%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % % A Search for Squarks of R-Parity Violating SUSY at HERA % % % % H1 Collaboration % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % % June 2000 % % % % Editors: E. Perez/G. Radel % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % %================================================================ % LaTeX file with preferred layout for the contributed papers to % the ICHEP Conference 98 in Vancouver %================================================================ \documentclass[12pt]{article} \usepackage{epsfig} \usepackage{amsmath} \usepackage{hhline} \usepackage{amssymb} \usepackage{times} \renewcommand{\topfraction}{1.0} \renewcommand{\bottomfraction}{1.0} \renewcommand{\textfraction}{0.0} \newlength{\dinwidth} \newlength{\dinmargin} \setlength{\dinwidth}{21.0cm} \textheight25cm \textwidth16.0cm \setlength{\dinmargin}{\dinwidth} \setlength{\unitlength}{1mm} \addtolength{\dinmargin}{-\textwidth} \setlength{\dinmargin}{0.5\dinmargin} \oddsidemargin -1.0in \addtolength{\oddsidemargin}{\dinmargin} \setlength{\evensidemargin}{\oddsidemargin} \setlength{\marginparwidth}{0.9\dinmargin} \marginparsep 8pt \marginparpush 5pt \topmargin -42pt \headheight 12pt \headsep 30pt \footskip 24pt \parskip 3mm plus 2mm minus 2mm \begin{document} %%%%%%%%%%%%%%%%%%% Start personal commands and re-definitions %%%%%%%% % special \newcommand{\Rp}{\mbox{$\not \hspace{-0.15cm} R_p$}} \newcommand{\lsim}{\raisebox{-1.5mm}{$\:\stackrel{\textstyle{<}}{\textstyle{\sim}}\:$}} \newcommand{\gsim}{\raisebox{-0.5mm}{$\stackrel{>}{\scriptstyle{\sim}}$}} % units \newcommand{\cm}{\mbox{\rm ~cm}} \def\GeV{\hbox{$\;\hbox{\rm GeV}$}} \newcommand{\picob}{\mbox{{\rm ~pb}~}} % styling \def\figurename{{\bf Figure}} \def\tablename{{\bf Table}} % % Journal macro \def\Journal#1#2#3#4{{#1} {\bf #2}, #3 (#4)} \def\NCA{\em Nuovo Cimento} \def\NIM{\em Nucl. Instrum. Methods} \def\NIMA{{\em Nucl. Instrum. Methods} A} \def\NPB{{\em Nucl. Phys.} B} \def\PLB{{\em Phys. Lett.} B} \def\PRL{\em Phys. Rev. Lett.} \def\PRD{{\em Phys. Rev.} D} \def\ZPC{{\em Z. Phys.} C} % here is an example how to use it : % \bibitem{ellis}R.K. Ellis, and P. Nason, %\Journal{\NPB}{312}{551}{1989}. % %%%%%%%%%%%%%%%%%%% End definitions of personal commands %%%%%%%%%%%%%% % % % \pagestyle{empty} \begin{titlepage} \noindent % {\bf H-UM \& JS: version of \today} \\[.3em] Submitted to the 30th International Conference on High-Energy Physics ICHEP2000, \\ Osaka, Japan, July 2000 \vspace*{3cm} \begin{center} \Large {\bf A Search for Squarks of {\boldmath $R$}-Parity Violating SUSY at HERA} \vspace*{1cm} {\Large H1 Collaboration} \end{center} \vspace*{3cm} \begin{abstract} \noindent A search for squarks of $R$-parity violating supersymmetry is performed in $ep$ collisions at HERA using H1 1994$\rightarrow$1997 data corresponding to an integrated luminosity of $37 \picob^{-1}$. Direct single production of squarks of each generation by $e^+$-quark fusion via a Yukawa coupling $\lambda'$ is considered and all possible $R$-parity violating decays and gauge decays of the squarks are taken into account. The dependence of the sensitivity to $\lambda'$ on the free parameters of the Minimal Supersymmetric Standard Model (MSSM) is studied in detail. The reach in the mass-coupling plane extends to domains unexplored in other direct or indirect searches. For a Yukawa coupling of the electromagnetic strength squark masses below $258 \GeV$ can be excluded at the $95 \%$ confidence level independently of the values of the MSSM parameters. This sensitivity still reaches $182 \GeV$ for a 100 times smaller coupling strength. In addition, for a fixed value of the Yukawa coupling $\lambda'$, HERA results are interpreted for the first time in terms of constraints on the parameters of the Minimal Supergravity model. \end{abstract} \vfill \begin{flushleft} {\bf Abstract: 957} \\ {\bf Parallel session: 11} \\ {\bf Plenary talk: 7~b } \end{flushleft} \end{titlepage} \pagestyle{plain} \section{Introduction} \label{sec:intro} The $ep$ collider HERA which provides both baryonic and leptonic quantum numbers in the initial state is ideally suited to search for new particles possessing couplings to an electron-parton pair. Such particles could be squarks, the scalar supersymmetric (SUSY) partners of the quarks, in SUSY models where $R$-parity is violated (\Rp) via Yukawa couplings $\lambda'$. These squarks could thus be resonantly produced at HERA, via the fusion of the $E^0_e=27.5 \GeV$ initial state positron with a quark coming from the $E^0_p=820 \GeV$ incident proton, up to the kinematic limit of $\sqrt{s} \simeq 300 \GeV$. % In 1996, both H1~\cite{H1HIGHQ2} and ZEUS~\cite{ZEUSHIGHQ2} % collaborations reported an excess % of events at very high $Q^2$ (i.e. very high energy of the % scattered positron), above the expectation of Standard Model (SM) % Neutral Current (NC) Deep Inelastic Scattering (DIS). % This relied in H1 on $\simeq 14 \picob^{-1}$ of $e^+ p$ data collected % between 1994 and 1996. % This and the apparent ``clustering'' of the H1 events at invariant % masses of $\simeq 200 \GeV$, although not supported by ZEUS % observations~\cite{DREES,BERNARDI}, has enhanced the interest in % theories beyond the SM which could possibly provide an interpretation % of the excess involving the $s$-channel resonant production of a new % particle such as a leptoquark or a squark in \Rp\ SUSY~\cite{RPVINTER}. The interest in such new bosons coupling to an electron-parton pair has been considerably renewed recently following the observation by the H1~\cite{H1HIGHQ2} and ZEUS~\cite{ZEUSHIGHQ2} experiments of a possible excess of events at very high masses and squared momentum transfer $Q^2$, above expectations from Standard Model (SM) neutral current (NC) and charged current (CC) deep-inelastic scattering (DIS). These early results were based on data samples collected from 1994 to 1996. Of particular interest was the apparent ``clustering'' of outstanding NC events at masses around $200 \GeV$ observed in H1. The mass range accessible for direct production of such ``leptoquark'' bosons at HERA is now severely constrained by the recent results of the TeVatron experiments~\cite{D01GENE,CDF1GENE} which restrict first generation leptoquark masses at 95\% confidence level to $ M > 242 \GeV$ ($M > 205 \GeV$)~\cite{TEVCOMBINED,D01GENE} for a branching ratio $\beta_{eq}$ of the new particle into $e+q$ of 1 (0.5). \Rp\-SUSY provides a framework in which $\beta_{eq}$ can be naturally small given the competition with gauge decay modes of the squarks, and thus leptoquark-like TeVatron constraints can be easily avoided. This strongly emphasizes the necessity~\cite{RPVINTER} to perform systematic searches for squarks covering both $\Rp$-decay modes and various possible gauge decay modes. In this paper, squarks are searched through single production via a \Rp\ coupling, considering both \Rp\ decays and decays via gauge couplings involving gluinos or mixed states of gauginos and higgsinos. The analysis uses the 1994 $\rightarrow$ 1997 $e^+ p$ data corresponding to an integrated luminosity of $37 \picob^{-1}$. This represents an increase of statistics of a factor $\sim 13$ compared to earlier published \Rp-violating squark searches at HERA~\cite{H1LQ94,H1RPV96}. The results reported here supersede the preliminary results presented at ICHEP'98~\cite{VANCOUVER} based on the same dataset. %======================================================================== \section{Phenomenology} \label{sec:pheno} The most general SUSY theory which preserves gauge invariance of the Standard Model allows for Yukawa couplings between one scalar squark ($\tilde{q}$) or slepton ($\tilde{l}$) and two known SM fermions. Such couplings induce violation of the $R$-parity defined as $R_p\,=\,(-1)^{3B+L+2S}$, where $S$ denotes the spin, $B$ the baryon number and $L$ the lepton number of the particles. $R_p = 1$ for particles and $-1$ for sparticles. We consider here the SUSY phenomenology at HERA in presence of $\Rp$ Yukawa couplings but maintain otherwise the minimal field content of the so-called Minimal Supersymmetric Standard Model (MSSM). % Of special interest for HERA are those Yukawa vertices which couple a squark to a lepton-quark pair. These are described in the superpotential by the terms $\lambda'_{ijk} L_{i}Q_{j}\bar{D}_k$, with $i,j,k$ being generation indices \footnote{In the usual superfields notation, $L_{i}$, $Q_{j}$ and $\bar{D}_k$ contain respectively the left-handed lepton doublet, quark doublet and the right handed quark singlet.}. % The corresponding part of the Lagrangian, expanded in fields, reads as~\cite{RPVIOLATION} : % \begin{eqnarray} {\cal{L}}_{L_{i}Q_{j}\bar{D}_{k}} &= & \lambda^{\prime}_{ijk} \left[ -\tilde{e}_{L}^{i} u^j_L \bar{d}_R^k - e^i_L \tilde{u}^j_L \bar{d}^k_R - (\bar{e}_L^i)^c u^j_L \tilde{d}^{k*}_R \right. \nonumber \\ \mbox{} &\mbox{} & \left. + \tilde{\nu}^i_L d^j_L \bar{d}^k_R + \nu_L \tilde{d}^j_L \bar{d}^k_R + (\bar{\nu}^i_L)^c d^j_L \tilde{d}^{k*}_R \right] +\mbox{h.c.} \nonumber \nonumber \end{eqnarray} % where the superscripts $^c$ denote the charge conjugate spinors and the $^*$ the complex conjugate of scalar fields. % % For the scalars the `R' and `L' indices distinguish independent % fields describing superpartners of right- and left-handed fermions. % Hence, with an $e^{\pm}$ in the initial state, the couplings $\lambda'_{1jk}$ allow for resonant production of squarks through $e-q$ fusion. For the nine possible $\lambda'_{1jk}$ couplings, the corresponding single production processes are given in table~\ref{tab:sqprod}. % % --- TABLE 1: Rp-violating production processes ----------------------- % \begin{table*}[htb] \renewcommand{\doublerulesep}{0.4pt} \renewcommand{\arraystretch}{1.2} \begin{center} % \begin{tabular}{p{0.40\textwidth}p{0.60\textwidth}} \caption {\small \label{tab:sqprod} Squark production processes at HERA ($e^+$ beam) via a $R$-parity violating $\lambda'_{1jk}$ coupling.} & % \begin{tabular}{||c||c|c||} \hline \hline $\lambda'_{1jk}$ & \multicolumn{2}{c||}{production process} \\ \hline 111 & $e^+ +\bar{u} \rightarrow \tilde{d}^*_R$ &$e^+ +d \rightarrow \tilde{u}_L $\\ 112 & $e^+ +\bar{u} \rightarrow \tilde{s}^*_R$ &$e^+ +s \rightarrow \tilde{u}_L $\\ 113 & $e^+ +\bar{u} \rightarrow \tilde{b}^*_R$ &$e^+ +b \rightarrow \tilde{u}_L $\\ 121 & $e^+ +\bar{c} \rightarrow \tilde{d}^*_R$ &$e^+ +d \rightarrow \tilde{c}_L $\\ 122 & $e^+ +\bar{c} \rightarrow \tilde{s}^*_R$ &$e^+ +s \rightarrow \tilde{c}_L $\\ 123 & $e^+ +\bar{c} \rightarrow \tilde{b}^*_R$ &$e^+ +b \rightarrow \tilde{c}_L $\\ 131 & $e^+ +\bar{t} \rightarrow \tilde{d}^*_R$ &$e^+ +d \rightarrow \tilde{t}_L $\\ 132 & $e^+ +\bar{t} \rightarrow \tilde{s}^*_R$ &$e^+ +s \rightarrow \tilde{t}_L $\\ 133 & $e^+ +\bar{t} \rightarrow \tilde{b}^*_R$ &$e^+ +b \rightarrow \tilde{t}_L $\\ \hline \hline \end{tabular} \end{tabular} \end{center} \end{table*} %....................................................................... % The $\tilde{u}^j_L$ ($\tilde{d}^{k*}_R$) production cross section approximately scales as $\lambda^{'2}_{1jk} \times d^k(x)$ ($\bar{u}^j(x)$) where $d^k(x)$ $(\bar{u}^j(x)$) are the probabilities to find a quark $d^k$ $(\bar{u}^j)$ in the proton with a momentum fraction $x=M^2_{\tilde{q}}/s$; $M_{\tilde{q}}$ denotes the squark mass and $\sqrt{s}$ is the available energy in the $ep$ centre of mass frame. % With an $e^+$ incident beam, HERA is best sensitive to couplings $\lambda'_{1j1}$, where mainly $\tilde{u}^j_L$ squarks could be produced via processes involving a valence $d$ quark. On the contrary, HERA $e^- p$ data taken in 1998-1999 will allow to better probe couplings $\lambda'_{11k}$ and $\tilde{d}^k_R$ squarks. \noindent In this paper, squarks are searched under the simplifying assumptions that one of the $\lambda'_{1jk}$ dominates\footnote{ The case where products of couplings $\lambda'_{1jk} \times \lambda'_{3jl}$ or $\lambda'_{1jk} \times \lambda'_{2jl}$ are non vanishing has been addressed in~\cite{H1LQ99} where a search for Lepton Flavor Violation is presented.}. % The squarks decay either via their Yukawa coupling into SM fermions, or via their gauge couplings into a quark and a neutralino $\chi_i^0$ ($i=1,4$), a chargino $\chi_j^{+}$ ($j=1,2$), or a gluino $\tilde{g}$. The mass eigenstates $\chi_i^0$ and $\chi_j^{+}$ are mixed states of gauginos and higgsinos and, as the $\tilde{g}$, are in general unstable. This latter point holds in \Rp\ SUSY also for the Lightest Supersymmetric Particle (LSP) which decays via $\lambda'_{1jk}$ into a quark, an antiquark and a lepton~\cite{RPVIOLATION}. This is in contrast % to the MSSM to $R_p$ conserving SUSY models and has important phenomenological and possibly cosmological consequences. %....................................................................... % % --- FIGURE 1:"Feynman" Diagrams" ------------------------------------- % \begin{figure}[htb] \begin{center} \begin{tabular}{cc} \mbox{\epsfxsize=0.45\textwidth % \epsffile{diag1.eps}} \epsffile{H1prelim-00-162.fig1a.eps}} & \mbox{\epsfxsize=0.45\textwidth % \epsffile{diag2.eps}} \\ \epsffile{H1prelim-00-162.fig1b.eps}} \\ % \mbox{\epsfxsize=0.45\textwidth % \epsffile{diag3.eps}} \epsffile{H1prelim-00-162.fig1c.eps}} & \mbox{\epsfxsize=0.45\textwidth % \epsffile{diag4.eps}} \\ \epsffile{H1prelim-00-162.fig1d.eps}} \end{tabular} \end{center} \caption[]{ \label{fig:sqdiag} {\small Lowest order $s$-channel diagrams for \Rp squark production at HERA followed by (a),(c) \Rp\ decays and (b),(d) gauge decays of the squark. In (b) and (d), the emerging neutralino, chargino or gluino might subsequently undergo a $R_p$ violating or $R_p$ conserving decay of which examples are shown in the dashed boxes for (b) the $\chi_1^{+}$ and (d) the $\chi_1^0$. }} \end{figure} %----------------------------------------------------------------------- % % RP-VIOLATING DECAYS OF THE SQUARKS : In cases where both production and decay occur through a $\lambda'_{1jk}$ coupling (e.g. Fig.~\ref{fig:sqdiag}a and c for $\lambda'_{1j1} \ne 0$), the squarks behave as scalar leptoquarks~\cite{BUCHMULL}. The ${\tilde{d}}^{k*}_R$ can decay either into $e^+ + {\bar{u}}^j$ or $\nu_e + {\bar{d}}^j$ while the $\tilde{u}^j_L$ only decays into $e^+ + d^{k}$ by gauge invariance. Hence, the final state signatures consist of a lepton and a jet and are, event-by-event, indistinguishable from the SM neutral and charged current DIS. % GAUGE DECAYS OF THE SQUARKS : In cases where the $\tilde{u}^j_L$ (resp. ${\tilde{d}}^{k*}_R$) undergoes a gauge decay into a $\chi^0_{\alpha}$, a $\chi^+_{\beta}$ or a $\tilde{g}$ (resp. a $\chi^0_{\alpha}$ or a $\tilde{g}$) (e.g. Fig.~\ref{fig:sqdiag}b and d) the final state will depend on the subsequent decay of the SUSY fermion. Neutralinos can undergo the \Rp\ decays $\chi^0_{\alpha} \rightarrow e^{\pm} q \bar{q}'$ or $\chi^0_{\alpha} \rightarrow \nu q \bar{q}$, the former (latter) being dominant if $\chi^0_{\alpha}$ is dominated by its photino (zino) component. Gluinos can undergo the same \Rp decays, both modes being equally probable if the squarks of $j^{th}$ and $k^{th}$ generation are degenerate. When a $\chi^0_{\alpha}$ or a $\tilde{g}$ decays via \Rp\ into a charged lepton, both the ``right'' and the ``wrong'' sign lepton (compared to incident beam) are equally probable leading to largely background free striking signatures for lepton number violation. On the contrary, the only \Rp\ decays for charginos are $\chi_{\alpha}^+ \rightarrow \nu u^j \bar{d}^k$ and $\chi_{\alpha}^+ \rightarrow e^+ d^k \bar{d}^j$. Neutralinos $\chi^0_{\alpha}$ with $\alpha > 1$ as well as charginos (resp. gluinos) can also undergo gauge decays into a lighter $\chi$ and two SM fermions (resp. two quarks), through a real or virtual gauge boson or sfermion (resp. squark). Radiative decays of a heavy $\chi$ into a photon or a Higgs boson and a lighter $\chi$ can also occur in particular cases. % SUMMARY OF EVENT TOPOLOGIES : The possible decay chains of the $\tilde{u}^j_L$ and ${\tilde{d}}^{k*}_R$ analysed in this paper are classified into eight distinguishable event topologies described in table~\ref{tab:sqtopo1}, and are labeled {\large{S1}} to {\large{S8}} following the notation introduced in~\cite{H1RPV96}. This classification relies on the number of charged leptons and/or jets in the final state, and on the presence of missing energy. Channels {\large{S1}} and {\large{S2}} are the ``leptoquark-like" decay modes of the squark, proceeding directly via \Rp. Channels {\large{S3}} to {\large{S5}} involve one or two SUSY fermion(s) denoted by $X$ and $Y$ in table~\ref{tab:sqtopo1}. As mentioned already only a neutral SUSY fermion (a $\chi^0_{\alpha}$ or a $\tilde{g}$) can be involved in the last step of a {\large{S4}} decay. Channels {\large{S7}} and {\large{S8}} necessarily involve two SUSY fermions. In the case where the $\chi^0_1$ has a very small decay width, such that it would decay outside the detector (i.e.\ when it is nearly a pure mixture of Higgsinos) the cascade decay of a squark into a chargino, followed by $\chi^+ \rightarrow l^+ \nu_l \chi^0_1$, would lead to an event topology which has been analysed previously in~\cite{H1RPV96} and labeled {\large{S6}}. Since the region of the MSSM parameter space which would allow a $\chi^0$ to escape detection has now been ruled out by recent results from LEP2~\cite{LEPNOS6}, this channel has not been considered here. Decay patterns involving more than two $\chi$ or $\tilde{g}$ are in general kinematically suppressed and are not considered in the analysis. The relative contributions of the channels {\large{S1}} to {\large{S8}} depend in particular on the value of the Yukawa coupling $\lambda'$ and on the gaugino-higgsino mixture of neutralinos and charginos. They will be shown as a function of the squark mass in section~\ref{sec:unconstrained} for some example cases. % % % --- TABLE 2: SUSY PROCESSES PART A ---------------------------------- % \begin{table}[htb] \renewcommand{\doublerulesep}{0.4pt} \renewcommand{\arraystretch}{1.0} \begin{center} \begin{tabular}{||c|l|c||} \hline \hline % Channel & \multicolumn{1}{c|}{Decay processes} & \multicolumn{1}{c||}{Signature} \\ % & \multicolumn{1}{c|}{ } & \multicolumn{1}{c||}{ } \\ \hline % S1 & \begin{tabular}{cccccc} $\tilde{q}$ & $\stackrel{\lambda'}{\longrightarrow}$ & $e^+$ & $q$ & & \end{tabular} & \begin{tabular}{c} High $P_T$ $e^+$ + 1 jet \end{tabular} \\ \hline %--------------------------------------------------------------------- S2 & \begin{tabular}{cccccc} $\tilde{d}^*_R$ & $\stackrel{\lambda'}{\longrightarrow}$ & $\nu_e$ & $\bar{d}$ & & \end{tabular} & \begin{tabular}{c} Missing $P_T$ + 1 jet \end{tabular} \\ \hline %--------------------------------------------------------------------- S3 & \begin{tabular}{ccccll} $\tilde{q}$ & $\longrightarrow$ & $q$ & $X$ & & \\ & & & $\stackrel{\lambda'}{\hookrightarrow}$ & $e^+ \bar{q} q$ & \\ % $\tilde{q}$ & $\longrightarrow$ & $q$ & $X$ & & \\ & & & $\hookrightarrow$ & $q \bar{q}$ & $\hspace{-0.5cm}Y$ \\ & & & & & $\hspace{-0.5cm} \stackrel{\lambda'}{\hookrightarrow}$ $e^+ \bar{q} q$ \\ % \vspace{-0.2cm} \\ % & & & & $\:\mid$ \vspace{-0.3cm} & \\ % & & & & $\:\rightarrow$ $q \:\: \bar{q}'$ & \end{tabular} & \begin{tabular}{c} $e^+$ \\ + multiple jets \end{tabular}\\ \hline %--------------------------------------------------------------------- S4 & \begin{tabular}{ccccll} $\tilde{q}$ & $\longrightarrow$ & $q$ & $\chi^0_{\alpha}, \tilde{g}$ & & \\ & & & $\stackrel{\lambda'}{\hookrightarrow}$ & $e^- \bar{q} q$ & \\ % $\tilde{q}$ & $\longrightarrow$ & $q$ & $X$ & & \\ & & & $\hookrightarrow$ & $q \bar{q}$ & $\hspace{-0.5cm}Y$ \\ & & & & & $\hspace{-0.5cm} \stackrel{\lambda'}{\hookrightarrow}$ $e^- \bar{q} q$ \\ % \vspace{-0.2cm} \\ % & & & & $\:\mid$ \vspace{-0.3cm} & \\ % & & & & $\:\rightarrow$ $q \:\: \bar{q}'$ & \end{tabular} & \begin{tabular}{c} $e^-$ \\ (i.e. wrong sign lepton) \\ + multiple jets \end{tabular}\\ \hline %--------------------------------------------------------------------- S5 & \begin{tabular}{ccccll} $\tilde{q}$ & $\longrightarrow$ & $q$ & $X$ & & \\ & & & $\stackrel{\lambda'}{\hookrightarrow}$ & $\nu (\bar{\nu}) \bar{q} q$ & \\ % $\tilde{q}$ & $\longrightarrow$ & $q$ & $X$ & & \\ & & & $\hookrightarrow$ & $q \bar{q}$ & $\hspace{-0.5cm}Y$ \\ & & & & & $\hspace{-0.5cm} \stackrel{\lambda'}{\hookrightarrow}$ $\nu (\bar{\nu}) \bar{q} q'$ \\ % \vspace{-0.2cm} \\ % & & & & $\:\mid$ \vspace{-0.3cm} & \\ % & & & & $\:\rightarrow$ $q \:\: \bar{q}$ & \end{tabular} & \begin{tabular}{c} Missing $P_T$ \\ + multiple jets \end{tabular}\\ \hline %--------------------------------------------------------------------- S7 & \begin{tabular}{ccccll} $\tilde{q}$ & $\longrightarrow$ & $q$ & $X$ & & \\ & & & $\hookrightarrow$ & $l \nu_l $ & $\hspace{0cm}Y$ \\ & & & & & $\hspace{0cm} \stackrel{\lambda'}{\hookrightarrow}$ $e^{\pm} \bar{q} q$ \\ % \vspace{-0.2cm} \\ % & & & & $\:\mid$ \vspace{-0.3cm} & \\ % & & & & $\:\rightarrow$ $q \:\: \bar{q}'$ & \end{tabular} & \begin{tabular}{c} $e$ \\ + $e$ or $\mu$ \\ + Missing $P_T$ + multiple jets \end{tabular}\\ \hline %--------------------------------------------------------------------- S8 & \begin{tabular}{ccccll} $\tilde{q}$ & $\longrightarrow$ & $q$ & $X$ & & \\ & & & $\hookrightarrow$ & $l \nu_l $ & $\hspace{0cm}Y$ \\ & & & & & $\hspace{0cm} \stackrel{\lambda'}{\hookrightarrow}$ $\nu \bar{q} q$ \\ % \vspace{-0.2cm} \\ % & & & & $\:\mid$ \vspace{-0.3cm} & \\ % & & & & $\:\rightarrow$ $q \:\: \bar{q}'$ & \end{tabular} & \begin{tabular}{c} $e$ or $\mu$ \\ + Missing $P_T$ + multiple jets \end{tabular}\\ %-------------------------------------------------------------------- \hline \hline \end{tabular} \caption[] {\small \label{tab:sqtopo1} Squark decay channels in \Rp\ SUSY classified per distinguishable event topologies. Only the final states which are analysed here are listed in the table. $X$ and $Y$ denote a gluino, a neutralino or a chargino, and quarks are generically denoted by $q$. } \end{center} \end{table} %--------------------------------------------------------------------- %======================================================================= \section{The H1 detector} \label{sec:h1det} A detailed description of the H1 detector can be found in~\cite{H1DETECT}. Here we describe only the components relevant for the present analysis in which the final state of the events involves either a positron\footnote{Unless otherwise stated, the analysis does not distinguish explicitly between $e^+$ and $e^-$.} with high transverse energy or a large amount of hadronic transverse energy flow. The positron energy and angle are measured in a liquid argon (LAr) sampling calorimeter~\cite{H1LARCAL} covering the polar angular\footnote{The $z$ axis is taken to be in the direction of the incident proton, and the origin of coordinates is the nominal $ep$ interaction point.} range 4$^{\circ} \le \theta \le$ 154$^{\circ}$ and all azimuthal angles. The granularity is optimized to provide fine and approximately uniform segmentation in laboratory pseudorapidity and azimuthal angle $\phi$. It consists of a lead/argon electromagnetic section followed by a stainless steel/argon hadronic section. Electromagnetic shower energies are measured with a resolution of $\sigma(E)/E \simeq$ $12\%$/$\sqrt{E/\GeV} \oplus1\%$ and pion induced hadronic energies with $\sigma(E)/E \simeq$ $50\%$/$\sqrt{E/\GeV} \oplus2\%$ after software energy weighting. These resolutions were measured in test beams with electron energies up to 166 GeV~\cite{H1CALEPI,H1CALRES} and pion energies up to 205 GeV~\cite{H1CALRES}. % The absolute energy scales are known to 3\% and 4\% for % electromagnetic and hadronic energies respectively. % The energy calibration was determined initially from test beam data with an uncertainty of $3\%$ and $4\%$ for electromagnetic and hadronic energies respectively. A new absolute energy scale calibration for positrons detected in the actual H1 experiment has been recently established~\cite{H1F2PAPER} {\it in situ} by using the over-constrained kinematics of NC DIS, QED Compton and $e^+ e^-$ pair production from two-photons processes. A precision of $0.7\%$ is reached in the LAr central barrel region $80^{\circ} \lsim \theta_e \lsim 145^{\circ}$, $1.5\%$ in $40^{\circ} \lsim \theta_e \lsim 80^{\circ}$ and $3.0\%$ in the forward region $5^{\circ} \lsim \theta_e \lsim 40^{\circ}$. This represents an improved understanding of the electromagnetic energy scale compared to~\cite{H1HIGHQ2}, made possible by the increase of statistics accumulated in 1997. % All analyses described in the following rely on this updated calibration. % The angular resolution on the positron measured from the electromagnetic shower in the calorimeter varies from $\sim 2$ mrad below 30$^{\circ}$ to $\lsim 5$ mrad at larger angles. A lead/scintillating-fibre backward calorimeter~\cite{H1SPACAL} extends the coverage\footnote{The detectors in the backward region were upgraded in 1995 by the replacement of the lead/scintillator tile calorimeter~\cite{H1BEMC} and a proportional chamber.} at larger angles (153$^{\circ} \le \theta \lsim$ 178$^{\circ}$). Surrounded by the calorimeters is the tracking system which is used here to determine the position of the interaction vertex. The main components of this system are central drift and proportional chambers (25$^{\circ} \le \theta \le$ 155$^{\circ}$), a forward track detector (7$^{\circ} \le \theta \le$ 25$^{\circ}$) and a backward drift chamber\footnotemark[5]. The tracking chambers and calorimeters are surrounded by a superconducting solenoid providing a uniform field of $1.15${\hbox{$\;\hbox{\rm T}$}} parallel to the $z$ axis within the detector volume. The instrumented iron return yoke surrounding this solenoid is used to measure leakage of hadronic showers and to recognize muons. In the very forward region ($\theta \le 15^{\circ}$) muons can also be detected in three double layers of drift chambers, forming the Forward Muon Detector (FMD). The luminosity is determined from the rate of Bethe-Heitler $e p \rightarrow e p \gamma$ bremsstrahlung events measured in a luminosity monitor. This consists of a positron tagger ($e$-tagger) and a photon tagger ($\gamma$-tagger), located $- 33$ m and $- 103$ m respectively from the interaction point, respectively. % -> Say something about new EM calibration % % The increase of statistics accumulated in 1997 allowed for the first % time to perform an {\it in situ} calibration of the electromagnetic % section of the LAr calorimeter exploiting~\cite{PHIL} the kinematic % constraints of NC DIS and elastic QED Compton events. % The large amount of data with a lepton scattered in the central % wheels of the LAr allowed a very fine calibration in this region % leading to a precision of $1 \%$ for $\theta$ between $80^{\circ}$ % and $150^{\circ}$ on the electromagnetic energy scale. % Moreover, in the forward region of the LAr calorimeter, the calibration % scale has globally been improved and it was verified that the % absolute calibration of positron energies ranges within the % $\pm 3 \%$ systematics originally estimated from extrapolations % based on CERN test beam results. % The analysis described in the following relies on this updated % calibration. For the acquisition of events we rely on the timing information from a time-of-flight system and on the LAr trigger system which provides a measurement of the energy flow using coarse trigger towers~\cite{H1LARCAL}. %======================================================================= \section{Monte Carlo Event Generators} \label{sec:dismc} %======================================================================= % BACKGROUND SIMULATION: A complete Monte Carlo simulation of the H1 detector response is performed for each possible background source. For the NC or CC DIS background estimates we use the DJANGO~\cite{DJANGO} event generator, which includes first order QED radiative corrections. Simulation of real bremsstrahlung photons, based on HERACLES~\cite{HERACLES}, is also included. % QCD radiation at all orders is treated following the approach of the Color Dipole Model~\cite{CDM} and is implemented using ARIADNE~\cite{ARIADNE}. The hadronic final state is generated using the string fragmentation model~\cite{JETSET74}. % % For DIS at high $Q^2$, in the range relevant for {\large{S1}} % topology, several samples of events have % been simulated, each amounting to at least $10$ times % the available integrated luminosity. % In particular, the statistics simulated for the tail % of the $Q^2$ distribution above $10000 \GeV^2$ corresponds % to $\simeq 1500$ times that of the data. % % For NC DIS at medium $Q^2$, which constitutes an important part % of the SM background for {\large{S3}} topology, a sample of % $\simeq 3$ times the integrated luminosity of the data % has been used. % The parton densities in the proton used to estimate DIS expectations are taken from the MRST~\cite{MRST} parametrization. For direct and resolved photoproduction of light and heavy flavours, we use the PYTHIA MC event generator~\cite{PYTHIA} which relies on first order QCD matrix element % corrections to first order in $\alpha_s$, and uses leading-log parton showers and string fragmentation~\cite{JETSET74}. The GRV LO (GRV-G LO) parton densities~\cite{SFGRVGLO} in the proton (photon) are used at low $Q^2$. % The statistics simulated amounts to at least $3$ times % that of the data. % SIGNAL SIMULATION: The simulation of the leptoquark-like signatures ({\large S1} and {\large S2} topologies) relies on the event generator LEGO~\cite{LEGOSUSS} which is described in more detail in~\cite{H1LQ}. % For squarks undergoing gauge decays, we use the SUSYGEN~\cite{SUSYGEN} event generator, recently extended~\cite{SUSYGEN3,HERAMC} to allow to generate SUSY events in $ep$ and hadronic collisions. Any gauge decay for the resonant squark can be generated, and the cascade decay of the subsequent $\chi$'s or $\tilde{g}$ are performed according to the corresponding matrix elements. % For squarks undergoing gauge decays leading to % $e^{\pm}$ and multiple jets final states (topologies % {\large{S3}} and {\large{S4}}), the event generator % SUSSEX~\cite{LEGOSUSS} based on the % cross sections given in~\cite{RPVIOLATION} is used. % In both LEGO and SUSYGEN % initial state bremsstrahlung % in the collinear approximation is simulated, initial and final state parton showers are simulated following the DGLAP~\cite{DGLAP} evolution, and string fragmentation~\cite{PYTHIA,JETSET74} is used for the non-perturbative part of the hadronization. In addition initial state bremsstrahlung in the collinear approximation is simulated in the LEGO generator. % The parton densities used~\cite{MRST} are evaluated at the scale of the squark mass. This scale is also chosen for the maximum virtuality of parton showers initiated by a quark coming from the squark decay. % Moreover in the SUSYGEN generator the parton showers modeling QCD radiation off quarks emerging from a $\chi$ or $\tilde{g}$ decay are started at a scale given by the mass of this SUSY fermion. Many samples of events corresponding to final states {\large{S1}} to {\large{S8}} have been generated and were passed through a complete simulation of the H1 detector. The squark mass for these simulations has been varied from $75 \GeV$ to $275 \GeV$ in steps of $\simeq 25 \GeV$. Gauge decays of squarks involving one or two SUSY fermion have been simulated separately. For gauge decays of squarks into a $\chi^0$ or $\chi^+$ which directly decays via \Rp (i.e. processes corresponding to the first line of the {\large{S3}}, {\large{S4}} and {\large{S5}} slots in table~\ref{tab:sqtopo1}) the process $\tilde{q} \rightarrow q \chi^0_1$ has been simulated, for $\chi^0_1$ masses ranging between $\sim 40 \GeV$ and $\sim 160 \GeV$. In order to study gauge decays involving two SUSY fermions (this is in particular the case for squarks decays into gluinos), the process $\tilde{q} \rightarrow q \chi^+_1 \rightarrow q \chi^0_1 f \bar{f'}$ has been simulated for $\chi^+_1$ masses ranging between $\sim 90$ GeV and $\sim M_{\tilde{q}} - 20 \GeV$, and for $\chi^0_1$ masses between $\sim$ half of the $\chi^+_1$ mass and $\sim M(\chi^+_1) - 20 \GeV$. Masses of the $\chi$'s were varied by steps of $\sim 20 \GeV$. These simulations allowed to determine signal selection efficiencies as a function of the % squark mass and of the $\chi^0$/$\chi^+$ masses, masses of the squark and of the involved SUSY fermion(s) for essentially all allowed scenarios. The relatively fine grid of simulated scenarios permits to interpolate linearly between them, and extrapolate for points in the parameter space slightly outside the simulated region. %======================================================================= \section{Analysis} \label{sec:analyz} % \subsection{Selection of {\boldmath $ep$} collisions} % \label{sec:selep} The data reduction starts by the rejection of non-colliding background. It is common to all channels presented below and requires that the event survives a set of halo and cosmic muon filters, and that it is properly in time relative to interacting bunch crossings. Moreover, a primary interaction vertex must be reconstructed in the range $\mid z - \bar{z} \mid < 40 \cm$ where the mean position $\bar{z}$ of the nominal interaction point varies between $\pm 5$ cm around $z=0$ depending on the HERA beam settings. % Moreover, events must fulfill an electron or large missing % transverse momentum trigger requirement~\cite{H1LARCAL}. % Moreover the events must have been accepted by a LAr trigger asking either for an electromagnetic cluster, for a large transverse energy in the central part of the calorimeter, or for a large imbalance in the transverse energy flow. % % Put here the spacal cut ? % % The selection criteria specific to each of the studied event topologies are % presented below. % These rely basically on the final state lepton finding % and on global energy-momentum conservation cuts optimized separately % for each case using Monte-Carlo simulation. In what follows, unless explicitly stated otherwise, the energy flow summations run over all energy deposits $i$ in the calorimeters (apart from the electron and photon taggers). Thus, the missing transverse momentum $P_{T,miss}$ is obtained as $P_{T,miss} \equiv \sqrt{ \left(\sum E_{x,i} \right)^2 + \left(\sum E_{y,i} \right)^2 } $ with $ E_{x,i} = E_i \sin \theta_i \cos \phi_i $ and $ E_{y,i} = E_i \sin \theta_i \sin \phi_i $. The momentum balance with respect to the incident positron is obtained as $\sum \left(E - P_z\right) \equiv \sum \left(E_i - E_{z,i}\right) $ with $ E_{z,i} = E_i \cos \theta_i$. $\sum \left(E - P_z\right)$ should peak at $2E^0_e$ for events where only particles escaping in the proton direction remain undetected. %------------------------------------------------------------ \subsection{Event Selection for topology {\large S1}} \label{sec:selS1} %------------------------------------------------------------ Squarks decaying via {\large S1} behave as scalar leptoquarks and are characterized by NC DIS-like signatures. The scattered positron is expected to have a high transverse energy $E_{T,e}$ due to the Jacobian peak at $M_{\tilde{q}}/2$ of the $E_{T,e}$ distribution. The squark mass is related to the usual Bjorken $x$ via $M = \sqrt{xs}$. % Squarks being scalar particles, they decay isotropically in their centre of mass (CM) frame. Hence, the usual DIS Bjorken scattering variable $y$, which is related to the positron polar angle $\theta^*_e$ in the $e-q$ CM frame via $y = (1 + \cos \theta^*_e)/2$, is uniformly distributed for such events. This contrasts with the steeply falling $1/y^2$ dependence expected for NC DIS at fixed mass (i.e. fixed $x$). % Hence the strategy is to look for resonances in NC DIS-like events at high $M$ and high $y$, i.e. at high $Q^2$. % The selection criteria are those described in~\cite{H1LQ99} where a search for leptoquarks based on the data used here is presented in detail. The main selection criteria are the following~: % \begin{enumerate} % 1 \item an isolated positron with $E_{T,e} > 15 \GeV$ found in the LAr calorimeter; the positron energy cluster should contain more than $98\%$ of the LAr energy found within a pseudorapidity-azimuthal cone of opening $\sqrt{ (\Delta \eta_e)^2 + (\Delta \phi_e)^2 } = 0.25$ where $\eta_{e} = -\ln \tan \frac{\theta_e}{2}$; at least one charged track is required within the positron isolation cone; % 2 \item a total transverse momentum balance $P_{T,miss}/\sqrt{E_{T,e}} \leq 4 \sqrt{\GeV}$ ; % 3 \item a limited reconstructed momentum loss in the direction of the incident positron such that $ 40 \leq \sum \left(E - P_z\right) \leq 70 \GeV$. \end{enumerate} % % The identification of the scattered positron relies on the properties % of electromagnetic showers~\cite{H1CALEPI,PHIL} and isolation criteria % described in~\cite{H1LQ94}. % We use in the following the measurement of the scattered positron energy % and angle to reconstruct the variables $M$, $y$ and $Q^2$, henceforth % labeled $M_e$, $y_e$ and $Q^2_e$. % Kinematic formulae can be found in~\cite{H1HIGHQ2,H1LQICHEP98}. % %% As stated in~\cite{H1HIGHQ2}, we use cut (2) instead of an absolute % The cut (2) maintains a high selection efficiency for NC DIS-like events up to the highest $E_{T,e}$, by taking into account the natural scale of the hadronic energy resolution for $e$ + jet events. % Cut (3) provides a powerful rejection of photoproduction contamination and also suppresses NC DIS-like events with a very hard $\gamma$ emitted from the initial state positron. % by exploiting the fact that % $\sum \left(E - P_z\right)$ should peak at $2E^0_e$ for events % where only particles escaping in the proton direction remain undetected. % Moreover the analysis is restricted to the kinematic domain $Q^2 > 2500 \GeV^2$ and $0.1 < y < 0.9$. We use here the measurement of the scattered positron energy and angle to reconstruct the variables $M$, $y$ and $Q^2$, henceforth labeled $M_e$, $y_e$ and $Q^2_e$. Kinematic formulae can be found in~\cite{H1LQ99}. The signal significance is then optimized by applying in addition a $M_e$ dependent $y_e$ cut~\cite{H1LQ99}. This $y_e$ cut varies from $y_e \gsim 0.6$ at $60 \GeV$ to $y_e \gsim 0.4$ at $200 \GeV$ and down to $y_e \gsim 0.2$ around $260 \GeV$. % We observe 310 events satisfying all the above requirements in the mass range $M_e > 62.5 \GeV$, which is in good agreement with the SM expectation of $301.2 \pm 22.7$ (the sources of systematic errors will be described in section~\ref{sec:syst}). The measured mass spectrum of these candidates is compared to the NC DIS expectation in Fig.~\ref{fig:dndmS1S2}a. % %....................................................................... % --- FIGURE 2: dNdM S1 and S2 channels ----- % \begin{figure}[htb] \begin{center} \begin{tabular}{cc} \hspace*{-0.9cm}\mbox{\epsfxsize=0.55\textwidth % \epsffile{h1.lq98.dndmnc.mrst.bw.v02.eps}} \epsffile{H1prelim-00-162.fig2a.eps}} & \hspace*{-0.8cm}\mbox{\epsfxsize=0.55\textwidth % \epsffile{h1.lq98.dndmcc.mrst.h12.v02.bw.eps}} \epsffile{H1prelim-00-162.fig2b.eps}} \end{tabular} \end{center} % \caption[]{ \label{fig:dndmS1S2} {\small Mass spectra for (a) NC DIS-like and (b) CC DIS-like final states for data (symbols) and DIS expectation (histograms). In (a), the NC DIS-like comparison is shown before (open triangles, white histogram) and after (closed dots, hatched histogram) a $y$ cut designed to maximize the significance of an eventual scalar LQ signal. The gray boxes indicate the $\pm 1 \sigma$ band combining the statistical and systematic errors of the NC and CC DIS expectations. }} \end{figure} %--------------------------------------------------------------------------- % % The observed mass spectrum is seen to be well described by the SM expectation, with nevertheless a slight excess in the mass range $ 200 \GeV \pm \Delta M / 2$ with $\Delta M = 25 \GeV$, where 8 events are observed while $2.87 \pm 0.48$ are expected. This ``clustering'' is however less significant than that observed with $94 \rightarrow 96$ data alone~\cite{H1HIGHQ2}. This figure also shows the important background reduction achieved when applying the optimized $y_{cut}$ instead of the fixed cut $y_e > 0.1$. For this channel, the \Rp\ SUSY signal detection efficiency is found to vary between $\simeq 40\%$ and $\simeq 75 \%$ for squark masses ranging from 75 to 275 GeV. % SELECTION CUTS FOR S2 TOPOLOGOGY: %------------------------------------------------------------- \subsection{Event Selection for topology {\large S2}} \label{sec:selS2} %------------------------------------------------------------- % Squarks undergoing {\large S2} decays lead to CC DIS-like signatures with high missing transverse momentum due to the high $E_T$ escaping neutrino. In contrast to the {\large S1} channel only $\tilde{d}^{k*}_R$ squarks, produced via a fusion between the incident $e^+$ and a $\bar{u}^j$ quark from the proton, can undergo such a decay. % HERA sensitivity with an $e^+$ incident beam is thus lowered in this channel since a high $x$ sea quark must participate in the fusion. % The same holds for leptoquarks undergoing charged current decays, % at least in minimal models~\cite{BUCHMULL}. The analysis performed to search for such leptoquarks and described in~\cite{H1LQ99} is also relevant to seek squarks decaying via {\large{S2}}. Hence only the main cuts and results are presented here. The {\large{S2}} selection mainly requires~: \begin{enumerate} % 1 \item no $e^{\pm}$ candidate with $E_T > 5 \GeV$ found in the LAr calorimeter, using the same electron identification algorithm as used for {\large{S1}}; % 2 \item a missing transverse momentum $P_{T,miss} > 30 \GeV$. \end{enumerate} % These cuts eliminate NC DIS and photoproduction backgrounds. As for the {\large{S1}} channel, we concentrate on the high $Q^2$ domain by requiring $Q^2_h > 2500 \GeV^2$. The kinematic variables are here reconstructed using the Jacquet-Blondel ansatz~\cite{JACQUET} by summing over all measured final state hadronic energy deposits, and in that case are labeled $M_h$, $y_h$ and $Q^2_h$. Kinematic formulae can be found in~\cite{H1LQ99}. We also require $y_h < 0.9$ to avoid the high $y_h$ domain where the resolution on the mass $M_h = \sqrt{x_h s}$ reconstructed from the hadronic energy flow becomes poor~\cite{H1HIGHQ2}. We observe 213 events satisfying these requirements in the mass range $M_h > 50 \GeV$, which agrees well with the CC DIS expectation of $199.1 \pm 11.5$. The observed and expected mass spectra are shown to be in good agreement in Fig.~\ref{fig:dndmS1S2}b. The \Rp\ SUSY signal detection efficiency in this channel, determined from Monte-Carlo, varies between $\simeq 32 \%$ for a $75 \GeV$ squark mass to $\simeq 79 \%$ at $275 \GeV$. In the lowest mass range the efficiency is limited due to the high $P_{T,miss}$ requirement. % SELECTION CUTS FOR S3, S4, S7, S8e TOPOLOGOGY: %----------------------------------------------------------------------------- \subsection{Selection for {\boldmath{ $e$ + jets + $X$}} topologies} \label{sect:e+jets} %----------------------------------------------------------------------------- When the squark undergoes a gauge decay leading to a positron, the final states can be classified into several topologies, namely {\large S3}, {\large S4}, {\large S7$e$}, {\large S7$\mu$} and {\large S8$e$}. The selection requirements which are common to all these $e$ + multijets channels are the following~: % % \begin{enumerate} % 1 \item one positron candidate in the angular range $5^{\circ} < \theta_e < 110^{\circ}$ with $E_{T,e} > 5 \GeV$, using the same positron identification criteria as used for {\large{S1}}; % one track has to be found within a pseudorapidity-azimuth cone % of radius $\sqrt{\Delta \eta^2 + \Delta \phi^2} = 0.25$ centered % on the $e$ candidate; % the impact point of this track at the inner surface % of the LAr must be at least $2^{\circ}$ in azimuth away % from each of the eight $\phi$ cracks separating % octants of the LAr calorimeter; % 2 \item at least two jets in the angular range $7^{\circ} < \theta < 145^{\circ}$ and with $E_T > 10 \GeV$; these are found using a cone algorithm in the laboratory frame with a radius $\sqrt{\Delta \eta^2 + \Delta \phi^2} = 1$; % the fraction of the jet energy deposited in the electromagnetic part % of the calorimeter must be below $5 \%$; moreover, the highest $P_T$ jet is required to satisfy $\theta > 10^{\circ}$ and $E_T > 15 \GeV$; % 3 \item the $y$ variable reconstructed using the energy and polar angle of the highest $E_T$ $e$ should satisfy $y_e > 0.4$; % 4 \item the jet among the two highest $P_T$ jets selected as explained above, for which the polar angle $\theta_{backward}$ is maximal should verify~: $$ y_e - 0.4 > (\theta_{backward} - 25^{\circ}) \times (0.9-0.4)/(145-25).$$ % 5 \item the minimum of the polar angles of the highest $E_T$ positron and of the two highest $E_T$ jets should verify $$\theta_{min} = Min( \theta_e, \theta_{j,1}, \theta_{j,2}) < 45^\circ$$ % \end{enumerate} For events where a positron comes from the gauge decay of a squark, the scattered $e$ arises from the decay of the last $\chi$ or $\tilde{g}$ appearing in the decay chain and it only takes away a fraction of the momentum of this fermion. Hence its energy can be quite small and the cut applied on $E_{T,e}$ is lower than that used in the {\large{S1}} analysis, in order to maintain a high enough efficiency for the searched signal. % The enhancement of $\gamma p$ contamination % induced by the loosening of $E_{T,e}$ cut is compensated by the % more stringent criteria applied to the $e$ candidate which % are described in cut (1). Moreover, final state $e$'s coming from a squark cascade decay are strongly boosted in the direction of the incident proton, such that the $\theta_e < 110^{\circ}$ requirement discriminates powerfully the signal from NC DIS background. % Cut (3), by selecting high $y_e$ events, strongly suppresses NC DIS background while retaining high efficiency for the signal. Indeed, the $y_e = 1-E_e/E^0_e \sin^2 (\theta_e/2)$ distribution reconstructed from the measurement of the scattered $e$ appears strongly shifted towards large $y_e$ in SUSY events for the reasons given above. % Cut (4) exploits the fact that, for high $y_e$ NC DIS events satisfying the above set of cuts, one hard jet is usually scattered in the backward region of the calorimeter. On the contrary, jets coming from a squark gauge decay will be boosted in the forward direction, independently of $y_e$. The effect of this cut and how it separates the signal from the remaining NC DIS background is illustrated in Fig.~\ref{fig:thetacut}. In Fig.~\ref{fig:thetacut}a, several sets of $(M_{\tilde{q}},M_{\chi})$ are combined. The effect of cut (4) on signal events depends on the masses of the involved sparticles but retains a high efficiency over the whole range considered here. % %....................................................................... % --- FIGURE 3: ye vs theta cut ----- %....................................................................... \begin{figure}[h] \begin{tabular}{p{0.60\textwidth}p{0.40\textwidth}} \raisebox{-200pt}{ \mbox{\epsfxsize=0.6\textwidth % \epsffile{thetaba.eps}}} \epsffile{H1prelim-00-162.fig3.eps}}} & \caption {\it \label{fig:thetacut} Correlation between the $y_e$ variable reconstructed from the $e$ measurement and the angle $\theta_{backward}$ of the most backward jet for (a) SUSY Monte-Carlo events in which the squark undergoes a gauge decay leading to $e$ + multijets +$X$ final states and (b) NC DIS Monte-Carlo events, when preselection cuts (1) to (3) are applied. Cut (4) only retains events above the diagonal line. } \end{tabular} \end{figure} %....................................................................... % Cut (5) requires that one of the squark decay products should be emitted in the forward direction and allows an additional reduction of $\sim 40 \%$ of the SM background, with a negligible efficiency loss on the signal. % In addition, against photoproduction and low $Q^2$ NC DIS, it is also required % that there be less than $7.5 \GeV$ in the backward calorimeter. % The photoproduction background is further reduced by imposing % $E-p_z > 20 \GeV$. This latter requirement induces a negligible % efficiency loss on the SUSY signal even in the channels with % neutrino(s) in the final state since the quite forward $\nu$(s) % do not take away a large fraction of $E-p_z$. % %----------------------------------------------------------- % --- FIGURE 4: Control Plots, NC gauge preselection %----------------------------------------------------------- \begin{figure}[htb] \begin{center} \mbox{\epsfxsize=0.7\textwidth % \epsffile{susy_commonpresel_nc.bw.eps}} \epsffile{H1prelim-00-162.fig4.eps}} \end{center} % \caption[]{ \label{fig:nc_control} {\it For the $e$ + multijets $+X$ preselected events, distributions of (a) the transverse energy $E_{T,e}$ of the highest $E_T$ positron; (b) $y_e$; (c) the transverse momentum of the most forward jet; (d) the transverse momentum of the most backward jet; (e) the polar angle $\theta_{backward}$ of the most backward jet; (f) the missing transverse momentum. Superimposed on the data points (symbols) are histograms of the SM expectation (DIS and $\gamma p$). The gray band indicates the uncertainty on the SM prediction. The contribution from $\gamma p$ processes alone is shown as the hatched histogram.}} \end{figure} %----------------------------------------------------------- Applying all the above selection criteria, 214 events are accepted, which is in good agreement with the SM prediction of $209.9 \pm 33.7$, including 47.3 expected events from photoproduction where e.g. a jet has been misidentified as an electron. Fig.~\ref{fig:nc_control} shows for these candidates the distributions of the transverse energy of the highest $E_T$ positron, $y_e$, the transverse momentum of the most forward and most backward jet, the polar angle of the most backward jet, and the missing transverse momentum. All distributions are seen to be well described by the SM expectation. In particular, the high $y_e$ domain dominated by misidentified photoproduction events is well under control. %----------------------------------------------------- \subsubsection{Event Selection for topology {\large S3}} %----------------------------------------------------- % \noindent For gauge decays of squarks leading to a ``right'' sign final state lepton (e.g. $ e^{+} q' \rightarrow \tilde{q} \rightarrow \chi_1^0 + q \rightarrow e^{+} q'' \bar{q}'' q'$) we require, in addition to the preselection requirements listed previously~: % \begin{enumerate} % 1 \item a total transverse momentum balance $P_{T,miss} < 20 \GeV$; % 2 \item $ 40 \leq \sum \left(E - P_z\right) \leq 70 \GeV$. \end{enumerate} % We find 160 candidates satisfying the above set of cuts, which is in good agreement with the mean SM background of $152.6 \pm 13.4$ expected from NC DIS and photoproduction. % ($\gamma p$ processes % contribute to less than $xxx \%$). %------------------------------------------------------ % --- FIGURE 5: Mass spectrum S3 %------------------------------------------------------ \begin{figure}[htb] \begin{center} \mbox{\epsfxsize=0.7\textwidth % \epsffile{dndm.s3.final.v03.eps}} \epsffile{H1prelim-00-162.fig5.eps}} \end{center} % \caption[]{ \label{fig:dndmS3} {\it Mass spectrum for $e$ + multijets final states (event topology {\large{S3}}) for data (symbols) and NC DIS expectation (histogram). The gray band indicates the uncertainty of the SM prediction.}} \end{figure} %--------------------------------------------------------------- % An invariant mass $M_{inv}$ is then calculated using the energy $E_{wrm} = \sum_{i} E_i$ where the sum runs over all energy deposits in the calorimeters at $\theta > 10^{\circ}$ in order to exclude the proton remnant. Ideally the squark mass should be equal to $\sqrt{4x E^0_e E_{wrm}}$. % Bad measurements of the hadronic flow can alter this relation, and the variable $\sum \left(E - P_z\right)$ is used to estimate the induced under- or over-estimation of the squark mass, which is thus reconstructed as~: % $$M_{inv}=\sqrt{4x E^0_e E_{wrm}}-\frac{ \sum \left(E- P_z\right) -2E^0_e}{2}$$ % This reconstruction method improves the peak mass resolution for squarks decaying via {\large{S3}} by a factor $\simeq 2$ compared to H1 previous published analysis~\cite{H1RPV96}, this resolution being typically $ 7 \GeV$ for a $200 \GeV$ squark mass. % For example this % peak resolution is $ \simeq 7 \GeV$ for a $200 \GeV$ squark. The measured mass spectrum of the {\large{S3}} selected events is shown in Fig.~\ref{fig:dndmS3} to be well described by the SM prediction. The previous analysis~\cite{H1RPV96} using only 1994 $e^+ p$ data showed a slight excess ($2.9 \sigma$) in the invariant mass spectrum for masses around $80 \GeV$. This is clearly not confirmed with the additional statistics analysed here. % In Fig~\ref{fig:dndmS3}a, a small excess of events % is observed at the highest masses % but this is not very significant taking into account the % total error on the SM expectation, as can be seen in % Fig.~\ref{fig:dndmS3}b where the lines above and below unity % specify the $\pm 1 \sigma$ error band determined using the combination % of statistical and systematic errors. In this channel, the \Rp\ SUSY signal detection efficiency depends mainly on the mass of the SUSY fermion(s) entering the decay chain. Note that experimentally the efficiencies for $ right \, sign$ and for $ unsigned $ events are summed. Typical values are $\simeq 50 \%$ for a $200 \GeV$ squark decaying into a $80 \GeV$ $\chi^0_1$, and $\simeq 35 \%$ when these masses are set respectively to $100 \GeV$ and $40 \GeV$. % SELECTION CUTS FOR S4 TOPOLOGOGY: %----------------------------------------------------- \subsubsection{Event Selection for topology {\large S4}} %----------------------------------------------------- For a gauge decay of the squarks leading to a ``wrong'' sign final state lepton (i.e. $ e^{+} q' \rightarrow \tilde{q} \rightarrow e^{-} q'' \bar{q}'' q'$) we apply the same requirements as for channel {\large{S3}} and perform a determination of the lepton charge using the tracking chamber information. % In addition to the {\large{S3}} selection cuts, we require % that there be only one track found in the $e$ isolation cone. We consider the track which, among the vertex fitted tracks found in the electron isolation cone, has the highest momentum projected on the axis defined by the event vertex and the centre of gravity of the calorimetric energy deposits associated to the electron. This track is required to correspond to a negatively charged particle and must moreover satisfy the following criteria~: % \begin{enumerate} % 1 \item the track momentum $P$ must match the calorimetric energy $E_e$ of the $e$ candidate within~: $P / E_e > 0.5 $; %2 \item the error on the track curvature $\kappa$ must verify $ \mid \kappa / \delta \kappa \mid > 2 $. \end{enumerate} % These cuts ensure a good quality of the track reconstruction at the expense of a reduced efficiency. We found that the fraction of {\large{S3}} selected candidates which fulfill these additional requirements is $\simeq 80 \%$, which is well reproduced by the NC DIS simulation. % This is well reproduced by the NC DIS simulation, which predicts % an efficiency loss of $\simeq 34 \%$ in the phase space % relevant for {\large{S3}} analysis. We thus rely on the SUSY Monte-Carlo to estimate the efficiency loss of the above cuts (1) and (2) on the signal. % as a function of the squark mass. % The difference of $4 \%$ on the determination of % $\varepsilon_{loss}$ obtained when using data or NC DIS % Monte-Carlo events reflects the level at which the % tracking performance is described by the simulation, and will % be taken as a systematic error on $\varepsilon_{loss}$. No wrong sign candidate is observed in the data, while the SM prediction as estimated from Monte-Carlo is $1.3 \pm 0.3$ (coming from NC DIS). % SELECTION CUTS FOR S7 TOPOLOGOGY: %----------------------------------------------------- \subsubsection{Event Selection for topology {\large S7}, {\boldmath $e$} channel ({\boldmath {\large S7$e$}})} %----------------------------------------------------- For gauge decays of squarks leading to several jets and two $e$'s in the final state, we require, in addition of the common preselection cuts listed previously~: % \begin{enumerate} \item a second $e$ candidate, again in the angular range $5^{\circ} < \theta_e < 110^{\circ}$ and with $E_{T,e} > 5 \GeV$, using the same positron identification criteria as used for {\large{S1}}. \end{enumerate} We observe no candidate satisfying this additional cut for an expectation of $0.7 \pm 0.1$ event from NC DIS processes. These criteria ensure a typical selection efficiency of $\sim 30 \%$ on the searched signal. % SELECTION CUTS FOR S7, mu TOPOLOGOGY: %----------------------------------------------------- \subsubsection{Event Selection for topology {\large S7}, {\boldmath $\mu$} channel ({\boldmath {\large S7$\mu$}}) } %----------------------------------------------------- % The second possibility for a {\large S7} topology is that the second lepton in the final state is a muon. We search for this signature by applying exactly the same cuts as for {\large S7e}, but instead of a second electron we require a muon candidate in the polar angular range of $10^{\circ} < \theta < 110^{\circ}$ with a transverse momentum $p_T^{\mu} >5$~GeV. %----------------------------------------------------------- % --- FIGURE 6: Control Plot - muon %----------------------------------------------------------- \begin{figure}[h] \begin{tabular}{p{0.50\textwidth}p{0.50\textwidth}} \raisebox{-200pt}{ \mbox{\epsfxsize=6cm % \epsffile[180 270 380 540]{ptmplot.bw.ps}} \epsffile[180 270 380 540]{H1prelim-00-162.fig6.eps}} } & \caption[]{ \label{fig:ptmuon} {\it Distribution of the transverse momentum $p_T^{\mu}$ % of an identified muon for events selected by the {\large % {S7$\mu$}} selection of the muon for events satisfying the common preselection criteria and where a muon has been identified in addition, for data (points) and SM MC (histogram). The muon is required to be in the polar angular range of $10^{\circ} < \theta < 110^{\circ}$.}} \end{tabular} \end{figure} %----------------------------------------------------------- A muon candidate is identified by a track, well measured in the central %($\theta >20^{\circ}$) or forward tracking system. %($6^{\circ} < \theta <25^{\circ}$). In the overlap region information from both tracking systems is combined. The track has to match geometrically an energy deposition in the LAr calorimeter, compatible with that expected from a minimum ionizing particle, and/or a track in the instrumented iron and/or a track in the forward muon detector. The muon properties were found to be well described by the simulation, as shown in Fig.~\ref{fig:ptmuon} for the example of the $p_T^{\mu}$ distribution. Depending on the masses of the supersymmetric particles the muon is not necessarily of very high $p_T$. % E.g.\ simulations with SUSYGEN show that % i.e.\ for the case $M_{\tilde{q}}= 200$~GeV, % $M_{\chi^+}= 167$~GeV,$M_{\chi^0}= 152$~GeV the % $p_T^{\mu}$ distribution is peaked around 5~GeV. Furthermore the muons are not necessarily expected to be well isolated. Hence we are not requiring any isolation criterion and the cut on $p_T^{\mu} >5$~GeV was chosen analogous to the {\large S7e} selection but was independently found to be optimal concerning the signal to background ratio. The final selection efficiency for the {\large S7$\mu$} signal is between 35 and $50\%$ for most of the SUSY parameter space. After this selection we observe 2 candidates where $4.2\pm 1.2$ are expected for SM processes (3.0 from NC DIS and 1.2 from photoproduction). % SELECTION CUTS FOR S8, el TOPOLOGOGY: %----------------------------------------------------- \subsubsection{Event Selection for topology {\large S8}, {\boldmath $e$} channel ({\boldmath {\large S8$e$}}) } %----------------------------------------------------- For gauge decays of squarks leading to $e$ + multijets + $P_{T,miss}$ final states, we require in addition to the common preselection criteria~: % \begin{enumerate} \item a missing transverse momentum $P_{T,miss} > 15 \GeV$ ; \item that the variables $y_e$ (see section~\ref{sec:selS1}) and $y_h$ (see section~\ref{sec:selS2}) verify~: $ y_e \times (y_e - y_h) > 5 \%$. \end{enumerate} % Cut (2) exploits the fact that, for events coming from a squark decaying via {\large{S8e}}, the escaping neutrino carries away a non-negligible part of $E-p_z$ leading the variable $y_h$ to be substantially smaller than $y_e$, while $y_e \sim y_h$ is expected for NC DIS events. % %------------------------------------------------------ % --- FIGURE 7: Figure for S8,e %------------------------------------------------------ \begin{figure}[hbt] \begin{center} \mbox{\epsfxsize=0.7\textwidth % \epsffile{cut_s8el.bw.eps}} \epsffile{H1prelim-00-162.fig7.eps}} \end{center} % \caption[]{ \label{fig:s8ecut} {\it (a) Distributions of the variable $y_e \times (y_e - y_h)$ for the 214 events satisfying the preselection criteria (symbols) and for the expectation from NC DIS and $\gamma p$ processes (white histogram). The gray error band on the white histogram indicates the uncertainty on the SM prediction. The hatched histogram shows how this variable is typically distributed for events coming from a squark decaying via {\large{S8e}}. The thick line shows the lower cut applied. Correlation of $\sum (E-p_z)$ and $y_e$ for signal (b) and NC DIS (c) events. The cut applied is indicated in this plane by the thick curve. }} \end{figure} %--------------------------------------------------------------- % Fig.~\ref{fig:s8ecut}a shows the distribution of $y_e \times (y_e - y_h)$ for the 214 events accepted by the preselection requirements and for the SM expectation. The hatched histogram shows how this variable would be distributed for events induced by a squark decaying via {\large{S8e}}. The thick line indicates the cut which is applied. This cut corresponds to a $y_e$ dependent upper cut on $\sum (E-p_z)$ and has been optimised to maximise the signal significance. Fig.~\ref{fig:s8ecut}b and c show how this cut, indicated by the thick curves, discriminates between SUSY and NC DIS events, in the $(\sum(E-p_z), y_e)$ plane. One candidate is observed in the data when applying the selection criteria listed above, in good agreement with the SM expectation of $3.2 \pm 1.2$ events, all coming from NC DIS processes. The above requirements ensure a typical selection efficiency of $\sim 30 \%$ on the searched signal. %----------------------------------------------------------------------------- \subsection{Selection for {\boldmath{ $\nu$ + jets + $X$}} topologies} %----------------------------------------------------------------------------- % SELECTION CUTS FOR S5 and S8mu % In case of a gauge decay of the squark we % consider two scenarios where the final state contains no positron or % electron, but where the squark decays into a neutrino. % Two channels are considered to cover cases where squarks undergo a gauge decay leading to a neutrino instead of a positron in the final state. % These final states, {\large{S5}} and {\large{S8$\mu$}}, are characterized by several jets and missing $P_T$ and are selected by the following requirements~: % \begin{enumerate} \item a transverse missing momentum $P_{T,miss} > 25$~GeV; \item at least two jets in the angular range $7^{\circ} < \theta < 145^{\circ}$ and with $E_T > 10 \GeV$, with the highest $P_T$ jet satisfying $\theta > 10^{\circ}$ and $E_T > 15 \GeV$. This cut is exactly the same as described in section~\ref{sect:e+jets}. \end{enumerate} % We observe 44 events satisfying the above selection criteria, in good agreement with the SM prediction of $46.5 \pm 6.9$, mainly coming from CC DIS processes. % %----------------------------------------------------------- % --- FIGURE 8: Control Plots, CC gauge preselection %----------------------------------------------------------- \begin{figure}[htb] \begin{center} \mbox{\epsfxsize=0.7\textwidth % \epsffile{susy_commonpresel_cc.bw.eps}} \epsffile{H1prelim-00-162.fig8.eps}} \end{center} % \caption[]{ \label{fig:cc_control} {\it For the $\nu$ + multijets $+X$ preselected events, observed (symbols) and expected (white histograms) distributions of the transverse momenta of the two highest $P_T$ jets (a),(b), and the polar angle of the highest $P_T$ jet (c). The shaded histograms show typical distributions of these variables for events coming from a squark decaying into $\nu + jets$. (d): The invariant mass $M_{rec}$ in the centre of mass of the hard subprocess, assuming that only one neutrino escapes detection; $M_{rec}$ should provide an estimate of the mass of a squark decaying via {\large{S5}} into $\nu + jets$, as shown by the shaded histogram in (d) where the case of a 200 GeV squark has been considered.}} \end{figure} %----------------------------------------------------------- % Fig.~\ref{fig:cc_control}a-c shows for these selected events the distributions of the transverse momenta of the two highest $P_T$ jets and of the polar angle of the highest $P_T$ jet. All distributions are well described by the SM expectation. The corresponding distributions expected from squarks decaying into $\nu + jets$ are also shown as shaded histograms, where several kinematic configurations have been merged. Assuming that all the missing energy is carried away by one neutrino only, it is possible to reconstruct the kinematics of this $\nu$ by exploiting the constraint~: $(E-p_z)_{had} + (E-p_z)_{\nu} = 55 \GeV$ between the $(E-p_z)$ of the hadronic final state and that of the escaping neutrino. The four-vector of this $\nu$ is then added to that of the hadronic final state to reconstruct the invariant mass $M_{rec}$ in the rest frame of the incoming electron and quark. The observed and expected distributions for $M_{rec}$ are in good agreement as shown in Fig.\ref{fig:cc_control}d. For squark decaying via the channel {\large{S5}}, $M_{rec}$ provides an estimate of the squark mass. The shaded histogram in Fig.~\ref{fig:cc_control}d shows the resulting mass spectrum for Monte-Carlo events where a 200 GeV squark decays into $\nu + jets$. The observed resolution of $\sim 40 \GeV$ is typical for the range of squark masses probed in this analysis. %----------------------------------------------------- \subsubsection{Event Selection for topology {\large S5}} %----------------------------------------------------- For squarks decaying via {\large{S5}} leading to $\nu$ + multijets final states, we apply a more stringent cut on the transverse momentum of the second highest $P_T$ jet by requiring $P_{T,{\mbox{jet 2}}} > 15 \GeV$. We observe 21 events satisfying these requirements, in very good agreement with the expectation of $22.9 \pm 3.5$ from SM processes. The efficiency to select events induced by a squark decaying via {\large{S5}} ranges between $\sim 20 \%$ and $\sim 60 \%$. % SELECTION CUTS FOR S8, mu TOPOLOGOGY: %----------------------------------------------------- \subsubsection{Event Selection for topology {\large S8}, {\boldmath $\mu$} channel ({\boldmath {\large S8$\mu$}}) } %----------------------------------------------------- To search for gauge decays of squarks into neutrinos, a muon and several jets, the only requirement in addition to the common selection described above is the presence of a muon. The muon candidate is identified in the same way as for the channel {\large S7$\mu$} and has to fulfill the same criteria: $p_T^{\mu}>5$~GeV and $10^{\circ} < \Theta < 110^{\circ}$. The selection efficiency for this {\large S8$\mu$} signal is typically $\sim 40\%$. No candidate is observed where $0.5\pm 0.2$ are expected from SM processes, CC DIS being the dominantly contributing process. % SYSTEMATIQUES %----------------------------------------------------------- \subsection{Systematic Errors} \label{sec:syst} %----------------------------------------------------------- In each channel analysed in the previous sections, the error on the mean expectation from Standard Model processes has been calculated by taking into account the systematic errors described below. \\ The experimental error sources considered are the following~: % \begin{itemize} \item the uncertainty of $\pm 1.5 \%$ on the integrated luminosity which affects equally the SM expectations for each channel; % \item the uncertainty of $\pm 3 \%$ on the absolute calibration of the % calorimeter for electromagnetic energies. % This constitutes the main error source for the estimation of NC % DIS background to channel {\large{S1}}. \item the uncertainty on the absolute calibration of the calorimeters for electromagnetic energies, ranging between $\pm 0.7\%$ in the central wheels and $\pm 3\%$ in the forward region of the LAr calorimeter; this constitutes the main error source for the estimation of NC DIS background to channel {\large{S1}}; \item the uncertainty of $\pm 4 \%$ on the absolute hadronic energy scale. For inclusive or monojet NC DIS final states, the over-constrained kinematics allows to reduce this uncertainty to $\pm 2 \%$~\cite{H1F2PAPER}, which then applies to channels {\large{S1}} and {\large{S2}}. This is the main error source for all considered channels but {\large{S1}}. \end{itemize} % The estimates of SM expectations also suffer from theoretical uncertainties which are summarized below~: % \begin{itemize} \item for NC DIS-like final states, the uncertainty of $\pm 5 \%$ on parton density distributions obtained by QCD fits; for CC DIS-like topologies, which are mainly induced by $d$ quarks whose density in the proton is less constrained, this uncertainty increases linearly with $Q^2$ up to $\simeq 20 \%$ at the highest $Q^2$ considered here; \item the value of the strong coupling constant $\alpha_S$, leading to an uncertainty of $\pm 4\%$; \item for channels {\large{S1}}, {\large{S3}}, {\large{S4}}, {\large{S7e}} and {\large{S8e}}, higher order QED corrections imply a $\pm 2 \%$ uncertainty in the $y$ range considered here. \end{itemize} % All the analyses have been repeated with a shift of the central value of each of the sources of errors by $\pm 1$ standard deviation to estimate their individual contribution. The overall systematic error on SM expectations is then determined as the quadratic sum of the resulting errors and of the statistical error on the Monte-Carlo simulation. \\ %======================================================================= \section{Results } \label{sec:results} %======================================================================= Apart from a slight excess at $M_e \sim 200 \GeV$ in channel {\large{S1}}, no significant deviation from the SM expectations has been found in the various $\Rp$ and gauge decay channels analysed in section~\ref{sec:analyz}. % Assuming that the observed excess of events in the NC DIS-like channel % is due to a statistical fluctuation (or, formally, that the observation Assuming that no signal has been observed (or, formally, that the observation contains at most two components, an unknown ``resonance'' signal and a known expectation from NC DIS), the various decay channels can be used and combined to set constraints on \Rp\ SUSY models. As mentioned in section~\ref{sec:pheno}, when HERA operates with an incident beam of positrons, the best probed \Rp\ couplings are $\lambda'_{1j1}$ which allow for resonant production of $\tilde{u}^j_L$ squarks. Hence we concentrate here on these $\lambda'_{1j1}$ couplings, assuming one of them is non-vanishing for a given index $j$. % In this section, mass dependent upper rejection limits on the Yukawa couplings $\lambda'_{1j1}$ are first derived using, for each contributing channel, the branching ratios, the signal detection efficiencies and the numbers of observed and expected events. Limits are first derived in a ``phenomenological'' version of the MSSM where the masses of the sfermions are not related to the SUSY soft-breaking terms. % , for few example cases. A scan is then performed in the % framework of the constrained MSSM, and conservative % bounds on the Yukawa couplings are set in this model. Scans are performed in the framework this ``phenomenological'' MSSM as well as in the constrained MSSM, and conservative bounds on the Yukawa couplings are set in these models. Results are finally interpreted in the framework of the the so-called Minimal Supergravity (mSUGRA) model. %--------------------------------------------------------------- \subsection{The Limits Derivation} %--------------------------------------------------------------- We assume here that one of the $\lambda'_{1j1}$ is non-vanishing and derive rejection limits on this coupling as a function of the $\tilde{u}^j_L$ mass, combining all contributing channels. As already mentioned before, gauge invariance forbids the $\tilde{u}^j_L$ to decay into $\nu + q$ and thus the channel {\large{S2}} is not considered in the limits derivation. Mass dependent upper limits on the production cross section $\sigma(e^+ + p \rightarrow \tilde{u}^j_L)$ are obtained assuming Poisson distributions for the SM background expectations and for the signal. % Each channel {\large{S$k$}} contributes in the limits derivation via its total branching ratio $\beta_k$, the numbers of observed and expected events satisfying {\large{S$k$}} selection cuts, and the corresponding selection efficiency. % For channels {\large{S1}}, {\large{S3}} and {\large{S5}}, the numbers of observed and expected events are integrated within a mass bin which slides over the accessible mass range. The width of the mass bin is adapted to the expected mass resolution in each channel, so that this bin contains approximately $68 \%$ of the signal at a given squark mass. For example, the mass bins used to constrain a $200 \GeV$ squark are $\left[ 186 ; 204 \right] \GeV$ and $\left[ 186 ; 206 \right] \GeV$ for {\large{S1}} and {\large{S3}} channels respectively. % For channels {\large{S4}}, {\large{S7}} and {\large{S8}}, where both the expectation and the observation are small, no mass restriction is imposed. \\ % Both systematic and statistical errors have been folded in channel by channel as described in~\cite{H1LQ94}. % In addition to the systematic errors on the SM expectations described % in the previous section, the following uncertainties % have been considered in the derivation of rejection limits~: % % % \begin{itemize} % \item the lack of knowledge of the $d$ quark density in the proton % leads to an uncertainty on the % $e^+ + d \rightarrow \tilde{u}^j_L$ cross section, % which varies between $\simeq 5 \%$ at low masses % and $\simeq 20 \%$ around $250 \GeV$; % \item choosing $Q^2_e$, or $P^2_{T,e}$ instead of % $M^2_{\tilde{q}}$ % as the hard scale at which the parton distributions % are estimated induces % an uncertainty of $\pm 7 \%$ on the cross section % $e^+ + d \rightarrow \tilde{u}^j_L \rightarrow e^+ + d$, % and thus on the squark production cross section; % \item for channel {\large{S1}}, the effect of the interference % between standard NC DIS and the % $e^+ + d \rightarrow \tilde{u}^j_L \rightarrow e^+ + d$ % process has been studied and was found to be negligible. %\end{itemize} % % The masses of the neutralinos and charginos, as well as the gauge couplings between any two SUSY particles and a standard fermion/boson, are determined by the usual MSSM parameters\footnote{ % The L-R mixing between sfermions is neglected here.}~: The trilinear couplings between three scalar fields are neglected here.}~: the ``mass'' term $\mu$ which mixes the Higgs superfields, the soft-breaking parameters $M_1$ and $M_2$ for $U(1)$ and $SU(2)$ gauginos, and the ratio $\tan \beta$ of the vacuum expectation values of the two neutral scalar Higgses. All these parameters are defined at the electroweak (EW) scale. We assume that the gaugino mass terms unify at the GUT scale to a common value $m_{1/2}$ leading to usual relations between $M_1$, $M_2$ and the $SU(3)$ soft breaking term $M_3$, and approximate the gluino mass by the value of $M_3$ at the EW scale. % For a fixed set of these MSSM parameters and specified values for the sfermions masses, the branchings $\beta_k$ in the different channels {\large{S$k$}} only depend on $\lambda'_{1j1}$\footnote{ Same values for the branchings are then expected for $j=1,2$, while they differ a priori in the case of stop production ($j=3$) due to the large top mass suppressing $\tilde{t} \rightarrow t \chi^0$ or $\tilde{t} \rightarrow t \tilde{g}$ decays.}. This also holds for the upper limit on the cross section $ \sigma_{lim}(\lambda')$ derived from the combination of the analysed channels. The upper limit on $\lambda'_{1j1}$ at a given squark mass is then obtained by solving the equation~: % $\sigma_{lim}(\lambda') = \sigma(e^+ p \rightarrow \tilde{u}^j_L)$ where the production cross section $\sigma(e^+ p \rightarrow \tilde{u}^j_L)$ approximately scales with $\lambda^{'2}_{1j1}$ but is calculated by taking into account the width of the resonant squark. Decay chains involving more than two SUSY fermions ($\chi$ or $\tilde{g}$) % (eg.\ $\tilde{q} \rightarrow q \tilde{g} \rightarrow can in principle contribute to the ``gauge'' channels analysed, and would lead to final states with very large jet multiplicities, for which the calculations of signal efficiencies are not straightforward. Hence, only cascades involving two SUSY fermions are taken into account in the calculation of the ``observed'' branching ratios into {\large{S3}}...{\large{S8}}. % As an example, the total branching in channel {\large{S3}} is determined as follows~: % \begin{eqnarray} \beta_3 & = & \sum_{X=\chi^0, \chi^+, \tilde{g}} \beta( \tilde{u}^j_L \rightarrow q X) \times \beta_X \nonumber \\ & + & \sum_{X=\chi^0, \chi^+, \tilde{g}} \beta( \tilde{u}^j_L \rightarrow q X) \times \sum_{Y=\chi^0, \chi^+, \tilde{g}, M(Y) < M(X)} \beta(X \rightarrow qq Y) \times \beta_Y \nonumber \end{eqnarray} % where $\beta_{X,Y}$ represents the branching of $X, Y = \chi^0, \chi^+, \tilde{g}$ decaying via $\Rp$ into $e^+$ + 2 jets. The decays $X \rightarrow qq Y$ can be mediated by a real or virtual boson or sfermion. Radiative decays into the lightest Higgs boson $h$, e.g. $\chi^0_2 \rightarrow \chi^0_1 h$, can also contribute at low $\tan \beta$. Such decays, when followed by $h \rightarrow b \bar{b}$, are included in the calculation of the branching ratios $\beta_k$. The branching ratios for $\chi^0_{\alpha} \rightarrow \chi^0_{\beta} h$ depend a priori on another parameter determining the mass spectrum of the Higgs sector, taken here to be the pseudoscalar Higgs mass $m_A$. When $m_A$ is not related to the other parameters % (as will be the % case in section~\ref{sec:msugra}) it has been set to 300 GeV. Limits however do not depend on this assumption. The program HDECAY~\cite{HDECAY} has been used to determine the spectrum of the Higgs sector and the branching ratios of the Higgs bosons. This determination of the branchings $\beta_k$ is conservative, and it has been checked that, in the mass range considered here, the ``observed'' branching is % always larger than $80 \%$. generally close to $100 \%$. % The relevant decay widths of all involved sparticles have been obtained using the SUSYGEN package, taking into account all possible \Rp\ and gauge decays. %---------------------------------------------------------------------------------- \subsection{Limits on {\boldmath $\lambda'_{1j1}$} in the ``phenomenological'' MSSM} \label{sec:unconstrained} %---------------------------------------------------------------------------------- We consider here a version of the MSSM where the parameters $\mu$, $M_2$ and $\tan \beta$ are only used to determine the masses and couplings of the $\chi$'s, while the sfermions masses are free parameters. We assume that all squarks are degenerate. This assumption only enters in the calculation of the branching ratios of the $\chi$'s and of the gluino, since we are mainly probing the $\tilde{u}^j_L$ squark. Sleptons are also assumed degenerate, and their mass is set either to the common squark mass, or to a fixed value (90 GeV), close to the lowest mass bound coming from sfermions searches at LEP2. %----------------------------------------------------------- % --- FIGURE 9: Limits on \lambda'_{1j1} vs M_squark ----- % and branchings in all channels for cases \gamma-like and Z-like %----------------------------------------------------------- \begin{figure}[b] \begin{center} \mbox{\epsfxsize=0.8\textwidth % \epsffile{photino.40gev.eps}} \epsffile{H1prelim-00-162.fig9.eps}} \end{center} % \caption[]{ \label{fig:lim_combine_photino} {\it (a): Exclusion upper limits at $95 \%$ CL for the coupling $\lambda'_{1j1}$ as a function of the squark mass, for a set of MSSM parameters leading to a $\sim 40 \GeV$ $\chi^0_1$ dominated by its photino component. Regions above the curves are excluded. The limits are given for two hypotheses on the slepton mass. (b): The relative contributions of all channels versus the squark mass, when sleptons and squarks are assumed to be degenerate; (c) : as (b) but assuming a slepton mass of 90 GeV. The thick curves in (b) and (c) indicate the total branching ``seen'' by the analysis. }} \end{figure} %----------------------------------------------------------- % %----------------------------------------------------------- % --- FIGURE 10: Limits on \lambda'_{1j1} vs M_squark % and branchings in all channels for Z-like %----------------------------------------------------------- \begin{figure}[b] \begin{center} \mbox{\epsfxsize=0.8\textwidth % \epsffile{zino.40gev.eps}} \epsffile{H1prelim-00-162.fig10.eps}} \end{center} % \caption[]{ \label{fig:lim_combine_zino} {\it (a): Exclusion upper limits at $95 \%$ CL for the coupling $\lambda'_{1j1}$ as a function of the squark mass, for a set of MSSM parameters leading to a $\sim 40 \GeV$ $\chi^0_1$ dominated by its zino component. Regions above the curves are excluded. The limits are given for two hypotheses on the slepton mass. (b): The relative contributions of all channels versus the squark mass, when sleptons and squarks are assumed to be degenerate; (c): as (b) but assuming a slepton mass of 90 GeV. The thick curves in (b) and (c) indicate the total branching ``seen'' by the analysis. }} \end{figure} %----------------------------------------------------------- Rejection limits obtained at the $95 \%$ confidence level (CL) on $\lambda'_{1j1}$ ($j=1,2$) as a function of the $\tilde{u}^j_L$ mass are shown in Fig.~\ref{fig:lim_combine_photino}a as the full (dashed) curve, under the assumption $M_{\tilde{l}} = 90 \GeV$ ($M_{\tilde{l}} = M_{\tilde{q}}$). % Channels {\large{S1}}, {\large{S3}}, {\large{S4}} and % {\large{S5}} have been taken into account here. % ({\it The mapping of the efficiencies for S7 and S8 is % underway..}) Domains above the curves are excluded. The MSSM parameters have here been set to $\mu = -200 \GeV$, $M_2 = 80 \GeV$ and $\tan \beta = 2$. With this choice of parameters, the lightest neutralino $\chi^0_1$ is mainly dominated by its photino component and its mass is about $40 \GeV$, while the $\chi^+_1$ and $\chi^0_2$ are nearly degenerate around $90 \GeV$. It is worthwhile to note that combining all the contributing channels improves the sensitivity considerably, up to a factor $\simeq 5$ at lowest masses, compared to what would be achieved using only the $e+q$ data (i.e. channel {\large{S1}}). % The relative contributions of all channels are shown in Fig.~\ref{fig:lim_combine_photino}b and Fig.~\ref{fig:lim_combine_photino}c against the squark mass, at the current sensitivity limit on the Yukawa coupling, under the assumption $M_{\tilde{l}} = M_{\tilde{q}}$ and $M_{\tilde{l}} = 90 \GeV$ respectively. % Assuming $M_{\tilde{l}} = M_{\tilde{q}}$, channels {\large{S3}} and {\large{S4}} have similar dominant contributions for masses up to $\simeq 230 \GeV$. Only at the largest masses, where a large Yukawa coupling is necessary to allow squark production, the increasing direct $\Rp$ decay of the $\chi^+_1$ into $e^+$ + jets enhances the {\large{S3}} contribution compared to that of {\large{S4}}. The contribution of {\large{S5}} is significantly smaller, as expected since the $\chi^0_1$ dominated by its photino component decays mainly into $e^{\pm}$ + jets. In the very high mass domain where the coupling probed $\lambda$ becomes large, the relative contribution of {\large{S1}} is largely enhanced. % The relative contribution of the different channels is significantly different when $M_{\tilde{l}} = 90 \GeV$ is assumed, as can be seen in Fig.~\ref{fig:lim_combine_photino}c. As in the previous case, {\large{S3}} and {\large{S4}} dominate in the lowest squark mass domain, but become sub-leading as soon as the squark decays into $\chi^+_1$ or $\chi^0_2$ are kinematically allowed. Indeed the subsequent decay of $\chi^+_1$ or $\chi^0_2$ mainly proceeds via a two-body decay mode into a lepton-slepton pair, mostly followed by a decay of the slepton into $\chi^0_1$. As a result, the contributions of the channels {\large{S7}} and {\large{S8}} are considerably enhanced. This remains the case when the decays of the $\chi$'s proceed via a slightly off-shell slepton. {\large{S7}} contributes more than {\large{S8}} since the $\chi^0_1$ mainly decays into $e^{\pm}$ and jets. {\large{S3}} has a larger contribution than {\large{S4}} due to decays $\chi^+_1 \rightarrow \tilde{\nu_e} e^+$ followed by a \Rp decay of the sneutrino into two jets. % Channels {\large{S7}} and {\large{S8}} being not yet included in % the limits derivation, the limits obtained in the case % $M_{\tilde{l}} = M_{\tilde{q}}$ are significantly better than % those obtained for $M_{\tilde{l}} = 90 \GeV$, unless in the % low $\tilde{q}$ mass domain where $\tilde{q} \rightarrow q \chi^0_1$ % is the only gauge decay mode, and at highest mass where % {\large{S1}} dominates due to the large couplings probed. Since the sensitivity of our analysis is similar in all gauge channels, the upper limits on the Yukawa coupling are close to those obtained assuming $M_{\tilde{l}} = M_{\tilde{q}}$. Not including the channels {\large{S7}} and {\large{S8}} would significantly hamper the limit, by a factor $\sim 2$ for squark masses between $\sim 100$ GeV and $\sim 230$ GeV. % as shown by the dotted % curve in Fig.~\ref{fig:lim_combine_photino}a. Similar results are shown in Fig.~\ref{fig:lim_combine_zino} for a set of values for $(\mu, M_2, \tan \beta)$ leading to a $40 \GeV$ $\chi^0_1$ dominated by its zino component. As expected, {\large{S5}} is now the dominant channel since the zino-dominated $\chi^0_1$ mainly decays into $\nu$ + jets. This remains the case under the assumption that $M_{\tilde{l}} = 90 \GeV$ because the $\chi^+_1$ is here slightly lighter than 90 GeV. However decays of the $\chi^+_1$ into a slightly off-shell slepton lead to the enhancement of the channel {\large{S8}}, as seen in Fig.~\ref{fig:lim_combine_zino}c. For the two sets of MSSM parameters chosen in Fig.~\ref{fig:lim_combine_photino} and Fig.~\ref{fig:lim_combine_zino}, the gluino mass is large due to the large $M_2$ values and thus squark decays into $\tilde{g}$ are not kinematically allowed. Moreover radiative decays of heavy neutralinos into the light Higgs $h$ are only important for the $\chi^0_3$, and decays of the $\tilde{u}^j_L$ into this neutralino are strongly suppressed due to the Higgsino dominance of the $\chi^0_3$ in these example cases. % Since the gauge decay width of the squark does not depend % on the Yukawa coupling $\lambda'_{1j1}$, the regions of the % plane $(\beta_1, M_{\tilde{q}})$ above the dotted lines % in Fig.~\ref{fig:lim_combine}b and Fig.~\ref{fig:lim_combine}d % are excluded at $95 \%$ CL by our combined analysis. % In particular the branching ratio of a $200 \GeV$ $\tilde{u}^j_L$ % squark into $e^+ + q$ is constrained to be smaller than % a few percent for the two choices of MSSM parameters % presented here. % It should be noted however that other choices of % $(M_2, \mu, \tan \beta)$ allow a $200 \GeV$ squark to % decay via {\large{S1}} with a branching ratio above % $10 \%$. %----------------------------------------------------------- % --- FIGURE 11: Unconstrained Scan %----------------------------------------------------------- \begin{figure}[b] \begin{center} \mbox{\epsfxsize=0.6\textwidth % \epsffile{scan2.tanb2.col.v2.eps}} \epsffile{H1prelim-00-162.fig11.eps}} \end{center} % \caption[]{ \label{fig:scan2} {\it Exclusion upper limits at $95 \%$ CL on the coupling $\lambda'_{1j1}$ as a function of the squark mass for $\tan \beta = 2$, in the ``phenomenological'' MSSM. For each squark mass, a scan on the MSSM parameters $M_2$ and $\mu$ has been performed and the largest (lowest) value for the coupling limit is shown by the upper (lower) curve. }} \end{figure} %----------------------------------------------------------- In order to allow a more systematic study of the dependence of our sensitivity on the MSSM parameters, a scan on the MSSM parameters $M_2$ and $\mu$ is performed, for $\tan \beta = 2$. The mass of the sleptons is set to 90 GeV. % The parameters $M_2$ and $\mu$ are varied in the range $70 \GeV < M_2 < 300 \GeV$ and $-300 \GeV < \mu < 300 \GeV$. Points which lead to a scalar LSP or to a LSP mass below $30 \GeV$ are not considered. This latter restriction, as well as the lowest allowed value for $M_2$, are motivated by the exclusion domains resulting from $\chi$'s searches in \Rp SUSY carried out by the LEP2 experiments. % ({\it{reference..}}). For each point in this $(\mu, M_2)$ grid the upper bound $\lambda'_{lim}$ on the coupling $\lambda'_{1j1}$ is obtained as explained above. The most extreme curves in Fig.\ref{fig:scan2} indicate the maximal and minimal values obtained for $\lambda'_{lim}$ as a function of the squark mass, for $\tan \beta = 2$. The spread of the domain spanned by the limits on the Yukawa coupling is not too large and decreases with increasing squark mass. Less favourable cases occur when the squark dominantly decays via the channel {\large{S5}}, for which the large $P_{T,miss}$ requirement induces an efficiency loss especially for low squark masses. In addition, unfavourable situations might occur when large higgsinos components of the involved neutralinos lead to an enhancement of the decay $\chi^0_2 \rightarrow \chi^0_1 \tau^+ \tau^-$, which are not taken into account in the analysis. The sensitivity of our limits on the parameter $\tan \beta$ is studied in the next section. % For a Yukawa coupling of the electromagnetic strength % $(\lambda'_{1j1} = 0.3)$ squarks masses below $\sim 261$ GeV % are excluded at 95 $\%$ CL. Our results are also compared in Fig.~\ref{fig:scan2} to the most stringent indirect limits. The production of a $\tilde{u}$ squark via a $\lambda'_{111}$ coupling is very severely constrained by the non-observation of neutrinoless double beta decay~\cite{BETA0NU} as shown by the dotted curve. The most severe indirect limit on the coupling $\lambda'_{121}$, which could allow for the production of squarks $\tilde{c}$, comes from Atomic Parity Violation~\cite{APV,INDIRDREINER} and is indicated by the dashed curve in Fig.~\ref{fig:scan2}. For squark masses below $\sim 240$ GeV H1 direct limits significantly improve this indirect constraint on $\lambda'_{121}$ by a factor up to $\simeq 3$. %---------------------------------------------------------------------------------- \subsection{Limits on {\boldmath $\lambda'_{1j1}$} in the constrained MSSM} %---------------------------------------------------------------------------------- % A more systematic study of the upper bounds on the coupling % $\lambda'_{1j1}$ as a function of the squark mass is here performed % in the so-called constrained MSSM, where the number of free parameters % is reduced. In this section we consider a ``constrained'' version of the MSSM where the number of free parameters is reduced. In addition to the GUT relation mentioned above relating $M_1$, $M_2$ and $M_3$, we assume a universal mass parameter $m_0$ for all sfermions at very high scale. The evolution of the sfermions masses towards low scales is then driven by the Renormalisation Group Equations (RGE) and depends on the gauge quantum numbers of the sfermions. As a result, the sfermions masses at the electroweak scale are related to each other and to the parameters determining the gaugino sector. The model is thus completely determined by e.g. $m_0$, $M_2$, $\mu$ and $\tan \beta$ ($m_A$ is set to 300 GeV as already mentioned, and we assume no mixing between the sfermions at the electroweak scale). For a given value of the $\tilde{u}^j_L$ squark mass, the requirement of sfermions unification at large scale imposes an upper bound on the parameter $M_2$, which is obtained using approximate solutions for the RGE. This upper bound on $M_2$ increases with the squark mass. We then perform a scan on $\mu$ ($-300 \GeV < \mu < 300 \GeV$), $\tan \beta$ ($2 \le \tan \beta \le 40$), and on $M_2$ in its allowed range defined by $M( {\tilde{u}}^j_L )$ and $\tan \beta$. As before points leading to a scalar LSP or to a LSP mass below $30 \GeV$ are not considered. This lower bound on the LSP mass forbids too small values of $M_2$ and hence imposes a lower bound on the $\tilde{u}^j_L$ mass. The most extreme curves in Fig.\ref{fig:scan3} indicate the maximal and minimal values obtained for $\lambda'_{lim}$ as a function of the $\tilde{u}^j_L$ mass $(j=1,2)$. % %----------------------------------------------------------- % --- FIGURE 12: Constrained SCan %----------------------------------------------------------- \begin{figure}[htb] \begin{center} \mbox{\epsfxsize=0.6\textwidth % \epsffile{scan3.bw.eps}} \epsffile{H1prelim-00-162.fig12.eps}} \end{center} % \caption[]{ \label{fig:scan3} {\it Exclusion upper limits at $95 \%$ CL for the coupling $\lambda'_{1j1}$ as a function of the mass of the $\tilde{u}^j_L$ ($j=1,2$), in the constrained MSSM. For each squark mass, a scan on the MSSM parameters $\mu$, $M_2$ and $\tan \beta$ has been performed and the largest (smallest) value for the coupling limit is shown by the upper (lower) curve. }} \end{figure} %----------------------------------------------------------- % % The large spread of the domain spanned by the limits $\lambda_{lim}$ % is mainly due to grid points at $ \mu > 0$ and small % $M_2$, where the masses of the $\chi$'s are small, leading to % a substantial efficiency loss on the squark signal in the ``gauge'' % channels and thus to a smaller sensitivity on the coupling. % However, for $75 \%$ of the scanned points, the limit $\lambda_{lim}$ lies % below the dashed line shown in Fig.\ref{fig:scan1}. % Moreover, when requiring that the mass of the LSP is above % 30 GeV (as suggested by neutralinos and charginos searches % carried out at LEP2), the area spanned by $\lambda_{lim}$ reduces to % the grayed domain. Note that this condition imposes a lower bound % for the mass of the $\tilde{u}^j_L$ in the considered model. % It can be seen that the spread of the domain spanned by the limits $\lambda'_{lim}$ is quite small, i.e. that the sensitivity of our analysis on $\lambda'$ does not depend too much on the free parameters of the model. The most optimistic limits are usually obtained for large $\tan \beta$ and are in general better than those derived previously in the ``unconstrained'' MSSM where only large values of $M_2$ were considered. Indeed, for moderate values of $M_2$ and large $\tan \beta$, the sneutrinos are very light, leading to an enhancement of the quasi background-free channels {\large{S7}} and {\large{S8}} via $\chi^+_1 \rightarrow l^+ \tilde{\nu}$. % On the other hand, the smallest sensitivities on the Yukawa coupling are obtained either when {\large{S5}} dominates, or when the gluino is light enough so that $\tilde{u}_L \rightarrow u \tilde{g}$ is the dominant decay mode, and when the coupling of the $\chi^0_1$ to ``right''-squarks is suppressed (i.e. when $\chi^0_1$ is dominated by its zino or higgsinos components). In this latter case the main decay mode of the $\tilde{g}$ proceeds via an heavier $\chi$. Such cascade decays of squarks, involving more than two SUSY fermions, are not taken into account as already mentioned. For a Yukawa coupling of the electromagnetic strength ($\lambda'_{1j1} = 0.3$), squark masses up to values between 258 and 267 GeV can be ruled out at $95 \%$ CL in the framework of the constrained MSSM. This extends far beyond the mass domain excluded from relevant searches for scalar leptoquarks performed by both the $D\emptyset$~\cite{D01GENE} and CDF~\cite{CDF1GENE} experiments at the TeVatron collider. These rule out $\tilde{u}^j_L$ squark masses below $205 \GeV$ as soon as the branching ratio of the squark into $e^+ + q$ is greater than $\simeq 50 \%$, but the excluded mass domain does not extend above $\simeq 110 \GeV$ for values of this branching below $10 \%$. Since in \Rp\ SUSY such a branching can be naturally small as seen in section~\ref{sec:unconstrained} % , as can be seen in Fig.~\ref{fig:lim_combine}b and d, such such leptoquark-like constraints are easily evaded. Comparisons with specific \Rp SUSY searches carried out at the TeVatron will be addressed in the next section. Moreover, for a coupling strength ten times smaller than $\alpha_{EM}$, the most conservative bound on the mass of the $\tilde{u}^j_L$ obtained from this analysis still reaches 182 GeV. %---------------------------------------------------------------------------------- \subsection{Limits on {\boldmath $\lambda'_{1j1}$} in mSUGRA} \label{sec:msugra} %---------------------------------------------------------------------------------- The model considered previously can still be more constrained by imposing that the breaking of the electroweak symmetry is driven by radiative corrections, leading to the so-called mSUGRA model. Requiring the Radiative Electroweak Symmetry Breaking (REWSB), the equations corresponding to the minimisation of the Higgs potential allow to express $| \mu |$ as a function of the other parameters. Only the sign of $\mu$ remains arbitrary. The program SUSPECT~1.2~\cite{SUSPECT} is used to obtain the REWSB solution for $|\mu|$ when the other parameters are fixed. It makes use of a Runge-Kutta algorithm to solve numerically the one-loop RGE. Assuming a fixed value for the $\Rp$ coupling $\lambda'_{1j1}$ ($j=1,2$), our negative searches can be expressed in terms of constraints on the mSUGRA parameters, for example on $(m_0, m_{1/2})$ when $\tan \beta$, the common trilinear coupling $A_0$ and the sign of $\mu$ are fixed. Values of the parameters leading to a LSP lighter than 30 GeV have not been excluded here. However a vanishing efficiency has been assumed for squarks undergoing a gauge decay ending by a SUSY fermion lighter than 30 GeV, since efficiencies in this mass domain have not been calculated (see section~\ref{sec:dismc}). For $\tan \beta = 2$, $A_0 = 0$ and $\mu < 0$, results obtained for a Yukawa coupling $\lambda'_{1j1} = 0.3$ are shown in Fig.~\ref{fig:sugrat2}a. % %----------------------------------------------------------- % --- FIGURE 13: Limits on (m0, m_1/2) % tan(beta) = 2, lambda' = 0.3 %----------------------------------------------------------- \begin{figure}[htb] \begin{center} \begin{tabular}{cc} \mbox{\epsfxsize=0.5\textwidth % \epsffile{tanb2.muneg.v2.eps}} \epsffile{H1prelim-00-162.fig13a.eps}} & \mbox{\epsfxsize=0.5\textwidth % \epsffile{tanb6.muneg.v2.eps}} \epsffile{H1prelim-00-162.fig13b.eps}} \end{tabular} \end{center} % \caption[]{ \label{fig:sugrat2} {\it Domain of the plane $(m_0, m_{1/2})$ excluded by this analysis for $\mu < 0$, $A_0 = 0$ and $\tan \beta = 2$ (a), and $\tan \beta = 6$ (b), for a \Rp coupling $\lambda'_{1j1} = 0.3$ (light shaded areas). In (b) the exclusion domain obtained for $\lambda'_{1j1} = 0.1$ is also shown as the dark gray area. The hatched domains correspond to values of the parameters where no REWSB is possible or where the LSP is a sfermion. The region below the dashed curves is excluded by the $D \emptyset$ experiment. Two isolines for the mass of the $\tilde{u}^j_L$ are also shown in (a) as dotted curves. }} \end{figure} %----------------------------------------------------------- % The obtained limit basically follows the squark mass isoline $M( {\tilde{u}}^j_L) \sim 260 \GeV$. At low $m_{1/2}$ value, the sensitivity is however decreased down to $M( {\tilde{u}}^j_L) \sim 210 \GeV$ due to the important branching ratio of the squark in cascade decays involving a very light (~$< 30 \GeV$) SUSY fermion, for which the efficiency has been conservatively set to zero. % % The sensitivity is slightly % decreased at low values of $m_0$ where the light sleptons % enhance the branching ratios into the channels {\large{S7}} % and {\large{S8}}, not yet included in the limits derivation. % The region of the $(m_0, m_{1/2})$ plane below the dashed curve is excluded from searches for SUSY where $R_p$ is violated by a $\lambda'_{1jk}$ coupling carried out at the $D\emptyset$ experiment~\cite{NIRMALYA}, relying on dielectrons events. % HERA and TeVatron sensitivities are quite similar in the low $m_0$ domain, but at larger $m_0$ HERA's sensitivity decreases due to the increasing squark mass, while sensitivity is still obtained in $p \bar{p}$ collisions via gluino production. Similar results are shown in Fig.~\ref{fig:sugrat2}b for $\tan \beta = 6$. The domains excluded by this analysis are shown for $\lambda'_{1j1}=0.3$ ($\lambda'_{1j1}=0.1$) as the light shaded (dark shaded) areas. For such large values of $\tan \beta$ the domain probed by this analysis considerably extends beyond the region excluded by the $D\emptyset$ experiment. This is due to the fact that, for large values of $\tan \beta$, the lightest neutralino is dominated by its zino component, so that its decay into $e^{\pm}$ is suppressed. As a result the sensitivity of the $D\emptyset$ analysis using the dielectron channel is decreased, while the dominant squark decay mode is still ``seen" in the H1 analysis via the {\large{S5}} and {\large{S8}} channels. % -> Comparison with TeVatron results % -------------------------------- % Relevant searches for scalar leptoquarks have been performed by both % the $D\emptyset$~\cite{D01GENE} and CDF~\cite{CDF1GENE} experiments % at the TeVatron collider. These rule out $\tilde{u}^j_L$ squark masses % below $200 \GeV$ as soon as the branching ratio of the squark into % $e^+ + q$ is greater than $\simeq 50 \%$, but the excluded mass domain does % not extend above $\simeq 110 \GeV$ for values of this branching % below $10 \%$. Since in \Rp\ SUSY such a branching can be naturally % small, as can be seen in Fig.~\ref{fig:lim_combine}b and d, such % leptoquark-like constraints are easily evaded. % % Specific SUSY searches have also been carried out at the TeVatron collider, % mainly in the Minimal Supergravity (mSUGRA) frame (imposing mass relations % between the sparticles) and assuming $R$-parity conservation. % Recently the $D\emptyset$ experiment~\cite{D0RPV} also studied the pair production % of squarks in \Rp\ mSUGRA, looking at like-sign dielectron events % accompanied with jets. Squark masses below $252 \GeV$ are ruled % out by this analysis assuming five degenerate squarks. % % % A similar analysis considering models in which $R$-parity is violated % by $\lambda'_{121}$ % has been carried out by the CDF experiment~\cite{CDFRPV}, % from which we infer that a five times smaller cross section would lead % to a squark mass limit of $\simeq 150 \GeV$, depending on the gluino and % neutralino masses. % Within the same model, the CDF experiment~\cite{CDFRPV} also % considered separately the pair production % of a light stop $\tilde{t}_1$ and excluded stop masses below % $\simeq 130 \GeV$ assuming that the stops decay into $c \chi^0_1$. % If $R$-parity is violated by a $\lambda'_{13k}$ coupling the \Rp\ % decays of the stops would dominate over loop decays into $c \chi^0_1$, % but be negligible compared to decays into $b \chi^+_1$ if this latter % mode is allowed (which implies $M(\tilde{t}_1) > M(\chi^+_1)$ and % that there is a % non-vanishing ``left'' component for the $\tilde{t}_1$ eigenstate). % The subsequent decays of the $\chi^+_1$ would then lead to final states % similar to those studied by CDF in~\cite{CDFRPV}. % Thus we conclude that $130 - 150 \GeV$ is a reliable estimate of the % TeVatron sensitivity on the light stop mass also in models in which $R$-parity % is violated by a $\lambda'_{13k}$ coupling. % % Hence TeVatron and HERA sensitivities are competitive in \Rp\ SUSY % models with five degenerate squarks, but models predicting a light stop % are probably better constrained at HERA provided that the \Rp\ % coupling $\lambda'_{13j}$ is not too small. % % % % %====================================================================== \section{Conclusions} We have searched for resonant squarks in $ep$ collisions at HERA in $R$-parity violating as well as gauge decay modes. %%Apart from $e$+ jet final states, for which it is %%not yet clear whether the excess of observed events compared to %%Standard Model expectation should be attributed to a statistical %%fluctuation, no significant evidence for the production of squarks was %%> % Notwithstanding an excess at $M_e \sim 200 \GeV$ in % channel {\large{S1}}, No significant evidence for the production of squarks was found and mass dependent limits on the $R$-parity violating couplings were derived. %%< In the MSSM framework, the existence of squarks coupling to a $e^+ d$ pair with masses up to $182 \GeV$ $(258 \GeV)$ is excluded at $95 \%$ confidence level for a strength of the Yukawa coupling equal to $0.01 \times \alpha_{em}$ ($\alpha_{em}$), independently of the values of the model parameters. 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