.2) \\ 3 & 2 $e/\gamma$ & 17 & 29 & 25 (5) \\ 4 & 2 $e/\gamma$ rel.. & 17 & 19 & 22 \\ 5 & $\mu+e/\gamma$ & 5+15 & 30 & 48 \\ 20 & $\mu +jet$ & 5+30 & 5 & 1.0 \\ 22 & $\mu + \tau$ & 5+25 & 21 & 34 \\ 23 & $\mu +MET$ & 5+45 & 10.5 & 17 \\ 26 & $e/\gamma+\tau$ & 14+52 & 12 & 11 \\ 30 & $\tau +MET$ & 35+40 & 16.5 & 20 \\ \hline \end{tabular} \end{center} \end{table} For the HLT the Low Luminosity (LL) menu {\sl 2$\times$1033HLT.xml} from ORCA 8.7.3 has been used. The distribution of the LM9 signal in HLT channels before and after offline selection is presented in Table ~\ref{tab:HLTtrigger}. The HLT algorithms and thresholds are still under optimization and the presented results are only indicative. \begin{table}[htb] \caption[]{HLT streams for the LM9 point before and after offline selection.} \label{tab:HLTtrigger} \begin{center} \begin{tabular}{|c|c|c|c|c|} \hline bit & HLT stream & threshold(LL) GeV/c & $\%$ & $\%$ offline selected \\ \hline 2 & single $e$ & 26 & 41 & 38 \\ 6 & 2 $e$ & 14.5 & 24 & 24 \\ 13 & 2 $e$ relax & 21.8 & 14 & 14 \\ 43 & $\mu$ & 19 & 56 & 82 \\ 54 & 2 $\mu$ & 7 & 37 & 70 \\ 88 & $e+\tau$ & 16+52 & 8 & 5 \\ 102 & $\mu + \tau$ & 15+40 & 7.5 & 13 \\ \hline \end{tabular} \end{center} \end{table} The cumulative dimuon and dielectron streams trigger efficiency for the LM9 is $E(L1+HLT)=8+91\%=78\%$. More details about the trigger efficiencies for the signal and backgrounds are presented in Table ~\ref{tab:cutsum}. The trigger efficiency depends on the kinematics of the leptons which in turn depends on the mSUGRA parameters. The triggers (L1+HLT) efficiency for the mSUGRA trileptons in the $m_0$, $m_{1/2}$ plane is presented in Figure ~\ref{fig:scantrigeff}. The scan was produced in FAMOS where the selection cuts have been applied to the offline reconstructed leptons and the trigger efficiency was normalized to the trigger efficiency at LM9 point obtained from the full simulation. For the large $m_{1/2}$ values the produced leptons are harder and the trigger efficiency is increasing, partially compensating a decrease in the cross section. \begin{figure}[hbtp] \begin{center} \includegraphics[width=0.45\textwidth]{Plots/tb10_Eff.eps} \includegraphics[width=0.45\textwidth]{Plots/tb50_Eff.eps} \caption[]{Trigger efficiency (L1+HLT) in mSUGRA $m_{0}$, $m_{1/2}$ plane for tan$\beta$=10(left) and 50(right).} \label{fig:scantrigeff} \end{center} \end{figure} \subsection{Leptons} The leptons in this analysis are used for the event selection and reconstruction of invariant masses. In the CMS the muons reconstruction efficiency depends on the P$_T^{\mu}$ and is above 80$\%$ for P$_T>$5 GeV/c. The muon momentum resolution in the CMS Muon system plus tracker is $\le 1.5\%$ for these energies. For electrons the reconstruction efficiency is defined by the ECAL thresholds and amounts to $\sim$80$\%$ at E$^e>10$ GeV. The electron momentum resolution using the combined Tracker and ECAL measurements is $\le 5\%$. %For electrons \par The muons have been reconstructed in ORCA and FAMOS with similar methods: {\sl GlobalMuonReconstructor} and {\sl FamosL3MuonReconstructor}, respectively. The isolation of the reconstructed muons has been done with the {\sl MuIsoByTrackerPt} and {\sl MuIsoByCaloEt} algorithms in the cone $\Delta R=\sqrt{\Delta\eta^2+\Delta\phi^2} <0.3$; the sum of the transverse track momenta (P$_T^{track}>0.8$ GeV/c) in this cone has to be less than 1.5 GeV/c and the sum of the transverse energy deposition in the calorimeter has to be less than 5 GeV. In Figure ~\ref{fig:lpt} the P$_T$ distribution of the MC tagged muon from the $\chi^{\pm}_1$ decay is plotted at generator level and after reconstruction with ORCA or FAMOS. The reconstruction efficiency of such muons with P$_T^{\mu}>5$ GeV/c and $\eta<$2.4 is listed in Table ~\ref{tab:leptons} for the events accepted by the trigger. In FAMOS a somewhat better efficiency is expected due to offline trigger selection. The P$_T$ distribution of muons ordered by P$_T$ is shown in Figure ~\ref{fig:leptons} for the signal and important backgrounds. A small peak at low P$_T$ for the highest P$_T$ muons corresponds to the single muon events, like $2e+\mu$. From Figure ~\ref{fig:leptons} it is clear that the first two highest P$_T$ muons can be selected with the trigger cuts ($>7$ GeV/c) but the third muon also should be relatively hard. \begin{figure}[hbtp] \begin{center} \includegraphics[width=0.9\textwidth]{Plots/lpttag.eps} \caption[]{Left: Normalized P$_T$ distribution of the generated and reconstructed muons from the $\chi^{\pm}_1$ decay in ORCA and FAMOS. Right: The P$_T$ distribution of the generated and reconstructed electrons from the $\chi^{\pm}_1$ decay. } \label{fig:lpt} \end{center} \end{figure} \begin{figure}[hbtp] \begin{center} \includegraphics[width=0.44\textwidth]{Plots/mpt.eps} \includegraphics[width=0.44\textwidth]{Plots/ept.eps} \caption[]{ Normalized P$_T$ distributions of the muons (left) and electrons (right) for the signal (LM9) and backgrounds, ordered by P$_T$.} \label{fig:leptons} \end{center} \end{figure} \par For electrons the offline {\sl ElectronCandidate} method was used for both, ORCA and FAMOS. For the final electron identification the {\sl ElectronLikelihood } selection was applied with the $eleID>0.65$ together with the other cuts: $\frac{E_{HCAL}}{E_{ECAL}}<0.05$, $E/P\in [0.9,1.5]$, $|1/E-1/P|<0.02$. The isolation by tracks requires $\sum P_t <$1.5 GeV/c in the cone $\Delta R <$0.3 similar to the muons. The P$_T$ distribution of electrons from the $\chi^{\pm}_1$ decay tagged by MC is shown in Figure ~\ref{fig:lpt}. A summary of the electron identification efficiencies is presented in Table ~\ref{tab:leptons}. The electron identification efficiency is slightly worse at low momentum in FAMOS because the cuts have been tuned to the full ORCA simulation. The P$_T$ distribution of electrons and muons ordered by P$_T$ is shown in ~\ref{fig:leptons} for the signal and backgrounds. Again, as for the muons, the lowest P$_T$ electron is important for the background suppression. \begin{table}[htb] \caption[]{Lepton reconstruction efficiencies for the signal in ORCA and FAMOS. } \label{tab:leptons} \begin{center} \begin{tabular}{|c|c||c|} \hline & ORCA & FAMOS \\ \hline \hline muons (P$_T>$ 5 GeV/c) & $GlobalMuonReconstructor$ & $FamosL3MuonReconstructor$ \\ reconstruction efficiency, $\%$ & 96 & 97.5 \\ efficiency after isolation , $\%$ & 78 & 83 \\ \hline \hline electrons (P$_T>$ 10 GeV/c) & $ElectronCandidate$ & $ElectronCandidate$ \\ reconstruction efficiency , $\%$ & 88 & 85 \\ efficiency after isolation, $\%$ & 66 & 61 \\ \hline \end{tabular} \end{center} \end{table} \subsection{Jets} The central jets with $|\eta| <$2.4 have been used to suppress the backgrounds, which contain jets. The signal and intrinsic backgrounds without jets ${\rm (Z, ZW, DY)}$ can also have some central jets from the initial or final state radiation or from the pile up events. In case of pile up the jet's veto can reduce the statistics for such channels by $\sim 10\%$ at low luminosity and up to $40\%$ at high luminosity. The jet reconstruction efficiency and the energy resolution drop rapidly with decreasing energy: for E$_T^{jets}<$20 GeV the efficiency is getting below 50$\%$ and the energy resolution degrades to $\sim40\%$. Such jets have a large contamination from the calorimeter's noise, underlying events and pile up. Nevertheless they can be used to estimate the hadronic activity in an event. \par The jets have been reconstructed in ORCA and FAMOS from the {\sl EcalPlusHcalTowerInput} with the {\sl IterativeCone} algorithm and with the seed energy $E_T^{seed}>0.5$GeV in the cone $\Delta R <$0.5. The energy of the jets was corrected using calibration from {\sl GammaJet}. The contamination of the jets at $|\eta | <$1 from the noise was reduced by applying a threshold on the seed energy of the jets $E^{seed}>0.8$ GeV. The jet was removed from the list if it matches within the $\Delta R<0.3$ cone with the reconstructed electrons. The E$_T$ distributions of the jets for signal and some background channels is shown in Figure ~\ref{fig:etjets} for all events. The number of selected central jets with E$_T>30 GeV$ and $|\eta | <$2.4 in signal and background data samples are shown on the right hand side of Figure ~\ref{fig:etjets}. \begin{figure} \begin{center} \includegraphics[width=0.43\textwidth]{Plots/jetset.eps} \includegraphics[width=0.43\textwidth]{Plots/njets.eps} \caption[]{Normalized distribution of E$_T^{jets}$ and number of jets per event with E$_T>30 GeV$ in the signal and background channels.} \label{fig:etjets} \end{center} \end{figure} \subsection{MET} In an ideal detector the Missing Transverse Energy (MET) is almost zero for the leptonic decays ($e,\mu$) in DY, ${\rm Z +}$ and ${\rm ZZ}$ backgrounds. In CMS, however, the MET resolution for the considered channels is $\sigma_{MET}\sim \sqrt{\sum E_T} \sim 30$ GeV. This uncertainty is mostly coming from the errors in the energy scale and can be improved during the LHC operation. Since the events have been selected with the jet veto, the MET was reconstructed using the {\sl METfromEcalPlusHcalTower} input in ORCA and {\sl METfromCaloTower} in FAMOS and corrected for the high P$_T$ muon tracks by default. The reconstructed MET and MET plus sum of the highest P$_T$ leptons are shown in Figure ~\ref{fig:met} for the signal and some backgrounds. Only ${\rm t\bar t}$ and SUSY backgrounds have a distinct larger MET, the others are comparable with the signal. Hence, the use of this parameter in the event selection is not very efficient in contrast to the other SUSY studies where the large MET is the main selection cut against SM backgrounds. The improvement of the MET reconstruction at low energy scale will allow significantly improve the suppression of Z+jets and DY background and is a subject for future study. \begin{figure} \begin{center} \includegraphics[width=0.43\textwidth]{Plots/met.eps} \includegraphics[width=0.43\textwidth]{Plots/meff.eps} \caption[]{Normalized MET and MET+$\sum P_T^{e,\mu}$ for the signal and background events in FAMOS.} \label{fig:met} \end{center} \end{figure} \section{Event selection} The event selection and background suppression is done in two steps. In the first step the simple sequential cuts have been applied. In the second step the selected data samples have been used for the Neural Network (NN) training. The NN allows to combine various observables in one output and perform an optimized selection for each type of background. An advantage of the NN in comparison to the usual cuts is that the correlations between parameters are taken into account. The drawback of this method can be a somewhat larger sensitivity to the details of the simulation and larger samples are required for the training. The effect of the NN selection is demonstrated for the LM9 point. \subsection{Selection with the sequential cuts}. The events have been selected using the following cuts: \begin{itemize} \item L1+HLT trigger \item No jets with $E_T>30$ GeV in $|\eta|<2.4$. \item At least three isolated leptons in acceptance of $|\eta|<2.4$. Among them two OSSF pair with the transverse momentum: $P_T^{\mu}>$10 GeV/c and $P_T^{e}>$17 GeV/c and the invariant mass below Z peak $M_{ll}<$ 75 GeV/c$^2$. The third lepton with $P_T^{\mu,e}>$10 GeV/c. \end{itemize} Evolution of statistics and selection efficiencies with these selection cuts are shown in Table ~\ref{tab:cutsum}. The simulated statistics is scaled to the $30 $fb$^{-1}$. The requirement of three isolated leptons with two OSSF and $M_{ll}< 75$ GeV is the most powerful selection for all backgrounds, the jets veto is important mostly for the ${\rm t\bar t}$. The biggest contribution to the background after selection is coming from the DY, Z+jets, $t\bar t$ and ZW. The W+jets and QCD backgrounds have the large cross section and only a small part of the required statistics have been simulated ($\sim 10^6$), see Table \ref{tab:bkgdata}. No events have been selected. The upper limit on the expected number for the full data sample can be estimated using the probability to select 3 leptons at generator level and the selection cut efficiencies from the Table ~\ref{tab:cutsum}. For the W+jets this number is below 100 and for the QCD below 5 events. \begin{small} \begin{table}[ht] \caption[]{Summary of the signal(LM1,LM9, LM7) and background statistics expected for $\int L= 30 $fb$^{-1}$ at different selection steps. The selection efficiency in respect to the previous cut is shown in brackets.} \begin{center} \begin{tabular}{|l|l|l|l|l|l|l|} \hline channel & $N_{ev}$ (30fb$^{-1}$) & L1 & HLT & NoJets & N$_{rec}^{l}>2$ & N$_{isolated}>2$ \\ & & & & & & {\tiny OSSF $M_{ll}< 75$GeV} \\\hline LM1 & 2640 & 1795~ ($68\%$) & 1544~ ($89\%$) & 864~ ($56\%$) & 337~ ($39\%$) & 70~ ($21\%$) \\ LM7 & 1540 & 1360~ ($88\%$) & 1250~ ($92\%$) & 738~ ($59\%$) & 310~ ($42\%$) & 91~ ($29\%$) \\ LM9 & 3700 & 3182~ ($86\%$) & 2896~ ($91\%$) & 1740~ ($60\%$) & 851~ ($49\%$) & 238~($28\%$) \\\hline ZW & 5.$10^4$ & 3.98 $10^4$~ ($79\%$) & 3.6 $10^4$~ ($92\%$) & 1.9~ $10^4$ ($53\%$) & 4900~ ($26\%$) & 173~ ($3.5\%$) \\ ZZ & 4800 & 3860~ ($80\%$) & 3530~ ($91.5\%$) & 1681~ ($48\%$) & 818~ ($49\%$) & 38~ ($4.6\%$) \\ ${\rm t\bar t}$ & 2.6 $10^6$ & 2.1 $10^6$~ ($81\%$) & 1.8~ $10^6$ ($86\%$) & 1.3~ $10^5$ ($7\%$) & 1.2~ $10^4$ ($9\%$) & 239~ ($2\%$) \\ ${\rm Z+}$jets(3l)& 4.6 $10^5$ & 4. $10^5$~ ($87\%$) & 3.7~ $10^5$ ($92.5\%$)& 9.8~ $10^4$ ($26.5\%$)& 6.4~ $10^4$ ($65\%$)& 504~ ($0.8\%$) \\ $Z b \bar b$ & 8.4 $10^4$ & 7.8 $10^4$ ($93\%$) & 7.3 $10^4$ ($94\%$ ) & 1.5 $10^4$ ($20\%$) & 1.1 $10^4$($73\%$) & 69 ~ ($0.6\%$) \\ DY(3l) & 4.5 $10^5$ & 3.6 $10^5$~ ($80\%$) & 3.2~ $10^5$ ($89\%$) & 1.4~ $10^5$ ($44\%$) & 8.~ $10^4$ ($57\%$) & 670~ ($0.9\%$) \\ ${\rm Wt}$+jets & 3. $10^5$ & 2.7 $10^5$~ ($90\%$) & 2.1~ $10^5$ ($78\%$) & 3.9~ $10^4$ ($18.5\%$)& 4910~ ($13\%$) & 52~ ($1\%$) \\ SUSY & 4 $10^5$ & 3.4 $10^5$~ ($85\%$)& 2.5~ $10^5$ ($74\%$) & 1.8~ $10^4$ ($7\%$) & 1.4~ $10^4$ ($78\%$)& 34~ ($0.24\%$) \\ WW+jets & 6.$10^5$ & 4.5 $10^5$~ ($75\%$) & 3.8~ $10^5$ ($84\%$) & 1.9~ $10^4$ ($50\%$) & 1.3~ $10^4$ ($68\%$)& 7~ ($0.05\%$) \\ W+jets & 5.4~10$^8$ & 1.9~10$^8$~($35\%$) & 1.2~10$^8$~($68\%$) & 7.8~10$^7$~($52\%$) & 7.8~10$^6$ ($0.1\%$) & 0; $<100$ \\ QCD & 7.4~10$^{11}$& 3.3~10$^{10}$~($4.5\%$) & 6.6$^{8}$~($2\%$) & 1.9~10$^7$~($3\%$) & 1.9 ~10$^3$ ($0.01\%$) & 0; $<5$ \\ \hline \end{tabular} \end{center} \label{tab:cutsum} \end{table} \end{small} \par %----- Invariant mass In case of trileptons of the same flavor or events with $N_l>$3 the dilepton invariant mass can be constructed from different OSSF combinations, for example the highest or lowest P$_T$ pairs. Probability of the correct pairing was analyzed at generator level and is almost the same for high or low P$_T$ combinations. However the high P$_T$ pairs are preferred because the low P$_T$'s are producing the lower invariant mass for the ZW, ZZ and Z+jets channels, thus moving the Z peak into the region of the signal. The dilepton invariant mass distribution of the signal events without background is presented on Figure ~\ref{fig:invsig}. The MC tagged OSSF pairs from the $\chi^0_2$ decays are plotted for comparison. The highest P$_T$ combinations ($2\mu, 2e$) have $93\%$ efficiency in respect to the MC tagged combination and reproduce well the shape of the invariant mass distribution. The three muon $3\mu$ ( three electron $3e$) states contribute $\leq 40\%$ in each of the $2\mu+l$ ($2e+l$) sample. This unbalance appears due to wrong combinations which can happen in the pure muon or electron states. Such combinations can have an invariant mass outside the considered region of $M_{ll}<$ 75 GeV/c$^2$. All OSSF pairs can be used to reconstruct the invariant mass. In $\sim27\%$ of the signal events another OSSF pair can be constructed, with one lepton originated from the $\chi^{\pm}_1$ decay instead $\chi^{0}_2$ . Since $m_{\chi^0_2}\sim m_{\chi^{\pm}_1}$, however, this 'wrong' invariant mass stays in the considered region and artificially enhances the significance. The invariant mass from all OSSF pairs is shown in Figure ~\ref{fig:invmall} (left) for signal and all backgrounds together with the different flavor opposite sign combinations $e^+\mu^- +e^-\mu^+$ (DFOS) which reflects the combinatorial background. The DFOS combinations have a maximum near the signal and its subtraction does not improve the significance for the LM9 point. The dielectrons contribute less than 25$\%$ to the signal as expected from the trigger selection. The significance calculated as $S_{c12}=2 (\sqrt{Nb+Ns}-\sqrt{Nb})$ for all OSSF combinations amounts to $\sim$ 6.1. More details about significance estimation and uncertainties can be found in the next section, see Table \ref{tab:sign}. The kinematic end point $M_{ll}^{max}$=$m_{\chi_2^0}-m_{\chi_1^0}$ is largely deteriorated by the background and can not be reconstructed at LM9. \begin{figure}[hbtp] \begin{center} \includegraphics[width=0.5\textwidth]{Plots/lm9inv_c.eps} \caption[]{Reconstructed invariant mass distribution of the signal produced from the highest P$_T$ dimuon or dielectron pairs, all OSSF pairs, DFOS and truly MC tagged pairs.} \label{fig:invsig} \end{center} \end{figure} \par Among the selected trilepton events some reconstructed leptons, among the selected three, are not traced back to the MC lepton at generator level. The tracing was done by matching reconstructed in FAMOS and generated MC lepton in the cone of $\Delta R <0.2$. These events are considered as a fake. The rate of the fake events $F_{e,\mu}$ for the selected trilepton is presented in Table \ref{tab:fake} for different backgrounds. For the electrons it is around $\sim10^{-5}$ per selected trilepton event and for the muons $\sim10^{-6}$. This includes leptons which appears at the reconstruction level (punch-through, gamma conversion, etc.) but also the miss-matched leptons with the large reconstruction errors, which can slightly overestimate the fake rate. The numbers are consistent with the estimation from the W+jets obtained in ~\cite{cmsin28} using full simulations. The fakes leptons, especially electrons, will significantly increase background for the channels preselected at generator level, like DY or Z+jets. The number of this fake events can be estimated from the probability to have a third fake reconstructed lepton($e$ or $\mu$) in addition to the two real selected leptons. In this case the number of fake events for the full sample can be estimated as following: $N^{fake}_{e,\mu}=F_{e,\mu}*N_{tot}*E_{2l}$, where $N_{tot}$ is the total number of events without preselection and $E_{2l}$ is the efficiency to have two real reconstructed leptons passed the selection criteria. This efficiency is estimated from the processed data samples. The expected number of the fakes for different background channels is presented in Table \ref{tab:fake}. For the W+jets and QCD only an upper limit can be set. The fake electrons from DY and Z+jets will almost double the background for the 2$\mu +e$, 2$e+e$ and 2$e+\mu$ combinations. The trimuon final state $2\mu+\mu$ suffers only from the fake muons with much smaller fake rate. Figure ~\ref{fig:invmall}(right) shows invariant mass distribution of the high $P_T$ muons in the trimuon final state including fakes, the significance is presented in the Table \ref{tab:sign}. \begin{table}[htb] \caption[]{The estimated numbers of events containing a fake $e$ or $\mu$ for different background channels at $30$fb$^{-1}$.} \label{tab:fake} \begin{center} \begin{tabular}{|c|l|l|l|l|l|l|} \hline channel & $N_{tot}$ $30$fb$^{-1}$& $F_{e}$ & $F_{\mu}$ & $E_{2l}$ & $N^{fake}_{e}$ & $N^{fake}_{\mu}$ \\ \hline DY & $1.7\cdot 10^9$ & $5.\pm 0.8\cdot 10^{-5}$ & $4.3\pm 2.5\cdot 10^{-6}$ & $1.8\cdot 10^{-2}$ & $1484\pm300$ & $127\pm73$ \\ ${\rm Z+}$jets & $3.4\cdot 10^8$ & $2.6\pm 0.2\cdot 10^{-5}$ & $2.2\pm\cdot 1.4 10^{-6}$ & $1.5\cdot 10^{-2}$ & $133\pm28$ & $12\pm 8$ \\ ZW & $1.2\cdot 10^6$ &$6\pm 4\cdot10^{-5}$ & $<10^{-5}$ & $6\cdot 10^{-3}$ & $<0.3$ & $<0.1$ \\ ZZ & $6\cdot 10^5$ & $<10^{-4}$ & $<10^{-4}$ & $1.2\cdot 10^{-2}$ & $<0.5$ & $<0.5$ \\ ${\rm t\bar t}$ & $2.4\cdot 10^7$ & $4.6\pm 1.8\cdot 10^{-5}$ & $<10^{-6}$ & $3.6\cdot10^{-2}$ & $3\pm1 $ & $<1$ \\ $Z b \bar b$ & $4\cdot 10^5$ & $3\pm2\cdot 10^{-5}$ & $<10^{-5}$ & $10^{-2}$ & $<0.5$ & $<0.5$ \\ ${\rm Wt}$+jets & $1.7\cdot 10^6$ & $3\pm 1.8\cdot10^{-5}$ & $<10^{-5}$ & $5.3\cdot 10^{-2}$ & $3\pm1 $ & $<1$ \\ W+jets($>30GeV/c$) & $5.4\cdot 10^8$ & $<10^{-4}$ & $<10^{-5}$ & $3.3\cdot 10^{-4}$ & $<18$ & $<1.8$ \\ QCD($>50 GeV/c$) & $7.4\cdot 10^{11}$ & $<10^{-4}$ & $<10^{-5}$ & $1.7\cdot 10^{-8}$ & $<1.3$ & $<0.1$ \\ \hline \end{tabular} \end{center} \end{table} \begin{figure}[hbtp] \begin{center} \includegraphics[width=0.48\textwidth]{Plots/hinvall_c.eps} \includegraphics[width=0.48\textwidth]{Plots/hmminv_c.eps} \caption[]{Left: Invariant mass for all OSSF combinations in each event for signal and backgrounds without fakes. Right: Invariant mass of the highest P$_T$ trimuon combinations including the estimated fakes contribution.} \label{fig:invmall} \end{center} \end{figure} \subsection{Selection with the Neural Network} In this study the Neural Network available from ~\cite{phit} was incorporated into the analysis code. As an example, the reference LM9 point has been used for the network training. The following procedure has been implemented: \begin{enumerate} \item All data samples are split in two parts; training samples ($\sim 30\%$ of the statistics for each channel) with a priory knowledge of signal and background, and the main sample. \item For each pair of signal-background a set of observables is defined. \item The NN is trained separately for each signal-background pair using the training samples. \item The selection cut of the NN outputs were optimized simultaneously in order to get a maximum significance. \item The main data samples are passed through the NN. \end{enumerate} First of all the number of networks has to be defined. The largest backgrounds found after selection with cuts (Z+jets, DY, $t\bar t$, ZW and ZZ) have been used to build five networks. The data samples have been preselected. In order to increase the statistics the somewhat looser selection cuts have been used: N$_{jets}$(E$_t>30$ GeV)$<2$ and $P_T^{\mu}>$5 GeV/c, $P_T^{e}>$10 GeV/c. The size of each training sample was 3000 events for signal and background. This statistics was considered sufficient since a smaller samples ($\sim$1000 events) produced similar results. The trilepton final state has a rather limited number of observables which can be used for selection. The main observables are related to the leptons kinematic because the MET is not well measured at low energy scale. The observables can be divided into different categories: \begin{itemize} \item Leptons (e,$\mu$) related:\\ P$_T^{1,2,3}$ - transverse momentum and $\eta$ - rapidity of three leptons ordered by P$_T$,\ M$_{\rm inv}^{h,\ell}$ - invariant mass of high and low P$_T$ OSSF pair combination, $\sum \rm P_t$ - sum of P$_T$ of all leptons in the event, $\sum \rm E^\ell$ - sum of the energy of all leptons in the event, $A=\frac{ \rm P_t^1-\rm P_t^2}{\rm P_t^1+\rm P_t^2}$ - asymmetry of the OSSF leptons, $\Theta_{\ell\ell}$ - angle between the two OSSF leptons, $\Theta_{\ell 1\ell 3}$ - angle between the highest and lowest P$_T$ leptons, $\Phi_{\ell\ell}$ - angle in transverse plan between two OSSF leptons, $\rm P_{2\ell}$ - transverse momentum of two OSSF leptons, N$_\ell$- number of selected leptons. \item Energy balance variables:\\ ${\rm MET}$, $\sum E_t$ - reconstructed MET and sum of E$_T$ in event, $\Theta ({\rm MET}, \rm P_{2\ell})$ - angle between MET and OSSF lepton pair, MET + $\sum \rm P_t$. \item Jets related:\\ Here the jets with too small E$_T$ (E$_T<30$ GeV) or too big rapidity ($|\eta |>$2.4), which cannot veto the event, have been used. $N_{\rm jets}$ - number of jets, $E_t^{hj}$- of the highest E$_T$ jet, $\eta_{hj}$ - rapidity of the highest E$_T$ jet. \end{itemize} The variables are automatically sorted according to the significance by the NN. A summary of the variables used in the training is presented in Table ~\ref{tab:nnpar}. The distribution of NN outputs after training for different signal-backgrounds are shown in Figure ~\ref{fig:nnout}. The solid lines show the signal efficiency and background contamination. \begin{table}[htb] \caption[]{NN variables for five neural networks used in analysis.} \label{tab:nnpar} \begin{center} \begin{tabular}{|c|l|} \hline NN & NN variables \\ \hline ${\rm Z+}$ jets & P3$_T$, Minv$_h$, $\eta_j$, $MET$, $\Theta_{ll}$, $\sum P_T$ \\ DY & P3$_T$, $P_{2l}$, $\sum P_T$, $\Theta_{ll}$, $MET$, $\Phi_{ll}$ \\ ${\rm t\bar t}$ & $MET$, $\sum P_T$, P3$_T$, $\Theta_{ll}$, $E_T^{hj}$, P2$_T$, Minv$_h$, P1$_T$ \\ ZW & $\sum P_T$, P2$_T$, Minv$_h$, Minv$_l$, $\sum E^l$, $\Theta_{ll}$, $\Phi_{ll}$, $A$, \\ ZZ & $\sum P_T$, $MET$, P2$_T$, Minv$_h$, $\Theta_{ll}$, P3$_t$,$\Phi_{ll}$, $A$, \\\hline \end{tabular} \end{center} \end{table} \begin{figure} \begin{center} \includegraphics[width=0.3\textwidth]{Plots/nnttbar.eps} \includegraphics[width=0.3\textwidth]{Plots/nnzw.eps} \includegraphics[width=0.3\textwidth]{Plots/nndy.eps} \includegraphics[width=0.3\textwidth]{Plots/nnzj.eps} \includegraphics[width=0.3\textwidth]{Plots/nnzz.eps} \caption[]{NN outputs for different signal-background pairs after training. The selection cuts optimized with Genetic Algorithm are shown as a vertical line. The efficiency and contamination are plotted as curved lines} \label{fig:nnout} \end{center} \end{figure} \par The selection cuts on the NN outputs have been optimized using the Genetic Algorithm (GA) \cite{ga}. First the main data samples have been preselected using the selection cuts defined in the Section ~4. It was found that such a preselection gives a better significance then using the looser cuts used for the training samples. It means that the trained network selection was less effective for the low $P_T$ leptons as compare with the cuts. The selected events have been passed through different NNs and the five NN outputs for each event were used as input for the GA optimization with each input weighted with the cross section of the background signature. The GA defines all possible combination of NN cuts in steps of $2.5\%$ of the scale and maximizes the significance $S_{c12}$. The obtained set of NN cuts for the final selection is shown in Figure ~\ref{fig:nnout}. The efficiencies of the optimized NN selection cuts are presented in Table ~\ref{tab:datasumnn}. The efficiency of each individual network was evaluated by enabling only one network at once. The NN$_{all}$ corresponds to the final selection when all networks have been activated. The final efficiencies of the signal and backgrounds separation are 66$\%$ and 26$\%$ respectively. The invariant mass distributions sfter NN selection of all OSSF combinations and the only trimuon final state including fakes are shown in Figure ~\ref{fig:invmallnn}. The NN selection improves the significance from $S_{c12}$=6.1 for the analysis with sequential cuts to 7.6 for the NN analysis. However the NN selects background events with the kinematics (and therefore invariant mass) similar to the signal, thus making the experiment more counting like, where the systematic uncertainties become more important. \par The stability of the NN selection can be verified by using NNs trained with another signal. The training and the cut optimization have been repeated for the LM7 benchmark point and the produced networks have been used for the LM7 and LM9 selection. The cuts changes the interplay between backgrounds and decreases the backgrounds rejection from $\sim 26\%$ to $\sim 20\%$ and the signal is reduced from $66\%$($62\%$) to $55\%$($56\%$) for the LM9(LM7) samples. The $S_{c12}$ significance for the LM9 decreases only from 7.6 to 7.3. \par For the LM7 and LM9 events the event topology is similar, which is not the case for the two body decays at the LM1 point. Therefore the training has to be done for this region separately, which is beyond the scope of this study given the small expected number of events for this point. \begin{small} \begin{table}[htb] \caption[]{Selection efficiencies with the neural networks trained for the LM9 point. The individual NN efficiencies correspond to the particular network enabled.} \label{tab:datasumnn} \begin{center} \begin{tabular}{|l|l|l|l|l|l|l|l|l|} \hline channel & $N_{ev}$, & E(cuts) & E($NN_{zw}$)& E($NN_{zz}$) & E($NN_{ttbar}$) & E($NN_{zj}$)& E($NN_{dy}$) & E($NN_{all}$) \\ & 30fb$^{-1}$ & ($N_{sel}$) & & & & & & ($N_{sel}$) \\ \hline LM1 & 2640 & $2.7\%$~(70) & $87\%$ & $72\%$ & $76\%$ & $52\%$ & $93\%$ & $24\%$~ (17) \\ LM7 & 1540 & $5.9\%$~(91) & $91\%$ & $87\%$ & $95\%$ & $81\%$ & $98\%$ & $62\%$~ (57) \\ LM9 & 3700 & $6.4\%$~(238) & $92\%$ & $92\%$ & $97\%$ & $81\%$ & $97.5\%$ & $68\%$~ (161)\\ \hline ZW & 5.$10^4$ & $0.3\%$~(173) & $65\%$ & $44\%$ & $86\%$ & $86\%$ & $97\%$ & $23\%$~ (44) \\ ZZ & 4800 & $0.8\%$~(38) & $74\%$ & $60\%$ & $91\%$ & $81\%$ & $95\%$ & $39\%$~ (15) \\ ${\rm t\bar t}$ & 2.6 $10^6$ & $0.01\%$~(239) & $76\%$ & $78\%$ & $65\%$ & $77\%$ & $98\%$ & $37\%$~ (89) \\ ${\rm Z}$+j(3l)& 4.6 $10^5$ & $0.1\%$~(504) & $81\%$ & $88\%$ & $94\%$ & $43\%$ & $88\%$ & $26\%$~ (129) \\ $Z b \bar b$ & 8.4 $10^4$ & $0.08\%$~(69) & $84\%$ & $90\%$ & $93\%$ & $42\%$ & $86\%$ & $26\%$~(18) \\ DY(3l) & 4.5 $10^5$ & $0.15\%$~(670) & $90\%$ & $85\%$ & $94\%$ & $30\%$ & $77\%$ & $19.5\%$~ (131) \\ ${\rm Wt}$+jets & 3.$10^5$ & $0.017\%$~(52) & $74\%$ & $74\%$ & $73\%$ & $71\%$ & $99\%$ & $38\%$~ (20) \\ SUSY & 4 $10^5$ & $0.009\%$~(34) & $76\%$ & $85\%$ & $65\%$ & $95\%$ & $98\%$ & $65\%$~ (22) \\ WWj & 6.$10^5$ & $0.001\%$~(7) & $83\%$ & $83\%$ & $67\%$ & $67\%$ & $100\%$ & $29\%$~ (2)\\ \hline Tot.bkg & 4.9 $10^6$ & $0.035\%$ ~(1786) & & & & & & $26\%$~ (470) \\ \hline \end{tabular} \end{center} \end{table} \end{small} \begin{figure}[hbtp] \begin{center} \includegraphics[width=0.48\textwidth]{Plots/hinvall_nn.eps} \includegraphics[width=0.48\textwidth]{Plots/hmminv_nn.eps} \caption[]{Left: Invariant mass distribution of all OSSF lepton combinations after selection with the NN trained for the LM9 benchmark point without fakes. Right: Invariant mass for the high P$_T$ dimuon combinations in the trimuon final state with the fakes included.} \label{fig:invmallnn} \end{center} \end{figure} \section{Significance and systematic uncertainties} % add statistical part The significance was calculated using definitions from ~\cite{scpf}. The systematic uncertainties are taken into account by the following formula: $S_{c12ts}=2 (\sqrt{Nb+Ns}-\sqrt{Nb+\Delta Nb})*factor$ , where Nb and Ns are the numbers of signal and background events in the considered range, $\Delta Nb$ - systematic uncertainties of Nb and the $factor=\frac{\sqrt{Nb+\Delta Nb}}{\sqrt{\sigma_s^2+Nb+\Delta Nb}}$ accounts for the statistical uncertainties of the background $\sigma_s$. The $S_{c12}$ corresponds to the significance without statistical and systematical uncertainties and is close to the likelihood significance $S_{cL}=\sqrt{2lnQ}$. The $S_{c12ts}$ includes all uncertainties. \par There are several sources of systematic uncertainties: \begin{itemize} \item Reconstruction and selection uncertainties. The errors on the jets energy scale and leptons momentum resolution have influence on the selection efficiency with cuts. The contribution of these errors to the relative number of selected events was studied varying the jet E$_T$ by 20$\%$ ($30\pm5$GeV) and leptons P$_T$ by 10$\%$ ($10\pm1$GeV/c). The number of signal and background events are decreased together and the residual reconstruction uncertainties, weighted according to the statistics obtained with selection cuts, amounts to $\Delta Nb \sim 1.1\%$. The changes in lepton thresholds contribute $\leq 30\%$ to this number. For the NN selection more variables are used and theirs contribution to the uncertainties is more difficult to evaluate. It can be roughly estimated as $\sim 3.5\%$ from the selection with NN trained with different signal samples (LM9 and LM7) and quadratically added with the $1.1\%$. \item PDF uncertainties. For the estimation of the PDF uncertainties the CTEQ6i set comprised of 41 subsets was used from the LHPDF library ~\cite{lhpdf}. The uncertainties have been estimated using the PDF reweighting technique. For each event a vector of weights for each $i$ subset was calculated as: $w_i=\frac{PDF_i (x_1,x_2,Q)}{PDF_0(x_1,x_2,Q)}$, where $x_{1,2}=p_L/s$ are the Bjorken variables of the partons ($q,g$) participating in the hard process, Q=$ s \sqrt{ x_1 x_2}$ is the energy scale of the event, $PDF_i$ and $PDF_0$ are the tested and the reference PDF subset. The reweighting was implemented in the analysis code and the PDF uncertainties calculated for the signal and backgrounds. The normalized number of selected events N=$\sum w_i$ is plotted in Figure ~\ref{fig:pdf} for signal and backgrounds. The background samples have been weighted according to the selection efficiencies. The total sigma of the background distribution is $\sigma =1.73\%$ and is uncorrelated with the signal. The $\sigma_{PDF}$ and the max-min spread for different channels are listed in Table ~\ref{tab:uncert}. \end{itemize} \begin{figure}[hbtp] \begin{center} \includegraphics[width=0.6\textwidth]{Plots/hallpdf.eps} \caption[]{ Distribution of the selected events with different reweighted CTEQ6i PDF subsets for the signal and backgrounds normalized according to the selection efficiencies.} \label{fig:pdf} \end{center} \end{figure} \begin{table}[htb] \caption[]{Systematic uncertainties of the LM9 signal and backgrounds.} \label{tab:uncert} \begin{center} \begin{tabular}{|c|c|c|} \hline channel & Reconstruction & PDF \\ & $\Delta N/N, \%$ & $\sigma_{\frac{Npdfi}{Npdfo}}$ ($min, max$), $\%$ \\ \hline LM9 3l & 22 & 1.2~~(-3.0 ~ +2.5) \\ \hline ZW & 14 & 1.2~~ (-3.0~ +2.2) \\ ZZ & 15 & 1.3~~ (-3.4 ~+2.4) \\ ${\rm t\bar t}$ & 37 & 0.9~~ (-3.5 ~+3.2) \\ ${\rm Wt}$+jets & 35 & 1.2~~ (-4.5 ~+4.2) \\ SUSY & 18 & 1.2~~ (-4.0~ +4.2) \\ $Z b\bar b$ & 30 & 1.4~~ (-5.0~+3.7) \\ DY & 15 & 2.1~~ (-6.2~+6.3) \\ ${\rm Z+}$ jets & 31 & 1.6~~ (-5.5 ~+3.7) \\\hline Tot.weighted $\%$ & 1.1 & 1.72 \\ \hline \end{tabular} \end{center} \end{table} The systematic uncertainty calculated as a quadratic sum of different contributions is $\Delta Nb= 2\%$ for the selection with cuts and $\Delta Nb= 4.1\%$ for the NN selections. In this estimate the theoretical uncertainties in the cross section calculations for signal and backgrounds were not taken into account. The significance was calculated from the invariant mass distributions in the expected range of M$_{\ell\ell} < $75 GeV/c$^2$. Table ~\ref{tab:sign} shows the $S_{c12}$ and $S_{c12ts}$ significance for the LM9 point for different dilepton combinations. The contribution of the fake combinations were taken into account for the trimuon final state and all OSSF combinations. The uncertainties in the estimation of the fake rate are treated as a statistical error in the number of background events $\sigma_s$ accounted by the $factor$ in the $S_{c12ts}$ formula. At the LM9 benchmark point the significance for all OSSF combinations without fakes is $S_{c12ts}=4.9$ for the analysis with sequential cuts and $S_{c12ts}=6.6$ for the selection with NN. The fakes reduce this number to 2.5 and 4.5 respectively. \begin{table}[htb] \caption[]{Significances for the LM9 benchmark point.} \label{tab:sign} \begin{center} \begin{tabular}{|c|c|c|c|c|} \hline channel & N$_{sig}$ & N$_{bkg}$ & S$_{c12}$ & S$_{c12ts}$ \\ \hline cuts selection & & & & \\ \hline 3$\ell$ & 238 & 1786 & 5.5 & 4.2 \\ 2$e + \ell$ & 62 & 586 & 2.5 & 2.0 \\ 2$\mu +\ell$ & 176 & 1200 & 4.9 & 4.1 \\ all OSSF & 304 & 2379 & 6.1 & 4.9 \\ all OSSF(+fakes) & 304 & 5014 & 4.2 & 2.5 \\ 3$\mu$ (+fakes) & 108 & 664 & 4.2 & 3.3 \\ \hline \hline NN selection & & & & \\ \hline 3$\ell$ & 161 & 470 & 6.9 & 6.0 \\ 2$e + \ell$ & 49 & 138 & 3.9 & 3.4 \\ 2$\mu +\ell$ & 112 & 332 & 5.7 & 5.0 \\ all OSSF & 200 & 596 & 7.6 & 6.6 \\ all OSSF (+fakes) & 200 & 1002 & 6.0 & 4.5 \\ 3$\mu$ (+fakes) & 80 & 230 & 5.0 & 4.2 \\ \hline \end{tabular} \end{center} \end{table} \section{CMS discovery reach} For the CMS discovery reach, the $m_0$, $m_{1/2}$ mSUGRA plane was scanned with FAMOS for two values of tan$\beta$ (tan$\beta$=10,50) and $m_{1/2}>140$ GeV/c$^2$. The $S_{c12ts}$ significance contours for all OSSF combinations selected with the NN including fakes and all systematic uncertainties are shown in Figure ~\ref{fig:discovery} for $L_{int}=30$fb$^{-1}$. Figure ~\ref{fig:discovery3m} shows the discovery reach for the trimuon final state with the fakes and all uncertainties included. Among the CMS benchmark points only LM9 can be marginaly seen and discovery reach is limited by the low value of $m_{1/2}$. The two body decay region is still visible for tan$\beta$=10 at low $m_0$. Further improvement of the NN selection is possible with the training performed for each region in $m_0$,$m_{1/2}$ plane. These different networks can be used for the regions separation afterward. \begin{figure}[htb] \begin{center} \includegraphics[width=0.45\textwidth] {Plots/Sc12ts_allossf_NN_tb10.eps} \includegraphics[width=0.45\textwidth] {Plots/Sc12ts_allossf_NN_tb50.eps} \caption[]{The $S_{c12ts}$ significance for the all OSSF combinations including estimated fake rates and systematic uncertainties in mSUGRA $m_ {1/2}$, $m_o$ plane for different tan$\beta$=10 (left) and 50 (right) at $L_{int}=30$fb$^{-1}$. Selection with the NN trained for LM9 point. } \label{fig:discovery} \end{center} \end{figure} % \begin{figure}[htb] \begin{center} \includegraphics[width=0.45\textwidth] {Plots/Sc12ts_3m_NN_tb10.eps} \includegraphics[width=0.45\textwidth] {Plots/Sc12ts_3m_NN_tb50.eps} \caption[]{The $S_{c12ts}$ significance for the trimuon final state with the systematic uncertainties and contribution from fakes at $L_{int}=30$fb$^{-1}$. Selection with the NN trained for LM9 point. } \label{fig:discovery3m} \end{center} \end{figure} \section{Conclusion} The direct neutralino-chargino $\chi^0_2 \chi^\pm_1$ production with the trilepton final state has been studied in presence of the most important backgrounds with the realistic CMS simulation. The trilepton events can be selected with the central jets veto and by requiring OSSF leptons with invariant mass $<$75 GeV/c$^2$. The selection with the neural network improves the significance from 6.1 to 7.6 for the LM9 ($m_{1/2}$=175, $m_{0}$=1450, tan$\beta$=50) benchmark point in comparison to the analysis with sequential cuts. The 5$\sigma$ signal can be observed for an integrated luminosity of 30fb$^{-1}$ for low $m_{1/2}<180$ GeV/c$^2$. The main background is coming from the DY and Z+jets channels and the fake leptons have an important contribution. The suppression of these backgrounds is difficult due to the small missing transverse energy in the signal events which makes discovery of the mSUGRA trilepton at CMS very challenging. The improvement of the MET reconstruction at low energy scale can significantly improve the discovery potential. At high luminosity the selection would require another optimization due to larger pile up events which will decrease the efficiency of the jets veto. \section{Acknowledgments} We would like to thank L.~Pape, M.~Spiroupulu, S.~Abdullin, F.~Moortgat, M.~Chiorbioli, M.~Galanti, M.~Chertok, L.~Dudko, S.~Bityukov and A.~Drozdetsky for useful discussions. We also thank G.Quast and Karlsruhe production team for the help in simulations. \begin{thebibliography}{99} \bibitem{cmsin039} W.~de Boer, M.Niegel, V.Zhukov., CMS IN 2005/039. \bibitem{fnal} A.Canapa, E.Lytken. 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