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\begin{titlepage}

\noindent
%%%Date:     03/31/2004 \\
%%%Version:  1.0        \\
%%%Editors:  Gerhard Brandt, Christian Veelken, Stefania Xella (junior editor: CD)\\
%%%Referees: Hinrich Meyer, David South \\
%%%%Comments by

%%%\vspace{2cm}

\vspace{1cm}
\begin{center}
{\large \bf H1prelim-04-061 }
\end{center}
\vspace{1cm}

\begin{center}
\begin{Large}

{\bf Search for events with $\tau$ leptons in $ep$ collisions at HERA}

\vspace{2cm}

H1 Collaboration

\end{Large}
\end{center}

\vspace{2cm}


\begin{abstract}
The production of $\tau$-leptons in $ep$ collisions is studied with the H1 detector at HERA by using an identification algorithm based on the search for isolated charged tracks associated to narrow hadronic jets detected in the calorimeters, a typical signature of the one-prong hadronic $\tau$ decay.  Using this identification procedure, a search for events with high-$P_T$ isolated $\tau$-leptons and missing transverse momentum is performed using a data sample corresponding to an integrated luminosity of
108 pb$^{-1}$  collected with the H1 detector at HERA in
the period 1996-2000. This search complements the observation of isolated electrons and muons in events with missing transverse momentum. 
In addition, a preliminary search for events with $\tau$-lepton pairs produced in elastic photon-photon collisions is performed. 
\end{abstract}

\vspace{1.5cm}

\begin{center}
Prepared for DIS 2004, Strbske Pleso, Slovakia
\end{center}

\end{titlepage}

%\newpage

\section{Search for events with isolated high-$P_T$ $\tau$-leptons and missing
transverse momentum.}

% \subsection{Data quality}
% 
% Data and Monte Carlo samples used for the analysis are requested, as
% very first step, to pass some quality criteria on noise level, HV on
% (for CJC1,CJC2,CIP,COP,ToF,LAr,Lumi detectors), on the difference
% between the actual primary central z vertex position and the
% run-period averaged one, on the difference between the actual CJC T0
% timing and the run-period averaged one, and against non ep events
% (e.g. beam gas events).
% 
% Additionally, the request of some  triggers on the data and MC
% photoproduction sample is applied.
% 
% For all other MCs the pseudo charged current trigger weights are applied.
% Additonal weights are applied, to the data for L4,L5 efficiencies, and
% to the MC for generator level cuts. 
% This is summarized in table \ref{dq}.
%  
% \begin{table}[hb]
% \begin{center}
% \begin{tabular}{|c c c|}
% \hline
% Requirement & DATA & MC\\
% \hline
% $L1 ~ 66 \| L1 ~ 67 \| (L1 ~ 71 \&\& L2 ~ 15) \| (L1 ~ 75 \&\& L2 ~
% 11) \| L1 ~ 77$ & yes & no (except for $\gamma$p sample)\\
% good or medium quality & yes & no \\
% Noisy runs & yes & no\\
% HV on  & yes & no \\
% $z_{vtx} - \overline{z_{vtx}}< 35.$ cm & yes & yes \\
% $CJC ~ T0 - \overline{CJC ~ T0} < 25$ clockbins & yes & no\\
% non ep finders IBG,IBGFM,IBGAM & yes & yes \\
% \hline
% \end{tabular}
% \caption{Data quality requirements for data and MC samples (yes or no
% meaning they have been applied to the given sample or not)}
% \label{dq}
% \end{center}
% \end{table}
% 
% \newpage
%  
\subsection{Search for events with $\tau$ leptons and missing transverse momentum}
\renewcommand{\arraystretch}{1.2}  
\begin{table}[hhh]
\begin{center}
\begin{tabular}{|r l|}
\hline
\multicolumn{2}{|c|}{\bf $P_T^{miss}$ Preselection} \\
\hline \hline
%Variable & Requirement \\
%\hline
\multicolumn{2}{|c|}{Data Quality (HV,triggers,vertex, timing)} \\
$P_T^{calo}$ & $>$ 12 GeV \\
$P_T^{miss}$ & $>$ 12 GeV \\
$\Delta \phi \left( Calo, \mbox{PLUG} \right)$ & $<$ $150^{\circ} + 30^{\circ}
\cdot \left( \frac{P_T^{calo} - 12}{13} \right)$ \\
$\Sigma (E-P_z)$ & $<$ 45 GeV \\
$N_{jets}$ & $\ge 0$ \\
$P_T^{jet}$ & $>$ 7 GeV \\
\hline
\end{tabular}
\caption{The preselection of events with missing
transverse momentum: $P_T^{calo}$ is the total calorimetric transverse momentum,
$P_T^{miss}$ is the total transverse momentum of all reconstructed particles,
$\Delta \phi \left( Calo, \mbox{PLUG} \right)$ is the acoplanarity between the momentum measured in the main calorimeter and the momentum measured in the forward PLUG calorimeter,
$\Sigma (E-P_z)$ sums the $E-P_z$ contributions of all measured particles and is 55.2GeV for events with fully measurable final state. At least one jet is required with a transverse momentum above 7 GeV.
}
\label{cuts1}
\end{center}
\end{table}


\begin{table}[hhh]
\begin{center}
\begin{tabular}{|r l|}
\hline
\multicolumn{2}{|c|}{\bf $\tau+P_T^{miss}$ Preselection} \\
\hline 
\hline
% Variable & Requirement \\
% \hline
$P_T^{miss}$ Preselection & (see table~\ref{cuts1}) \\
$P_T^{jet}$ & $>$ 7 GeV \\
$\theta^{jet}$ & from 20$^\circ$ to 120$^\circ$  \\
$N_{tracks}$ & $=1$ \\
$P_T^{track}$ & $>$ 2 GeV \\
$R^{\eta\varphi}_{e,\mu,jets}$ & $>$ 1.0 \\
\hline
\end{tabular}
\caption{ The preselection of events with significant missing transverse momentum and a single track jet, corresponding to a $\tau$ candidate. The jet polar angle $\theta^{jet}$  is required to be in the central region and to contain exactly one charged track $N_{tracks}=1$ with a transverse momentum above 2~GeV. The jet is required to be isolated by asking the minimum distance in the $\eta-\varphi$ plane $R^{\eta\varphi}$ of electrons, muons or other jets in the event to be above 1. }
\label{cuts2}
\end{center}
\end{table}

\begin{table}[hhh]
\begin{center}
\begin{tabular}{|c c|}
\hline
\multicolumn{2}{|c|}{\bf $\tau+P_T^{miss}$ Final Selection} \\
\hline
$P_T^{miss}$ Preselection & (see table~\ref{cuts1}) \\
$P_T^{calo}$          & $>$ 20 GeV \\
 & \\
$P_T^{jet}$ & $>$ 7 GeV \\
$\theta^{jet}$ & from 20$^\circ$ to 120$^\circ$  \\
$N_{tracks}$ & $=1$ \\
$P_T^{track}$ & $>$ 5 GeV \\
$R^{\eta\varphi}_{e,\mu,jets}$ & $>$ 1.0 \\
$\Delta \phi (jet,X)$ & $< 170^{\circ}$ \\
 &  \\
$R^{jet}$             & $<$ 0.12 GeV \\
\hline
\end{tabular}
\caption{Final selection of events with isolated $\tau$ candidates and missing transverse momentum. 
Narrow calorimetric deposits are identified using the variable $R^{jet}$ (jet size), defined by
$ R_{jet} = \sum_i \frac{E_i \Delta^i(\varphi,\eta)}{E^{jet}}$ ( $i$ runs
over all particles in the jet, $E_i$ is the  particle energy and  $\Delta^i(\varphi,\eta)$ the  distance in $\eta-\varphi$ plane to the jet axis). The hadronic final state
excluding the $\tau$ candidate jet is denoted by $X$. A significant acoplanarity requirement  $\Delta \phi (jet,X)< 170^{\circ}$ ensures further background rejection. 
}
\label{cuts3}
\end{center}
\end{table}

\newpage

% \section{Data samples}
% 
% The analysis uses data and Monte Carlo samples processed with the
% H1 object oriented software, from release 2.5.8. 
% 
% All data from 1996 to 2000, corresponding to a luminosity of 108
% pb$^{-1}$  have been used.
% 
% Concerning the Monte Carlo samples, the FCNC single top production is
% simulated using the generator ANOTOP. 
% Standard Model W production is generated using the generator EPVEC, and the sample used corresponds
% to a luminosity of 100068 pb$^{-1}$.
% Charged Current, Neutral Current and Photoproduction samples are
% generated using respectively DJANGOH1.2, RAPGAP and PYTHIA generators,
% for luminosities of about 134000, 2037, and 2000 pb$^{-1}$ (composed
% of two samples, one with $P_T^{HAT}>3$ GeV and one with $P_T^{HAT}>10$
% GeV). 
% The NC and Photoproduction sample have also additional cuts at the
% generator level, to make the sample production reasonably fast (``MAP
% selection'').
% $\gamma \gamma$ processes have also been taken in consideration, with
% final states $e^+e^-$,$\mu^+\mu^-$ and $\tau^+\tau^-$, and with
% luminosity respectively 30000, 50000, and 100000 pb$^{-1}$.
% 
% 

\begin{figure}[hhh]
\setlength{\unitlength}{1mm}
\begin{center}
\begin{picture}(150,150)(0,0)
\put(-2,80){\mbox{\epsfig{file = H1prelim-04-061.fig1a.ps,
                          bbllx=-2,bblly=1,bburx=577,bbury=574, angle=0, clip=, width=8.2cm}}}
\put(75,80){\mbox{\epsfig{file = H1prelim-04-061.fig1b.ps,
                          bbllx=-2,bblly=1,bburx=577,bbury=574, angle=0, clip=, width=8.2cm}}}
\put(37,0){\mbox{\epsfig{file = H1prelim-04-061.fig1c.ps,
                          bbllx=-2,bblly=1,bburx=577,bbury=574, angle=0, clip=, width=8.2cm}}}
\end{picture}
\end{center}
\caption{The distributions of  $\Sigma (E - P_z)$, $P_T^{calo}$ and the highest
$P_T^{jet}$ 
in the data compared to the Monte Carlo simulation for the $P_T^{miss}$ event preselection described in table \ref{cuts1}.}
\end{figure}

%\newpage
\newpage

\begin{figure}[hhh]
\setlength{\unitlength}{1mm}
\begin{center}
\begin{picture}(150,75)(0,0)
\put(-2,0){\mbox{\epsfig{file = H1prelim-04-061.fig2a.ps,
                          bbllx=-2,bblly=1,bburx=577,bbury=574, angle=0, clip=, width=7.2cm}}}
\put(75,0){\mbox{\epsfig{file = H1prelim-04-061.fig2b.ps,
                          bbllx=-2,bblly=1,bburx=577,bbury=574, angle=0, clip=, width=7.2cm}}}
\end{picture}
\end{center}
\caption{The distributions of $R^{jet}$ and $P_T^X$ in the data compared with the Monte Carlo simulation for the $P_T^{miss}$ event preselection described in table \ref{cuts1}. The SM $W$ contribution is still negligible at this level.}
\end{figure}

\begin{figure}[hhh]
\setlength{\unitlength}{1mm}
\begin{center}
\begin{picture}(150,75)(0,0)
\put(-2,0){\mbox{\epsfig{file = H1prelim-04-061.fig3a.ps,
                          bbllx=-2,bblly=1,bburx=577,bbury=574, angle=0, clip=, width=7.2cm}}}
\put(75,0){\mbox{\epsfig{file = H1prelim-04-061.fig3b.ps,
                          bbllx=-2,bblly=1,bburx=577,bbury=574, angle=0, clip=, width=7.2cm}}}
\end{picture}
\end{center}
\caption{The distributions of $R^{jet}$ and $P_T^X$ in the data compared with the Monte Carlo simulation for the $\tau+P_T^{miss}$ event preselection described in table \ref{cuts2}. Note that the jet radius $R^{jet}$ of jets selected in the Standard Model $W$ Monte Carlo are narrow, as expected 
from $\tau$-jets. A cut $R^{jet} < 0.12$ will be applied in the final selection.
 }
\end{figure}

\newpage

\begin{figure}[hhh]
\setlength{\unitlength}{1mm}
\begin{center}
\epsfig{file = H1prelim-04-061.fig4.ps,
        bbllx=0,bblly=0,bburx=577,bbury=574, angle=0, clip=, width=7.2cm}
\end{center}
\caption{ The distribution of the hadronic transverse momentum $P_T^X$ in the data compared with the Monte Carlo simulation for the $\tau+P_T^{miss}$ final selection described in table \ref{cuts3}. No events are observed in the high $P_T^X$ region, where
events for the template signal process single $top$ production are expected.}
\end{figure}

\vspace{2cm}

\begin{table}[hhh]
\begin{center}
{\large H1 Preliminary}
\begin{tabular}{|r || c | c || c | c|}
\hline
H1 Data 96-00 & \multirow{2}{18mm}{Data} & All SM &
\multirow{2}{18mm}{SM W} & Single top \\
108 pb$^{-1}$ & & Processes & & Efficiency * BR \\
\hline
\hline
Full Sample          & 5 & 5.81 $\pm$ 1.36 & 0.87 $\pm$ 0.15 & 0.52 $\%$ \\
\hline
$P_T^{X}$ $>$ 25 GeV & 0 & 0.53 $\pm$ 0.10 & 0.26 $\pm$ 0.05 & 0.49 $\%$ \\
\hline
$P_T^{X}$ $>$ 40 GeV & 0 & 0.22 $\pm$ 0.05 & 0.12 $\pm$ 0.03 & 0.42 $\%$ \\
\hline
\end{tabular}
\caption{Observed and predicted number of events in the 1996-2000 dataset after the final selection.
         The last column quotes the expected efficiency for an anomalous single
         top production
         Monte Carlo, used as a template process with high-$P_T$ isolated $\tau$-leptons
         in the final state.
         }
\label{results}
\end{center}
\end{table}

\clearpage
\newpage

\section{Observation of $\tau$-pairs in elastic $\gamma\gamma$-processes.}

As a supplementary investigation of the H1 detector capabilities to detetect $\tau$ leptons, a preliminary search for $\tau$-pair production in $ep$ collision is performed in the channel where one $\tau$ decays leptonically and the other hadronically.
Events are selected by requiring one identified electron or muon  and one hadronic $\tau$  candidate
(1-prong or 3-prong) with $P_T>2$~GeV.  The hadronic $\tau$ signature is performed by using a neural network algorithm based mainly on hadronic cluster shape and trained differently for one-- or three-prong channels. In order to select elastic $\tau$--pair production channel, events with other hadronic deposits besides the hadronic $\tau$ candidate are rejected.
\vspace{2.5cm}

\begin{figure}[hhh]
\setlength{\unitlength}{1mm}
\begin{center}
\epsfig{file = H1prelim-04-061.fig5.ps,
               bbllx=11,bblly=142,bburx=493,bbury=639, height=7.2cm}
\end{center}
\caption{The $\Sigma(E-P_z)$ distribution of the pre-selected $\tau$-pair candidate events in data compared with the Monte Carlo simulation.}
\end{figure}

\begin{figure}[hhh]
\setlength{\unitlength}{1mm}
\begin{center}
\begin{picture}(150,75)(0,0)
\put(-2,-3){\mbox{\epsfig{file = H1prelim-04-061.fig6a.ps,
                          bbllx=11,bblly=142,bburx=493,bbury=639,clip=, height=7.2cm}}}
\put(77,-3){\mbox{\epsfig{file = H1prelim-04-061.fig6b.ps,
                          bbllx=11,bblly=142,bburx=493,bbury=639,clip=, height=7.2cm}}}
\end{picture}
\end{center}
\caption{Control Plots of the visible transverse momentum distributions of the 
hadronically decaying $\tau$-lepton;
on the left for opposite charges of the two
decaying $\tau$-candidates, on the right for equally charged $\tau$-candidates.
In $\gamma\gamma \rightarrow \tau^{+} \tau^{-}$ processes only candidates of
opposite charge are expected. }
\end{figure}


\begin{figure}[hhh]
\setlength{\unitlength}{1mm}
\begin{center}
\begin{picture}(150,150)(0,0)
\put(-40,150){\mbox{\epsfig{file = H1prelim-04-061.fig7.ps, angle=270, width=19cm }}}
\end{picture}
\end{center}
\caption{ $\tau$-pair candidate event with one $\tau$-lepton decaying 
leptonically to a muon, and the other $\tau$-lepton decaying to  
three charged hadrons (3-prong topology). The scattered positron is also
detected in the backward calorimeter.}
\end{figure}

\end{document}




