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\begin{document}  


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\begin{titlepage}

\noindent

\vspace{5cm}

\begin{center}
\begin{Large}

{\bf Search for Bosonic Stop Decays in R-Parity Violating Supersymmetry in {\boldmath $e^+ q$} Collisions at HERA}

\vspace{2cm}

H1 Collaboration

\end{Large}
\end{center}

\vspace{2cm}

\begin{abstract}
A search for scalar top quarks in R-parity violating supersymmetry is performed in $e^+ p$ collisions at HERA using the H1 detector. 
The data taken at \mbox{$\sqrt{s}=319\gev$} and \mbox{$\sqrt{s}=301\gev$}, correspond to an integrated luminosity of $105.8\pbarnt$.
The resonant production of scalar top quarks $\tilde{t}$ in positron quark fusion via a Yukawa coupling $\lambda'$ is considered with the subsequent bosonic stop decay $\tilde{t}\rightarrow \tilde{b} W$.
The R-parity violating decay of the sbottom quark $\tilde{b}\rightarrow d \bar\nu_e$ is considered and leptonic and hadronic $W$ decay channels are analysed.
No evidence for stop production is found in the bosonic stop decay nor in the direct R-parity violating decay $\tilde{t}\rightarrow eq$.
Mass dependent limits on $\lambda'$ are obtained in the framework of the Minimal Supersymmetric Standard Model.
Stop quarks with masses below $275\gev$ are excluded at $95\%$ confidence level in a large part of the parameter space for a Yukawa coupling of electromagnetic strength.
\end{abstract}

\vspace{1.5cm}


\end{titlepage}

\newpage

\begin{table}[p]
  \begin{center}
    \begin{tabular}{|c|l|c|}
      \hline
      {\bf Channel} & {\bf Decay processes} & {\bf Signature}\\
      \hline
      & $\tilde{t} \rightarrow \tilde{b}\;W$ &\\
      & \hspace{0.8cm}$\stackrel{\lambda'}\hookrightarrow d\bar{\nu}_e$ &\\
      $je$\ptmiss & \hspace{1.1cm}$W \rightarrow e{\nu}_e$ & jet + $e$ + \ptmiss\\
      & \hspace{1.7cm}{\small $\rightarrow \tau{\nu}_\tau\rightarrow e\nu\nu\nu$} & \\
      $j\mu$\ptmiss & \hspace{1.1cm}$W \rightarrow \mu{\nu}_{\mu}$ & jet + $\mu$ + \ptmiss\\
      & \hspace{1.7cm}{\small $\rightarrow \tau{\nu}_\tau \rightarrow \mu\nu\nu\nu$} & \\
      $jjj$\ptmiss & \hspace{1.1cm}$W \rightarrow q\bar{q}'$ & 3 jets + \ptmiss\\
      \hline
      $ed$ & $\tilde{t} \stackrel{\lambda'}\rightarrow ed$ & jet + high $P_T$ $e$\\
      \hline
    \end{tabular}
  \end{center}
  \caption{Stop decay channels in \Rp\hspace{0.075cm} SUSY analysed.
    The \Rp\hspace{0.075cm} process is indicated by the coupling $\lambda'$.}
  \label{tab:decays}
\end{table}
\begin{table}[p]
  \begin{center}
    \begin{tabular}[t]{|l|c|l|c|l|c|l|}
      \hline
      \multicolumn{7}{|c|}{\large \bf H1 preliminary}\\
      \hline
      Channel & \multicolumn{2}{c|}{$\sqrt{s} =301\gev$} & \multicolumn{2}{c|}{$\sqrt{s} =319\gev$} & \multicolumn{2}{c|}{all} \\
      & data & SM expectation & data & SM expectation & data & SM expectation \\
      \hline
      \hline 
      $je$\ptmiss & $1$ & $1.16 \pm 0.28$ & $2$ & $2.68 \pm 0.64$ & $3$ & $3.84 \pm 0.92$ \\
      &  & {\small (W: $0.75 \pm 0.12$)} & & {\small (W: $1.80 \pm 0.29$)} & & {\small (W: $1.55 \pm 0.25$)}\\
      \hline
      $j\mu$\ptmiss & $4$ & $0.84 \pm 0.14$ & $4$ & $1.85 \pm 0.33$ & $8$ & $2.69 \pm 0.47$ \\
      &  & {\small (W: $0.57 \pm 0.09$)} & & {\small (W: $1.36 \pm 0.22$)} & & {\small (W: $1.93 \pm 0.31$)} \\
      \hline
      $jjj$\ptmiss & $1$ & $1.91 \pm 0.54$ & $4$ & $4.33 \pm 1.21$ & $5$ & $6.24 \pm 1.74$ \\
      \hline
      $ed$ & $366$ & $383.5 \pm 44.9$ & $734$ & $736.2 \pm 86.3$ & $1100$ & $1119.7 \pm 131.3$ \\
      \hline
    \end{tabular}
  \end{center}
  \caption{Total number of selected events for the $e^+p$ H1 data set of the stop decay channels at $\sqrt{s} =301\gev$, $\sqrt{s} =319\gev$ and the combined data set. For the $je$\ptmiss channel and the $j\mu$\ptmiss channel the SM expectation arising from $W$-production are given in brackets.}
  \label{tab:evex}
\end{table}
\begin{table}[p]
  \begin{center}
    \begin{tabular}{|c|}
      \hline
      {\bf SUSY Parameter Range}\\
      \hline
      $M_{2} = 1000\gev$\\
      $400\gev < \mu < 1000\gev$\\
      $\tan\beta = 10$\\
      $180\gev < M_{\tilde t_1} < 290\gev$\\
      $100\gev < M_{\tilde b_1} < 210\gev$ \\
      $0.6$ rad $< \theta_{\tilde t}, \theta_{\tilde b} < 1.2$ rad \\
      $A_t = A_b = -100\gev$\\
      \hline
    \end{tabular}
  \end{center}
  \caption{The chosen SUSY parameter range in the unconstrained MSSM.}
  \label{tab:para}
\end{table}

%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
\begin{figure}[p]
  \begin{center}
    \includegraphics[width=0.6\textwidth]{fig1_prelim}
  \end{center}
  \caption{An example of the branchig ratios of stop decay modes for $M_{\tilde{b}}=100\gev$ and $\lambda'_{131}=0.3$ as a function of the stop mass, when the gauge fermionic decay modes of the stop are kinematically not allowed. The solid lines show the branchig ratios for $\theta_{\tilde{b}}=0.6$ rad and the dashed lines for $\theta_{\tilde{b}}=1.2$ rad.}
  \label{fig:br}
\end{figure} 

\begin{figure}[p]
  \begin{center}
    \includegraphics[width=0.9\textwidth]{fig2_prelim}
  \end{center}
  \caption{Lowest order s channel diagram for \Rp\hspace{0.075cm} stop production at HERA followed by a) the bosonic decay of the stop and b) the \Rp\hspace{0.075cm} decay of the stop.}
  \label{fig:feynman}
\end{figure} 

\begin{figure}[p]
  \begin{center}
%    \includegraphics[scale=0.38]{fig3a_prelim}
%    \hspace{0.5cm}\includegraphics[scale=0.38]{fig3b_prelim}\\
%    \vspace{1cm}

%    \includegraphics[scale=0.38]{fig3c_prelim}
%    \hspace{0.5cm}\includegraphics[scale=0.38]{fig3d_prelim}
    \includegraphics[width=1\textwidth]{fig3_prelim}
  \end{center}
  \vspace{-0.5cm}
  \caption{Mass spectra for the $e^+p$ H1 data set: a) transverse mass of the $je$\ptmiss channel; b) transverse mass of the $j\mu$\ptmiss channel; c) reconstructed mass of the $jjj$\ptmiss channel; d) $M_e$ distribution of the $ed$ channel. The shaded error band indicates the systematic uncertainty on the SM background. }
  \label{fig:mass}
\end{figure}

\begin{figure}[p]
  \begin{center}
    \includegraphics[width=0.5\textwidth]{fig4_prelim}
  \end{center}
  \vspace{-0.8cm}
  \caption{Allowed stop cross section regions $\sigma_{\tilde{t}}\pm \Delta\sigma_{\tilde{t}}$ depending on the stop mass for all bosonic stop decay channels. Only statistical errors are shown.}
  \label{fig:band}
\end{figure} 

\begin{figure}[p]
  \begin{center}
    \includegraphics[scale=0.39]{fig5a_prelim}
    \includegraphics[scale=0.39]{fig5b_prelim}
  \end{center}
  \caption{Exclusion limits at $95\%$ CL in the $(M_{\tilde t}, M_{\tilde b})$ plane for a) $\lambda'_{131}=0.1$ and b) $\lambda'_{131}=0.3$ from a scan of the MSSM parameter space as indicated in the figures. The two full curves indicate the strongest and the weakest limits on the masses in the parameter space investigated.}
  \label{fig:limit}
\end{figure}
\begin{figure}
  \begin{center}
    \includegraphics[scale=0.42]{fig6_prelim}
  \end{center}
  \caption{Exclusion limits at $95\%$ CL on the \Rp\hspace{0.075cm} coupling $\lambda'_{131}$ as a function of the stop mass from a scan of the MSSM parameter space as indicated in the figure. The sbottom mass is set to $M_{\tilde b}=100\gev$. The two full curves indicate the strongest and the weakest limits on $\lambda'_{131}$ in the parameter space investigated.}
  \label{fig:limitlambda}
\end{figure}

\end{document}