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\begin{document}

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\noindent
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%{\it {\large version of \today}} \\[.3em] 
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\multicolumn{4}{l}{{\bf
               X International Workshop on Deep Inelastic Scattering (DIS2002) },
                May~2,~2002,~Cracow} \\
 {\bf ICHEP 2002:} 
                 & Abstract:        & {\bf 1021}    &\\
                 & Parallel Session & {\bf 10}   &\\[.7em] \hline
 & \multicolumn{3}{r}{\footnotesize {\it
    www-h1.desy.de/h1/www/publications/conf/conf\_list.html}} \\[.2em]
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\begin{center}
  \Large
  {\bf     Muon Pair Production \\
   \bf in ep collisions at HERA \\}     
  \vspace*{2cm}
    {\Large H1 Collaboration} 
\end{center}
\vspace*{1 cm}

\begin{abstract}

\noindent
Events containing pairs of isolated muons at high invariant masses have been measured at HERA with the H1 detector in a data sample corresponding to an integrated luminosity of 70.9~pb$^{-1}$.
The results are compared to Standard Model predictions which are dominated by photon-photon collisions.


\end{abstract}


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\section{Introduction}
Isolated muon pair production, $ep \longrightarrow e \mu \mu X$, at high di-muon masses has been studied by H1 using the data from 1999 and 2000. Isolated muon pairs are dominantly produced via the two-photon process,
$\gamma \gamma \longrightarrow \mu^+ \mu^-$, depicted in fig. \ref{fig:feynman:bh}.  
As well as testing QED and the photon spectrum of the proton this analysis provides constraints on backgrounds to searches for new physics. In particular, it complements the analysis of  multi electron pair production where possible deviations from the standard model have been observed at large di-electron masses \cite{Vallee:2002}. It is also  of interest  in relation to the analysis of events  with a lepton and missing transverse  momentum \cite{Adloff:1998aw}. 
\begin{figure}[h]
\label{fig:feynman:bh}
  \begin{center}
    \epsfig{file=H1prelim-02-051.fig1.eps,width=2.2cm}
%\hspace{2 cm}
%    \epsfig{file=feyn_gross_CP2.eps,width=2.2cm}
\caption{Muon pair production in the two-photon process (here for the deep inelastic case).}
 \end{center}
\end{figure}

\section{Selection}

%A full description of the H1 detector and its various components can be found elsewhere \cite{Abt:1997hi,Abt:1997xv}.

The muon selection is based on measurements using the central tracker and the muon detector of H1 \cite{Abt:1997hi}.
Muon candidates are selected from charged tracks measured in  the central tracker at polar angles 
between 20$^\circ$ and 160$^\circ$, which are linked to tracks  measured in the muon detector.
For low momentum muons the finding efficiency is increased by accepting also minimal 
ionising particles in the Liquid Argon Calorimeter which are linked to a central track.
The momentum and charge measurement is based on central tracker information.
The analysis  is carried  out in the phase space  given  by a cut on the invariant mass of the
muon pair ($M_{\mu,\mu} > 5$~GeV), requirements  of minimal  transverse  momenta ($P_{t}^{\mu_1}>2.0$~GeV and $P_{t}^{\mu_2}>1.75$~GeV) and
the given polar angle region. 
Background is suppressed by dedicated cuts against cosmic ray muons and an isolation requirement: 
the distance  of the muons  to the nearest  track or jet in the pseudorapidity-azimuthal-plane \begin{math} D_{Track,Jet}^{\mu}\end{math} has to be greater than \begin{math}  1.0 \end{math}.  For  muons  with high transverse momentum ($P_{t}^{\mu} > 10$~GeV)  only $D_{Track,Jet}^{\mu} >0.5$ is required.


%One of the muon candidates must have a transverse momentum 
%greater than  2.0 GeV, while  for the second muon  a  minimal  transverse momentum  of 1.75 GeV is required. \\

%Events with at least two muon candidates with an invariant mass above 5 GeV are selected.
%Cosmic Background is suppressed by a cut on the opening angle \begin{math}  \alpha < 165 \end{math}  of the two
%muons. \\
\section{Inclusive Isolated Muon Pair Production}


Pair production of isolated muons is measured inclusively and compared to the Standard Model prediction, 
which is strongly dominated by electroweak production, especially by the two-photon process.
Electroweak muon pair production is simulated with the GRAPE generator \cite{Abe:2001cv}, which uses the calculation program `GRACE' \cite{Ishikawa:1993qr} to determine the Feynman amplitudes of the corresponding diagrams in leading order. 
Contributions from  diagrams  corresponding to Bremsstrahlung with subsequent photon conversion into a muon pair and  electroweak contributions like real $Z^0$-production with decay to $\mu^+\mu^-$ are considered in addition to the two-photon process (fig. \ref{fig:feynman:bh}). Not simulated is the negligible contribution from the Drell-Yan process in resolved photoproduction events \cite{Arteaga-Romero:1991wn}.
To compare the contribution of the two-photon process  to the full electroweak calculation (GRAPE), 
the two-photon process alone is simulated also with the LPAIR generator \cite{Baranov:1991yq,Vermaseren:1983cz}.
Other sources of di-muon production have been simulated using  DIFFVM \cite{List:1993} for the $\Upsilon$-resonance,
LPAIR for muons arising from $\gamma \gamma \longrightarrow \tau \tau$  and AROMA \cite{Ingelman:1997mv} for muons stemming  from semi-leptonic decays in open heavy quark production ($c\bar{c}$ and $b\bar{b}$).
Having corrected the data for detector effects, cross sections in the observed  phase space  are derived.   \\
Fig. \ref{fig:invariantmass}  presents the  visible cross section as a function  of the invariant mass
of the muon pair. 
The mass spectrum falls steeply over more than four decades and extends  up to 80~GeV.  The two-photon process almost saturates the data. The shaded  histograms show  the  expectation from  the $\Upsilon$  and $Z^0$ resonances.
At small masses minor contributions from open heavy flavour quark production, which are strongly suppressed due to the isolation requirement, and  $\tau$-decays are expected.
The lower figures show the relative difference between data and the sum of all Standard Model contributions. 
The agreement  between data and the standard model is very good. \\
The inclusive cross section as a function of the muon transverse momenta is presented  in figure \ref{fig:pt}.    
The distribution of the transverse hadronic momentum $P_t^X$ is depicted in fig. \ref{fig:ptx}.
The measured cross section is described within errors.
Fig. \ref{fig:wgammap} shows  the cross section as a
function of the invariant mass  of the  proton and the photon coupling to the electron and fig.  \ref{fig:ptmiss} depicts  the distribution of the missing transverse momentum. 
Both agree well with the prediction. 
%Events with $P_t^X$ up to 50~GeV have been measured. In the tail the data is a bit too high, but described within errors by the Monte Carlo.

\section{Elastic and Inelastic Muon Pair Production}
Elastic $ep \longrightarrow e\mu\mu p$ and inelastic $ep \longrightarrow e\mu\mu X$  muon pair production are separated from
each other by tagging the proton remnant $X$ using forward detectors \cite{Adloff:2002re}.
92 \% of the inelastic events lead to activity in either the Proton Remnant Tagger or the Forward Muon System or the forward  part of the Liquid Argon Calorimeter.  
Fig.  \ref{fig:ewcrosssectionsela} and \ref{fig:ewcrosssectionsine} show the resulting mass spectra for the elastic  and the inelastic  data samples.
Elastic muon production dominates the small mass region, but both spectra extend to similar high masses and match very
well with the Standard Model prediction. The error arising from  the uncertainty in the separation of the two  production mechanisms is conservatively estimated to be 10~\%.      

The total cross section of muon pair production in the observed  phase space was found to be (46.5 $\pm$1.3 $\pm$ 4.7)~pb,  which agrees  well with
the GRAPE  prediction of 46.2~pb.  For inelastic di-muon production a total cross section of (20.8 $\pm$0.9 $\pm$ 3.3)~pb  was measured, which agrees  within errors with  the expected  cross section of 21.5~pb.  

\section{Summary}
Isolated muon pair production at high invariant masses has been analysed by H1 and both  the inclusive  cross section and the elastic and inelastic cross section have been found to agree very well  with the Standard Model prediction. 
No excess in the mass  or other spectra  has been observed. An increase in  the integrated luminosity and extension to the $\mu e$  channel will shed further light on the high mass excess reported for multi-electron production in \cite{Vallee:2002}.


\begin{thebibliography}{99}


%\bibitem{Malden:2002}
%N.~Malden,
%\textit{Single top (isolated leptons and missing pt) at HERA},
%%X International Workshop on Deep Inelastic Scattering (DIS2002),~Cracow. 
%these proceedings.

\bibitem{Vallee:2002}
C.~Vall\'{e}e,
%\textit{Lepton pair production at high transverse momentum at HERA},
X International Workshop on Deep Inelastic Scattering (DIS2002),~Cracow. 

\bibitem{Adloff:1998aw}
H1 Collaboration,
%\textit{Observation of events with an isolated high energy lepton and missing  transverse momentum at HERA},
Eur.\ Phys.\ J.\ C {\bf 5} (1998) 575
[arXiv:hep-ex/9806009].
%%CITATION = HEP-EX 9806009;%%


%%these proceedings.
%\cite{Abt:1997hi}
\bibitem{Abt:1997hi}
H1 Collaboration,
%\textit {The H1 detector at HERA},
Nucl.\ Instrum.\ Meth.\ A {\bf 386} (1997) 310. \\
%%CITATION = NUIMA,A386,310;%%
%
%\cite{Abt:1997xv}
%\bibitem{Abt:1997xv}
H1 Collaboration,
%\textit {The Tracking, calorimeter and muon detectors of the H1 experiment at HERA},
Nucl.\ Instrum.\ Meth.\ A {\bf 386} (1997) 348.
%%CITATION = NUIMA,A386,348;%%
%

%\cite{Abe:2001cv}
\bibitem{Abe:2001cv}
T.~Abe,
%``GRAPE-Dilepton (Version 1.1): A generator for dilepton production in  e p collisions,''
Comput.\ Phys.\ Commun.\  {\bf 136} (2001) 126
[hep-ph/0012029].
%%CITATION = HEP-PH 0012029;%%
%
\bibitem{Ishikawa:1993qr}
T.~Ishikawa et.al.,
%% ``GRACE manual: Automatic generation of tree amplitudes in Standard Models: Version 1.0,'' 
KEK-92-19, (1992).
%
\bibitem{Arteaga-Romero:1991wn}
N.~Arteaga-Romero, C.~Carimalo and P.~Kessler, 
%\textit{High $P_{t}$ lepton pair production at e p colliders: Comparison between various production mechanisms},
Z.\ Phys.\ C \textbf{ 52} (1991) 289.

%
\bibitem{Baranov:1991yq}
S.~P.~Baranov, O.~D\"unger, H.~Shooshtari and J.~A.~Vermaseren,
%``LPAIR: A generator for lepton pair production,''
{\it  In *Hamburg 1991, Proceedings, Physics at HERA, vol. 3* 1478-1482.% (see HIGH ENERGY PHYSICS INDEX 30 (1992) No. 12988)
}
%
\bibitem{Vermaseren:1983cz}
J.~A.~Vermaseren,
Nucl.\ Phys.\ B {\bf 229} (1983) 347.
%%CITATION = NUPHA,B229,347;%%
%
%
\bibitem{List:1993}
B.~List,
%\textit{Diffraktive J$/\Psi$~-Produktion in Elektron-Positron-St"o"sen am Speicherring HERA}, 
diploma thesis, Technische Univerist\"at Berlin, (H1-10/93-319) (1993).
%
\bibitem{Ingelman:1997mv}
G.~Ingelman, J.~Rathsman and G.~A.~Schuler,
%\textit{AROMA 2.2 - A Monte Carlo Generator for Heavy Flavour Events in $ep$ Collisions},
Comput.\ Phys.\ Commun.\  {\bf 101} (1997) 135
[hep-ph/9605285].
%%CITATION = HEP-PH 9605285;%%
%\cite{Adloff:2002re}
\bibitem{Adloff:2002re}
H1 Collaboration,
%\textit{Diffractive photoproduction of psi(2S) mesons at HERA},
[arXiv:hep-ex/0205107].
%%CITATION = HEP-EX 0205107;%%

%\bibitem{Schmidt:2001} 
%D.~Schmidt, 
%\textit{Diffraktive Photoproduktion von Charmonium im H1-Detektor bei HERA},
%Ph.D. thesis,  Hamburg, (2001).

\end{thebibliography}

\begin{figure}[h]
  \begin{center}
    \epsfig{file=H1prelim-02-051.fig2.eps,width=14cm}
    \caption{Invariant di-muon mass in comparison to the electroweak (EW) prediction using GRAPE.
The contribution of the most important electroweak muon pair production processes are also  plotted individually, i.e. the contribution from the two photon process $\gamma \gamma \rightarrow \mu \mu$ (using LPAIR)  and $Z^{0}$-resonance. 
 The contribution of additional sources of muon pair production are $\gamma \gamma \longrightarrow \tau \tau$,  boson-gluon fusion ($c\bar{c}$ and $b\bar{b}$) and the decay  of the $\Upsilon$ resonances.  Also shown is the relative difference between data and  all Standard Model contributions (lower figures). The inner error bars represent the statistical errors. The outer  error bars represent the statistical  and systematical errors added in quadrature.}
%  \end{center}
\label{fig:invariantmass}
  \end{center}
\end{figure}
%
\begin{figure}[h]
  \begin{center}   
   \epsfig{file=H1prelim-02-051.fig3.eps,width=14cm}
   \caption{Cross section as a function of the muon transverse momenta (with two entries in the cross section per muon). For details see  figure \ref{fig:invariantmass}. }
   \label{fig:pt}
 \end{center}
\end{figure}
%
\begin{figure}[h]
  \begin{center}
    \epsfig{file=H1prelim-02-051.fig4.eps,width=14cm}
    \caption{Cross  section as a function of the hadronic transverse momentum. For details see  figure \ref{fig:invariantmass}.}
    \label{fig:ptx}
 \end{center}
\end{figure}
%
\begin{figure}[h]
  \begin{center}
    \epsfig{file=H1prelim-02-051.fig5.eps,width=14cm}
\caption{Cross  section as a function of the invariant mass of the $\gamma$-proton system for di-muon events. For details see figure \ref{fig:invariantmass}. }
\label{fig:wgammap}
 \end{center}
\end{figure}
%
\begin{figure}[h]
  \begin{center}
    \epsfig{file=H1prelim-02-051.fig6.eps,width=14cm}
    \caption{Distribution of the missing transverse  momentum uncorrected
for detector resolution.  The data are compared to the full standard  model expectation (SM), which  is dominated by the diagrams  simulated with the GRAPE Monte Carlo.}
    \label{fig:ptmiss}
 \end{center}
\end{figure}

\begin{figure}[h]
  \begin{center}   
    \epsfig{file=H1prelim-02-051.fig7.eps,width=14cm}
    \caption{Cross  section as a function of the invariant mass  of elastically  produced muon pairs.}
 \label{fig:ewcrosssectionsela}
 \end{center}
\end{figure}


\begin{figure}[h]
  \begin{center}
    \epsfig{file=H1prelim-02-051.fig8.eps,width=14cm}
    \caption{Cross  section as a function of the invariant mass  of inelastically produced muon pairs.}
    \label{fig:ewcrosssectionsine}
 \end{center}
\end{figure}




%\begin{figure}[t]   
%  \begin{minipage}[h]{16 cm}
%    \begin{center}  
%      \includegraphics [width=4.7 cm]{/x01/usr/leissner/dis/bilder/feynman/feyn_CP1_b.eps}
%      \hspace{2 cm}
%      \includegraphics [width=4.7 cm]{/x01/usr/leissner/dis/bilder/feynman/feyn_CP3.eps}
%      \hspace{2 cm}
%    \end{center}
%  \end{minipage}
%  \begin{minipage}[h]{16 cm}
%    \begin{center}  
%      \vspace{2 cm}
%      \includegraphics [width=4.7 cm]{/x01/usr/leissner/dis/bilder/feynman/feyn_CP2.eps}
%      \hspace{2 cm}
%      \includegraphics [width=4.7 cm]{/x01/usr/leissner/dis/bilder/feynman/feyn_CP4.eps}
%    \end{center}
%    \vspace{1 cm}
%  \end{minipage}
%  \caption{Bremsstrahlungs processes (QED Compton). 
%The diagrams  for $Z^0$-production can be derived, if the radiated  photon is replaced  by a $Z^0$ boson.}
%  \label{fig:muonprod:cp}
%\end{figure}

%\begin{figure}[t]
%\label{fig:inclusivecrosssections1}
%  \begin{center}
%    \epsfig{file=H1prelim-02-051.fig7.eps,width=6.2cm}
%    \epsfig{file=H1prelim-02-051.fig2.eps,width=6.2cm}
%    \caption{Invariant di-muon mass (left) and transverse muon momenta (right) of di-muons in comparison to the electroweak (EW) prediction using GRAPE, the $\gamma \gamma \rightarrow \mu \mu$ contribution using LPAIR as well as contributions  from $\gamma \gamma \longrightarrow \tau \tau$, $c\bar{c}$ and $b\bar{b}$, $\Upsilon$  and $Z^{0}$ decays.  Also shown is the relative difference between data and  all Standard Model contributions (lower figures).}
%  \end{center}
%\end{figure}
%\end{figure*}




%\begin{figure}[h]
%\label{fig:inclusivecrosssections2}
%  \begin{center}
%    \epsfig{file=H1prelim-02-051.fig3.eps,width=6.2cm}
%\caption{Hadronic transverse momentum distribution in di-muon events. For details see fig. \ref{fig:inclusivecrosssections2}.}
% \end{center}
%\end{figure}




%%\clearpage
%\vspace{3cm}
%\begin{figure}[h]
%  \label{fig:ewcrosssections}
%  \begin{center}
%    \epsfig{file=H1prelim-02-051.fig6.eps,width=6.2cm}
%    \epsfig{file=H1prelim-02-051.fig5.eps,width=6.2cm}
%    \caption{Invariant di-muon mass  of elastic (left) and inelastic (right) produced muon pairs.}
% \end{center}
%\end{figure}
%%\section{Differential Cross Sections} 

\end{document}





