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\begin{document}

\pagestyle{empty}
\begin{titlepage}

\noindent
\begin{center}
                                %{\it {\large version of \today}} \\[.3em] 
  \begin{small}
    \begin{tabular}{llrr}
                                %Submitted to & \multicolumn{3}{r}{\footnotesize Electronic Access: {\it http://www-h1.desy.de/h1/www/publications/conf/conf\_list.html}} \\[.2em] \hline 
                                %Submitted to & \multicolumn{3}{r}{\footnotesize {\it www-h1.desy.de/h1/www/publications/conf/conf\_list.html}} \\[.2em] \hline 
      Submitted to & & &
      \epsfig{file=/h1/www/images/H1logo_bw_small.epsi,width=2.cm} \\[.2em] \hline
      \multicolumn{4}{l}{{\bf
                XXII International Symposium on Lepton-Photon Interactions at High Energy},
                June~30,~2005,~Uppsala} \\
                 & Abstract:        & {\bf 419}    &\\
                 & Session: & {\bf Electroweak physics and beyond}   &\\ \hline
      & \multicolumn{3}{r}{\footnotesize {\it
          www-h1.desy.de/h1/www/publications/conf/conf\_list.html}} \\[.2em]
    \end{tabular}
  \end{small}
\end{center}
\vspace*{2cm}

\begin{center}
  \Large
  {\bf 
    Search for Lepton Flavor Violation \\
    in \boldmath{$e^{+}p$} Collisions at HERA\\
  }
  \vspace*{1cm}
    {\Large H1 Collaboration} 
\end{center}

\begin{abstract}
\noindent
A search for lepton flavor violating (LFV) processes mediated by leptoquarks (LQ) is performed with the H1 experiment 
at HERA. Final states with a muon or a tau and a hadronic jet are searched for in a data sample collected in the period 
1999-2000 corresponding to an integrated luminosity of $66~{\rm pb^{-1}}$. No evidence for LFV is found. Limits are derived 
on the Yukawa coupling of LQs to a muon or tau and a light quark, $\lambda_{\mu q,\tau q}$, in the Buchm\"uller-R\"uckl-Wyler 
effective model, as well as on the branching ratio, $BR_{{\rm LQ}\rightarrow \mu q,\tau q}$, for the LQ decaying to a muon 
or tau and a light quark.

\end{abstract}


\end{titlepage}

\pagestyle{plain}

\section{Introduction}

In the Standard Model, all known interactions involving leptons conserve the lepton
flavors individually. However, from a theoretical point of view, there is no underlying gauge 
symmetry supporting this experimental observation. In fact, experimental evidence 
for lepton flavor violation (LFV) in atmospheric neutrino oscillations has already been reported in 
1998 ~\cite{supK}.\par
In $e^{+}p$ collisions at HERA, a LFV process can induce the appearence of a muon or tau instead of the positron in the 
final state. A convenient concept to explain such exotic signatures is the exchange of a {\it leptoquark} (LQ). 
Leptoquarks couple 
to both quarks and leptons and can therefore be resonantly produced in $e^{+}p$ collisions at HERA.
With this analysis we present a search for LFV processes, where the exchange of a leptoquark leads to a 
muon or tau in the final state.\par

\section{Phenomenology and Model}
 
Leptoquarks are color triplet scalar or vector bosons, carrying both lepton ($L$) and baryon ($B$) number. 
The fermion number $F = L + 3\,B$ is conserved and takes 
values of $F=2$ for $e^-q$ and $F=0$ for $e^+q$ states. In this analysis, the search for 
leptoquarks is preformed in $e^+p$ collisions and therefore only leptoquarks with $F=0$ are considered. 
Figure~\ref{lqfeynman} illustrates the exotic leptoquark subprocesses in $e^+p$ collisions compared to the 
hard subprocess in neutral current deep-inelastic scattering (NC DIS).
An overview of the Buchm\"uller-R\"uckl-Wyler (BRW) effective model~\cite{BRW} using the Aachen 
notation~\cite{aach} for the leptoquark coupling to $u$ and $d$ quarks is given in table~\ref{lqBRW}.\par
For the determination of the signal detection efficiencies the LEGO~\cite{lego} event generator is used and 
the complete H1 detector response is simulated. The contributions from several SM background processes 
which may mimic the signal through measurement fluctuations are evaluated in 
this analysis. These processes include NC DIS, lepton pair production, W-production, photoprodution 
and charged current deep-inelastic scattering (CC DIS) modelled by the generators descibed in ~\cite{RAPGAP,GRAPE,EPVEC,PYTHIA,DJANGO}. 

\section{Data Selection and Analysis Method}

During the years 1999/2000, data have been collected with the H1 detector at {\sc Hera} corresponding 
to an integrated luminosity of $66~\pb^{-1}$ of $e^+p$ collisions at a center of mass energy $\sqrt{s} = 319~\GeV$.\par
A detailed description of the H1-detector can be found in~\cite{detect}.
The recording of the events is mainly based on the Liquid Argon Calorimeter (LAr) with a trigger efficiency close to 
100\%. Background events not originating from $e^+p$ collisions are rejected by the requirement that the 
$z$-position\footnote{The incoming proton beam defines the $z$-axis.} 
of the primary vertex is reconstructed within $\pm35{~\rm cm}$ around the nominal interaction vertex. 
Further reduction of this background is obtained by using a set of topological 
filters and by requiring a matching between the event time measured by the central drift chambers and the bunch crossing time.\par
In the following, an isolated track pointing to a compact electromagnetic cluster is related to an electron. 
A muon candidate is identified by a track measured in the inner tracking system geometrically matching with signals in the muon system. 
The hadronic final state is reconstructed from the deposits in the LAr calorimeter in combination with tracking information. The hadrons are 
then combined into jets using a $k_T$-algorithm~\cite{ktjet}. The identification of the tau is performed in the hadronic decay channel. The 
signature is a narrow hadronic jet. \par
The DIS Lorentz invariants $Q^2, y, x$ are used to determine the leptoquark mass, $M^{LQ}$, with
\begin{equation*}
M^{LQ}=\sqrt{xs}=\sqrt{\frac{Q^2}{y}}~.
\end{equation*}
Here, $Q^2$ denotes the negative squared momentum transfer, $y$ is the inelasticity of the scattering process and $x$ represents the 
Bj{\o}rken scaling variable. \par
In order to minimise the dependency on the hadronic energy measurement, the reconstruction of 
$Q^2, y,$ and $x$ is based on the double angle method~\cite{DAmeth}. For a LQ decaying into a 
muon and a quark, the angle of the outgoing muon and the angle of the highest transverse momentum ($P_T$) jet are taken to reconstruct the 
mass of the LQ. In the case of the LQ decaying into a high $P_T$ tau and a quark, the angle of the tau is associated with the visible 
$\tau$-jet and used together with the hadronic jet to reconstruct the kinematics.

\subsection{High $P_{T}$ Muon Signatures}

LQs with couplings to second generation leptons, leading to $\mu+q$ final states, show a clear signature 
in the detector, i.e. an isolated high $P_T$ muon ``back-to-back'' in the azimuthal angle, $\phi$, and balanced in $P_T$ with 
the hadronic final state. In general, a muon deposits only a very small fraction of its energy in the 
LAr calorimeter, so the signal is expected to exhibit large $P_T^{Calo}$, where $P_T^{Calo}$ is the measured $P_T$ 
reconstructed from all clusters recorded in the calorimeter.\par
The selections applied in this analysis in the muon channel to identify the LFV signature are:

\begin{itemize}
\item Isolated muon preselection: \par
  \begin{enumerate}
  \item At least one muon with transverse momentum $P_T^\mu > 10{\rm~GeV}$ is required.
  \item The polar angle, $\theta^\mu$, of the muon track is restricted to be within 10$^{\circ}$ to 140$^{\circ}$.
  \item The muon is required to be isolated with respect to tracks and jets in the event:
    \begin{itemize}
    \item The distance of the highest $P_{T}$ muon track to the nearest vertex fitted track in the 
      $\eta\phi$-plane\footnote{Pseudorapidity $\eta = -\ln[\tan(\frac{\theta}{2})]$} must be greater than $0.5$.
    \item The distance of the highest $P_{T}$ muon track to the nearest jet in the $\eta\phi$-plane is required to be greater 
      than $1.0$.
    \end{itemize}
  \item Events with a ratio $V_{ap}/V_P$ lower than 0.3 are selected to reject most of the photoproduction 
    and neutral current events, where the variables
    \begin{eqnarray*}
      V_{p~}&=&\sum_i\frac{P^{X}_T\cdot P^{i}_T}{P^{X}_T}~~{\rm for}~~P^{X}_T\cdot P^{i}_T>0~~,\\
      V_{ap}&=&\sum_i\frac{P^{X}_T\cdot P^{i}_T}{P^{X}_T}~~{\rm for}~~P^{X}_T\cdot P^{i}_T<0
    \end{eqnarray*}
    are deduced by summing over all particles in the detector and where $P^{X}_{T}$ is the total transverse momentum.
  \item Only events with calorimetric transverse momentum ($P_T^{Calo}$) greater than 12 GeV are selected.
  \end{enumerate}
\item Subsequent LFV signal selection: \par
%%Then the following restrictions are added to select LFV signature: 
  \begin{enumerate}
  \item Events are required to have no electron in the electromagnetic LAr.
  \item Exactly one isolated muon is required.
  \item Events are selected with an azimuthal angle between the hadronic final state and the 
    isolated muon (acoplanarity) greater than 170$^{\circ}$.
  \item $P_T^{Calo}$ is required to be greater than $25~{\rm GeV}$.
  \end{enumerate}
\end{itemize}
Figure~\ref{mucontrol} shows control distributions of acoplanarity, $V_{ap}/V_P$, $P_T^{Calo}$ and $P_t^{\mu}$
after applying the isolated muon selection. The selected data is well described by the SM Monte Carlo simulation.

\subsection{High $P_{T}$ Tau Signatures}

We restrict the search for leptoquarks possessing couplings to a third generation lepton leading to $\tau+q$ 
final states to the hadronic decays of the $\tau$. The hadronic decays of a high 
$P_T$ tau lead to a typical signature of a high $P_T$ ``pencil-like'' $\tau$-jet. 
This $\tau$-jet is characterised by a narrow shape in the calorimeter and low track multiplicity, i.e. one to three 
tracks in the identification cone of the jet. The neutrinos from the decay of the tau are boosted  
with the hadrons in the direction of the $\tau$-jet. Therefore, the signal topology is a dijet event with no leptons.
The missing transverse momentum in the event carried by the neutrino is aligned with the second highest $P_T$ jet (jet2), 
which has to fulfil the $\tau$-jet criteria.\par
The following selection criteria are applied:
\begin{itemize}
\item Selection of high $P_T$ dijet events with no lepton:
  \begin{enumerate}
  \item There is no $e^\pm$ or $\mu^\pm$ found in the event.
  \item There are at least 2 jets in the event with:
    \begin{itemize}
    \item $P_T^{\rm jet1} > 25\;{\rm GeV}$
    \item $P_T^{\rm jet2} > 15\;{\rm GeV}$
    \item both jets in the angular range $7^\circ<\theta^{\rm jet}<145^\circ$
    \item electromagnetic fraction of both jets: $f_{em}^{\rm jet} < 0.95$
    \end{itemize}
                                %  \item Veto events with jet2 pointing to regions between calorimeter modules.
  \end{enumerate}
\item Selection of events with jet2 fulfilling $\tau$-jet criteria:
  \begin{enumerate}
  \item Large missing transverse momentum: $P_T^{\rm miss} > 20\;{\rm GeV}$.
  \item Number of tracks in identification cone of jet2: $1 \le N_{\rm tracks}^{\rm jet2} \le 3$.
  \item No tracks in an outer cone in the $\eta\phi$-plane around jet2 with $0.12 < D_{track} < 1.0$.
  \item Mass of jet2: $M^{\rm jet2} < 7\;{\rm GeV}$.
  \item Radius of jet2 in $\eta\phi$-plane: $R^{\rm jet2} < 0.12$.
  \item $P_T^{\rm miss}$ in direction of jet2: $|\phi^{\rm jet2}-\phi^{\rm miss}|<30^\circ$.
  \end{enumerate}
\end{itemize}
Figure~\ref{taucontrol} shows control distributions for $P_T^{\rm miss}$, $R^{\rm jet2}$, 
$D_{track}$ and $M^{\rm jet2}$, which are well reproduced by the SM expectation.

\subsection{Systematic Uncertainties}
Table~\ref{bgsys} lists the systematic uncertainties for the MC simulation of the dominant SM background 
processes. These uncertainties are deduced from the agreement between data and simulation in the control studies.\par
The experimental uncertainties on the muon energy is 5\%. The errors attributed to the polar and azimuthal angle 
measurement are 3~mrad and 1~mrad respectively. The muon identification uncertainty is 6\%.
The uncertainty on the hadronic energy scale is 2\% and the uncertainty of the polar 
and azimuthal angles of the hadronic system are 10~mrad each.
The uncertainty on the luminosity measurement is 1.5\%.
The following uncertainties are related to the modelling of the LQ signal and the CTEQ5 parametrisation of the 
parton density functions~\cite{cteq}: 
\begin{itemize}
\item The theoretical uncertainty on the signal cross section due to uncertainties in the
  parton densities varies from 7\% for $e^{+}u \rightarrow {\rm LQ}$ at low LQ masses up to 50\% at high LQ 
  masses for $e^{+}d \rightarrow {\rm LQ}$.
\item Choosing either $Q^2$ or the square of the transverse momentum of the final state lepton instead of the center of 
  mass energy of the hard subprocess, $\sqrt{sx}$, as the hard scale at which the proton distributions are estimated, yields 
  an uncertainty of 7\% on the signal process.
\end{itemize}

\section{Results}
The results of the selections in the muon and tau channel are summarized in table~\ref{resnum}. The final mass spectra for both 
selections are shown in figure~\ref{mass}. \par
No event is selected in the muon channel with an expectation of $0.74\pm0.25$ events from the Standard Model processes.
The largest contribution to this SM background comes from muon-pair production. 
The selection efficiency for LQs decaying to $\mu + q$ is 60\% for a vector LQ of mass $100\;{\rm GeV}$ and rises up to
75\% at masses $150-200\;{\rm GeV}$. Near the kinematic limit it falls steeply to 33\%. This fall due to the high $P_T$ requirements 
observed for vector LQs in both the muon and tau decay channel can be explained by the behaviour of the signal cross section near the 
kinematic limit~\cite{lego}.
%Due to 
%the steep decrease of the parton density function at high values of $x$ inside the resonance width, additional $u$-channel and 
%off-shell $s$-channel contributions, the signal cross section shows up a large off-resonant fraction at high LQ masses. 
%The requirements for large $P_T$ in the events reject most of these off-resonant events.
For a scalar LQ the efficiency is 65\% at masses of $100\;{\rm GeV}$ and reaches 70\% at $150\;{\rm GeV}$ and then falls 
gradually to 40\% above the kinematic limit. 
%In contrast to the vector LQ, the decay of a scalar LQ is spherically symmetric and the 
%selection efficiency is therefore less affected by the $P_T$ requirement.
\par
One data event is found as a high $P_T$ tau candidate from a LQ decay compared to a SM expectation of $0.56\pm0.16$. This SM 
background is dominated by NC DIS and photoproduction. The selection efficiency for the LFV 
signal of scalar LQs decaying to a $\tau+q$ final state varies between 12\% at a LQ mass of $100\;{\rm GeV}$ and 24\% at 
$200-250\;{\rm GeV}$. For vector LQs the efficiency rises up to 32\% and falls steeply near the kinematic limit of 
$\sqrt{s}=319~{\rm GeV}$ to become stable at 10\% above the kinematic limit.\par
In order to set limits on the signal cross section, the mass spectra are scanned for signals using 
a sliding mass window with optimised borders. Within this window the number of data events, background events and the selection 
efficiency are used to calculate an upper limit on the signal at a 95\% confidence level (CL)~\cite{Junk}. These limits are converted 
into limits on the couplings $\lambda_{\mu q}$ and $\lambda_{\tau q}$. The obtained limits are shown in figure~\ref{lambdalimtaumu} 
for scalar and vector LQs with an assumed LFV branching ratio of $0.5$. \par
Figure~\ref{lambdalimtaumuele} illustrates the limits on the coupling constants for the scalar LQ  $S_{1/2}^L$  and the vector LQ 
$V_1^L$ of the present analysis in comparison with previous limits set by the H1 experiment on LQs coupling to first generation 
leptons only. These previous results are obtained with additional data of luminosity ${\cal L}=37~{\rm pb^{-1}}$ at a centre 
of mass energy $\sqrt{s}=301$~\GeV~\cite{lqeq}. \par
The limit calculation is extended to different branching 
ratios fixing $\lambda_{eq}$ at the electromagnetic coupling strength of 0.3. Figure~\ref{BRlimtaumu} shows limits on 
\mbox{$BR_{{\rm LQ}\rightarrow\mu q,\tau q}$} with the scalar LQ $S_{1/2}^L$ and the vector LQ $V_1^L$ in both decay 
channels, ${\rm LQ}\rightarrow\mu q$ and ${\rm LQ}\rightarrow\tau q$.

\clearpage

\section{Conclusions}
A search for LFV mediated by LQs coupling to second and third generation leptons in $e^{+}p$~collisions has been performed at 
HERA using a data sample corresponding to an integrated luminosity ${\cal L}=66~{\rm pb^{-1}}$ collected with the H1 detector 
at a centre of mass energy \mbox{$\sqrt{s}=319$~\GeV}. No evidence has been found for lepton flavor violation in the muon or tau decay channel. 
Exclusion limits for coupling constants and branching ratios have been set in a LQ mass range of 100 to 400~\GeV. 
Taking a Yukawa coupling constant of electromagnetic strength, couplings of scalar (vector) LQs with masses up to 275-300
(288-330)~\GeV~to second generation leptons and couplings of scalar (vector) LQs with masses up to 260-284 (278-300)~\GeV~to third generation 
leptons are excluded.
A comparison with previous limits on the coupling constant for LQs coupling to first generation leptons 
show a similar behaviour. 

%\section{Acknowledgements}
%We are grateful to the {\sc Hera} machine group whose outstanding efforts have made this experiment possible. We thank
%the engineers and the technicians who constructed and maintain the detector, our funding agencies for financial and support
%and the DESY directorate for the support and hospitality extended to the non-DESY members of the collaboration.
%%\clearpage
%
%   References for LFV paper
%

\clearpage

\begin{thebibliography}{99}

  
                                % leptoquarks
  
\bibitem{supK} Y. Fukuda {\em et al.} [Super-Kamiokande Collaboration],
  Phys. Rev. Lett. {\bf 81} (1998) 1562 [hep-ex/9807003].
  
\bibitem{BRW}  W. Buchm\"uller, R. R\"uckl and D. Wyler,
  Phys. Lett. B~{\bf 191} (1987) 442.

\bibitem{aach} B. Schrempp, Physics at HERA: Proceedings of the Workshop,   
  eds. W. Buchm\"uller and G, Ingelmann, Vol. 2, pp.1034-1042, Hamburg, Germany, 1991.

\bibitem{lego} K. Rosenbauer, dissertation RWTH Aachen (in German), PITHA 95/16, July 1995.


\bibitem{RAPGAP} 
                                %\cite{Jung:1993gf}
                                %\bibitem{Jung:1993gf}
  H.~Jung, Hard diffractive scattering in high-energy $ep$ collisions and the Monte Carlo generation RAPGAP,
  Comput.\ Phys.\ Commun.\  {\bf 86} (1995) 147; 
  %%CITATION = CPHCB,86,147;%%
  RAPGAP program manual (1998) unpublished [http://www-h1.desy.de/$\sim$jung/RAPGAP.html].

\bibitem{GRAPE}
  T.~Abe, GRAPE-Dilepton (Version 1.1): A generator for dilepton production in $ep$ collisions,
  Comput.\ Phys.\ Commun.  {\bf 136} (2001) 126 [hep-ph/0012029].
  %%CITATION = HEP-PH 0012029;%%
                                %\cite{Abe:2000cv}

\bibitem{EPVEC}
% H1 generator based on EPVEC 1.0;
 U.~Baur,J.~A~.M.~Vermaseren and D.~Zeppenfeld, H1 generator based on EPVEC 1.0,
 Nucl.\ Phys.\ B {\bf 375} (1992) 3.

\bibitem{PYTHIA}
  T. Sj\"{o}strand, PYTHIA~5.7,
  CERN-TH-6488 (1992), Comp. Phys. Comm. {\bf 82} (1994) 74.
  
\bibitem{DJANGO}
  G.A.~Schuler and H.~Spiesberger, DJANGO~2.1,
  Proc. of the Workshop ``Physics at HERA'' (1991),
  Eds. W.~Buchm\"uller and G.~Ingelman, Vol. 3, p. 1419.

\bibitem{detect} I. Abt {\em et al.} [H1 Collaboration], Nucl. Instrum. Meth. A~{\bf 386} (1997) 310; \\
I. Abt {\em et al.} [H1 Collaboration], Nucl. Instrum. Meth. A~{\bf 386} (1997) 348.

\bibitem{ktjet}  J.M. Butterworth, J.P. Couchman, B.E. Cox, B.M. Waugh,  KTJET: A C++ implementation of the
  k-perpendicular clustering algorithm, Comput. Phys. Commun. {\bf 153} (2003) 85 [hep-ph/0210022]. 

\bibitem{DAmeth} U. Bassler, G. Bernardi,
  Nucl. Instrum. Meth. A~{\bf 426} (1999) 583 [hep-ex/9801017].

%\bibitem{isolep} V.~Andreev {\em et al.} [H1 Collaboration],
%  Phys. Lett. B~{\bf 561} (2003) 241 [hep-ex/0301030].

\bibitem{cteq} H.L. Lai {\em et al.} [CTEQ collaboration], Eur. Phys. J. C~{\bf 12} (2000) 375 [hep-ph/9903282].
 
                                % CLS method
  
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  Int. Europhysics Conf. on High Energy Physics, Jul 17-23, 2003, Aachen, Abstract 105, Parallel Session 13 .

  
\end{thebibliography}


\clearpage

\begin{center}
\begin{figure}
  \begin{fmffile}{graph}
    \setlength{\unitlength}{1mm}
    \begin{fmfgraph*}(30,25)
      \fmfright{oq,ol}
      \fmfleft{iq,il}
      \fmflabel{$e^+$}{il}
      \fmflabel{$e^+$}{ol}
      \fmflabel{$q_i$}{iq}
      \fmflabel{$q_i$}{oq}
      \fmf{fermion}{il,v1,ol}
      \fmf{fermion}{iq,v2,oq}
      \fmf{photon,label={$\gamma/Z$},l.side=left}{v1,v2}
      \fmfdot{v2}
      \fmfdot{v1}
    \end{fmfgraph*}
    \hspace{2cm}
    \setlength{\unitlength}{1mm}
    \begin{fmfgraph*}(30,25)
      \fmfright{oq,ol}
      \fmfleft{iq,il}
      \fmflabel{$e^+$}{il}
      \fmflabel{$\mu^+,\tau^+$}{ol}
      \fmflabel{$q_i$}{iq}
      \fmflabel{$q_j$}{oq}
      \fmf{fermion}{il,v1}
      \fmf{fermion}{iq,v1}
      \fmf{dbl_plain,label={$LQ$},l.side=left}{v1,v2}
      \fmf{fermion}{v2,ol}
      \fmf{fermion}{v2,oq}
      \fmflabel{$\lambda_{ei}$}{v1}
      \fmflabel{$\lambda_{lj}$}{v2}
      \fmfdot{v2}
      \fmfdot{v1}
    \end{fmfgraph*}
    \hspace{2cm}
    \setlength{\unitlength}{1mm}
    \begin{fmfgraph*}(30,25)
      \fmfright{oq,ol}
      \fmfleft{iq,il}
      \fmflabel{$e^+$}{il}
      \fmflabel{$\mu^+,\tau^+$}{ol}
      \fmflabel{$\bar{q}_i$}{iq}
      \fmflabel{$\bar{q}_j$}{oq}
      \fmf{fermion,tension=2}{il,v2}
      \fmf{fermion,tension=2}{iq,v1}
      \fmf{dbl_plain,label={$LQ$},l.side=left}{v1,v2}
      \fmf{phantom}{v2,ol}
      \fmf{phantom}{v1,oq}
      \fmf{fermion}{v2,oq}
      \fmf{fermion}{v1,ol}
      \fmflabel{$\lambda_{il}$}{v1}
      \fmflabel{$\lambda_{ej}$}{v2}
      \fmfdot{v2}
      \fmfdot{v1}
    \end{fmfgraph*}
  \end{fmffile}
  \vspace{1cm}
\caption{
  Left: NC deep-inelastic scattering. Centre: s-channel resonant LQ production and  
  decay mediating LFV. Right: u-channel exchange of a LQ possessing couplings to second 
  or third generation leptons.}
\label{lqfeynman}
\end{figure}
\end{center}

\begin{table}[htb]
  \begin{small}
  \begin{center}
    \setlength{\extrarowheight}{4pt}
      \begin{tabular}{c|c|c|c|c||c|c|c|c|c}
%%%        \multicolumn{5}{c||}{\rule[-1.8mm]{0mm}{4mm}$e^{-}p$ sensistivity} & \multicolumn{5}{c}{\rule[-1.8mm]{0mm}{4mm}$e^{+}p$ sensistivity}\\
%%%        \hline
        Q & $F=2$ & Prod./Decay & Coupl. & $BR$ & Q & $F=0$ & Prod./Decay & Coupl. & $BR$ \\
        \hline
        \multicolumn{10}{c}{\rule[-1.8mm]{0mm}{4mm}Scalar Leptoquarks} \\
        \hline
        +1/3 & $S_0^L$ & $e^+_L\bar{u}_L\rightarrow l^+\bar{u}$ & $\lambda_L$ & 1/2 & +5/3 & $S_{1/2}^L$ & 
        $e^+_Lu_L\rightarrow l^+u$ & $\lambda_L$ & 1 \\
        +1/3 & $S_0^R$ & $e^+_R\bar{u}_R\rightarrow l^+\bar{u}$ & $\lambda_R$ & 1 & +5/3 & & 
        $e^+_Ru_R\rightarrow l^+u$ & $\lambda_R$ & 1 \\
        \cline{1-5}
        +4/3 & $\tilde{S}_0^R$ & $e^+_R\bar{d}_R\rightarrow l^+\bar{d}$ & $\lambda_R$ & 1 & +2/3 & 
        \raisebox{1.8ex}[-1.8ex]{$S_{1/2}^R$} & $e^+_Rd_R\rightarrow l^+d$ & $-\lambda_R$ & 1 \\
        \hline
        +1/3 & & $e^+_L\bar{u}_L\rightarrow l^+\bar{u}$ & $-\lambda_L$ & & & & & & \\
        +4/3 & \raisebox{1.8ex}[-1.8ex]{$S_1^L$} 
        & $e^+_L\bar{d}_L\rightarrow l^+\bar{d}$ & $-\sqrt{2}\lambda_L$ 
        & \raisebox{1.8ex}[-1.8ex]{$\frac{1/2\bar{u}+2\bar{d}}{\bar{u}+2\bar{d}}$} 
        & \raisebox{1.8ex}[-1.8ex]{+2/3} 
        & \raisebox{1.8ex}[-1.8ex]{$\tilde{S}_{1/2}^L$} 
        & \raisebox{1.8ex}[-1.8ex]{$e^+_Ld_L\rightarrow l^+d$} 
        & \raisebox{1.8ex}[-1.8ex]{$\lambda_L$} 
        & \raisebox{1.8ex}[-1.8ex]{1}\\
        \hline
        \multicolumn{10}{c}{\rule[-1.8mm]{0mm}{4mm}Vector Leptoquarks} \\
\hline
        +4/3 & $V_{1/2}^L$ & $e^+_L\bar{d}_R\rightarrow l^+\bar{d}$ & $\lambda_L$ & 1 & +2/3   & 
        $V_0^L$ & $e^+_Ld_R\rightarrow l^+d$ & $\lambda_L$ & 1/2\\
        +1/3 & & $e^+_R\bar{u}_L\rightarrow l^+\bar{u}$ & $\lambda_R$   & 1 & +2/3   & $V_0^R$ & 
        $e^+_Rd_L\rightarrow l^+d$ & $\lambda_R$ & 1\\       
        \cline{6-10}
        +4/3 & \raisebox{1.8ex}[-1.8ex]{$V_{1/2}^R$} 
        & $e^+_R\bar{d}_L\rightarrow l^+\bar{d}$ 
        & $\lambda_R$ & 1 & +5/3 & $\tilde{V}_0^R$ 
        & $e^+_Ru_L\rightarrow l^+u$ & $\lambda_R$ & 1\\
        \hline   
        & & & & & +5/3 & & $e^+_Lu_R\rightarrow l^+u$ & $\sqrt{2}\lambda_L$ & \\
        \raisebox{1.8ex}[-1.8ex]{+1/3} 
        & \raisebox{1.8ex}[-1.8ex]{$\tilde{V}_{1/2}^L$} 
        & \raisebox{1.8ex}[-1.8ex]{$e^+_L\bar{u}_R\rightarrow l^+\bar{u}$} 
        & \raisebox{1.8ex}[-1.8ex]{$\lambda_L$}  
        & \raisebox{1.8ex}[-1.8ex]{1}
        & +2/3 
        & \raisebox{1.8ex}[-1.8ex]{$V_1^L$} 
        & $e^+_Ld_R\rightarrow l^+d$ & $-\lambda_L$ & \raisebox{1.8ex}[-1.8ex]{$\frac{1/2d+2u}{d+2u}$}\\       
      \end{tabular}
  \end{center}
  \end{small}
\caption{
  Isospin families of leptoquarks in the Buchm\"uller-R\"uckl-Wyler model~\cite{BRW} and the decay channels considered in this
  analysis. The superscript of the leptoquark 
  indicates the chirality of the lepton involved, 
  whereas the subscript corresponds to the weak isospin. Different chiralities between the lepton and the quark lead to 
  vector leptoquarks with Spin $I=1$ and equal chiralities give scalar leptoquarks with Spin $I=0$. For left-handed 
  leptoquarks with whole-numbered weak isospin, the branching 
  ratio $BR$ accounts for an additional charged current decay channel, i.e. the decay into a neutrino and a quark. 
}
\label{lqBRW}
\end{table}

%%\vspace{2cm}
\begin{figure}[p] 
  \begin{center}
   \epsfig{file=eps/mudhi/MP_Data_MuonAcopolanarity.eps,clip=,scale=0.48}
   \epsfig{file=eps/mudhi/MP_Data_VRatio.eps,clip=,scale=0.48}
   \epsfig{file=eps/mudhi/MP_Data_CalorimetricTransverseMomentum.eps,clip=,scale=0.48}
   \epsfig{file=eps/mudhi/MP_Data_MuonTransverseMomentum.eps,clip=,scale=0.48}
  \end{center}
  \caption{
    Distributions of H1 data in the muon channel after the isolated muon selection step with SM expectation and arbitrarily 
    normalised LFV signal mediated by a vector LQ, $V^L_0$, of mass 250~\GeV~decaying to a muon and a quark. 
    The acoplanarity (top left), shows the clear back-to-back nature of the LQ decay products (hatched histogram) where the 
    azimuthal angle between the hadronic system and the muon is
    around $180^{\circ}$. $V_{ap}/V_P$ (top right) shows the lack of isotropy in the
    selected events. $P_T^{Calo}$ (bottom left) and
    $P_T^{\mu}$ (bottom right) show the transverse momentum sum deposited in the
    calorimeter and the muon transverse momentum, respectively.
  }
  \label{mucontrol}
\end{figure} 

%%\vspace{2cm}
\begin{figure}[p] 
  \begin{center}
   \epsfig{file=eps/JjTau_PtMiss.eps,clip=,scale=0.48}
   \epsfig{file=eps/JjTau_Jet2Size.eps,clip=,scale=0.48}
   \epsfig{file=eps/JjTau_JetTauTrackDistToNearestTrack.eps,clip=,scale=0.48}
   \epsfig{file=eps/JjTau_Jet2Mass.eps,clip=,scale=0.48}
  \end{center}
  \caption{
    Distributions of H1 data in the tau channel after the first selection step for $\tau+q$ signatures with SM expectation and 
    arbitrarily normalised LFV signal mediated by a vector LQ, $V^L_0$, of mass 250~\GeV~decaying to a tau and a quark. 
    Top left: Missing transverse momentum before the cut at $20\;{\rm GeV}$ to enhance the LFV signal with respect to the 
    SM background. Top right: Radial size of jet2 in the $\eta\phi$-plane with the signal showing the typical very narrow 
    shape of a $\tau$-jet. Bottom left: Distance of the nearest track to the leading track of jet2 showing the 
    difference of isolation between the LFV signal and SM background. Bottom right: Mass of jet2 indicating the low 
    mass of a $\tau$-jet compared to an ordinary hadronic jet.
  }
  \label{taucontrol}
\end{figure} 

%%\vspace{2cm}
\begin{figure}[p] 
  \begin{center}
   \epsfig{file=eps/mudhi/Final_Data_LQMass_doubleAngleMethod.eps,clip=,scale=0.48}
   \epsfig{file=eps/JjFinal_LQMass.eps,clip=,scale=0.48}
  \end{center}
  \caption{
    Mass spectra after the final selection for $\mu+q$ signatures (left) and $\tau+q$ signatures (right) compared to a vector LQ, 
    $V^L_0$, of mass 250~\GeV~decaying to a muon and a quark (left) or a tau and a quark (right).
  }
  \label{mass}
\end{figure} 


%%\vspace{2cm}
%%\vspace{2cm}
\begin{figure}[p] 
  \begin{center}
   \epsfig{file=eps/MuLimit_Scalar.eps,clip=,scale=0.38}
   \epsfig{file=eps/TauLimit_Scalar.eps,clip=,scale=0.38}
   \epsfig{file=eps/MuLimit_Vector.eps,clip=,scale=0.38}
   \epsfig{file=eps/TauLimit_Vector.eps,clip=,scale=0.38}
  \end{center}
  \caption{
Limits on the coupling constant strength $\lambda_{lq}$ at 95\% C.L. as a function of LQ mass for scalar (top) and vector
(bottom) LQs in the muon (left) and tau (right) decay channels.
  }
  \label{lambdalimtaumu}
\end{figure} 

\begin{figure}[p] 
  \begin{center}
   \epsfig{file=eps/CompLimit_Scalar.eps,clip=,scale=0.38}
   \epsfig{file=eps/CompLimit_Vector.eps,clip=,scale=0.38}
  \end{center}
  \caption{
 %   95\% C.L. limits on $\lambda_{\tau q}$ for different $F=0$ scalar (top left) and vector (bottom left) LQs as 
%    function of the LQ mass. The legend indicates to which quark flavor, $u$ and/or $d$, the LQ couples to. Here, a 
%    branching ratio of 0.5 between the LQ decaying under change of lepton flavor into $\tau+q$ and under its 
%    conservation into $e+q$ is assumed. On the right-hand side, for two LQs a limit on the branching ratio 
%    $\beta_{\tau}$ is shown for different values of the coupling $\lambda_{eq}$ at the LQ production vertex. 
Limit on the coupling strength $\lambda_{lq}$ at 95\% C.L. for $S_{1/2}^L$ and $V_1^L$ decaying into leptons of the
first, second and third generations.
  }
  \label{lambdalimtaumuele}
\end{figure} 

\begin{figure}[p] 
  \begin{center}
   \epsfig{file=eps/BRLimit_Scalar.eps,clip=,scale=0.60}
  \end{center}
  \caption{
    Mass limit of LQs $S_{1/2}^L$ and $V_1^L$ at 95\% C.L. as a function of the branching ratio for 
    ${\rm LQ}\rightarrow\mu q$ and ${\rm LQ}\rightarrow\tau q$ with a fixed coupling to first generation leptons at
    $\lambda_{eq}=0.3$.
  }
  \label{BRlimtaumu}
\end{figure} 

\begin{table}[htb]
  \begin{center}
    \begin{tabular}{|c|c|c|c|}
      
      \hline
     SM Process          &     Event generator   &   MC uncertainty(\%)  \\
      \hdick                                          
       NC DIS            &    Rapgap      &        10             \\
  Lepton pair         &    Grape       &        10             \\
  W-Production        &    Epvec       &        15             \\
%  $J/$\psi$-Production &    Jpsi        &        15             \\
  Photoproduction     &    Pythia      &        30             \\
 % Heavy flavor        &    Aroma       &        30             \\
 %      CC             &    Django      &        30             \\
      \hline
    \end{tabular}
  \end{center}
  \caption{Systematic uncertainties for the dominant SM MC used in the analysis.}  
\label{bgsys}
\end{table}

\begin{table}[htb]
  \begin{center}
    \setlength{\extrarowheight}{5pt}
    \begin{tabular}{|c||c|c|}
      \hline
      \multicolumn{3}{|c|}{\rule[-1.8mm]{0mm}{4mm}\bf\Large{\bf H1 Preliminary, }\boldmath{${\cal L}=66~{\rm pb^{-1}}$}}\\
      \hdick
      &  ${\rm LQ}\rightarrow\mu+q$ & ${\rm LQ}\rightarrow\tau+q$   \\
      \hline
      Data  &           0       &              1       \\
      Total SM    &    0.74 $\pm$ 0.25   &    0.56 $\pm$ 0.16 \\
      \hline
      NC DIS      &   0.09 $\pm$ 0.05 &   0.37 $\pm$ 0.13\\
      Lepton Pair      &   0.50 $\pm$ 0.24  &   -  \\
%%      Charged Current      &    0 $\pm$ 0       &   0.002 $\pm$ 0.001 \\
      Photoproduction &   0.06 $\pm$ 0.07   &   0.13 $\pm$ 0.04 \\
      $W$-Production   &   0.08 $\pm$ 0.02  &   0.06 $\pm$ 0.02  \\
      \hline
        \end{tabular}
  \end{center}
\caption{
Numbers of events after the final selection with their total errors. Statistical and systematic 
errors are added in quadrature.
}
\label{resnum}
\end{table}

\end{document}
