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\noindent
{\bf  H1-prelim-02-061 \hfill 
  \epsfig{file=/h1/www/images/H1logo_bw_small.epsi,width=2.cm} 
} \\
\noindent February 2002 
\vspace*{3cm}
\begin{center}
  \Large
  {\bf 
        Muon Pair Production in ep Collisions  at HERA}\\

  \vspace*{1cm}
    {\Large H1 Collaboration} 
\end{center}


\begin{abstract}
\noindent
Events containing pairs of isolated muons at high invariant masses have been detected at HERA with the H1 detector in a 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 collision.

\end{abstract}
\end{titlepage}

\pagestyle{plain}
%
The data have been collected with the H1 detector at {\sc Hera} and correspond to an 
integrated luminosity of $70.9~pb^{-1}$ of $e^{\pm}p$ scattering at $\sqrt{s} = 318$~GeV.\\
The muon selection is based on central tracker and muon detector measurements.
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.
The finding efficiency for low momentum muons is improved by  identifying minimal 
ionising particles in the Liquid Argon Calorimeter which are linked to an inner track.
The momentum and charge measurement is based on central tracker information.
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. \\
For the final data sample isolated muons are required, i.e.
their distance \begin{math} D_{Track,Jet}\end{math} in the pseudorapidity-azimuthal-plane  from other tracks or jets is
greater than \begin{math}  1.0 \end{math}.
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. \\


The data is compared to a Standard Model prediction. 
The two photon  process  $\gamma \gamma  \longrightarrow \mu \mu $ forms the major  part  of the cross section.
 To Monte Carlo  Generators are used  to simulated this  process:
GRAPE \cite{Abe:2001cv} and LPAIR \cite{Baranov:1991yq,Vermaseren:1983cz}. GRAPE  uses the automatic calculation program `GRACE'
\cite{Ishikawa:1993qr} to determine the feynman amplitudes of the corresponding diagrams.
GRAPE allows to simulate the two boson muon production processes $\gamma \gamma$, $\gamma Z^{0}$ and $Z^{0} Z^{0}$ as well as the QED Compton  type process $\gamma \longrightarrow \mu \mu $ and $Z^{0}\longrightarrow \mu \mu $. 
It allows to include initial and final state radiation. 
The plots show the total standard model prediction which is determined using GRAPE, the 
contribution of  the $\gamma \gamma $ process determined with LPAIR. 
Other sources of 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 open heavy flavour quark production 
($c\bar{c}$ and $b\bar{b}$). \\

The total cross section  for di-muon production was found to be (46.5 $\pm$1.3 $\pm$ 4.7)~pb,
for inelastic di-muon production a total cross section of (20.8 $\pm$0.9 $\pm$ 3.3)~pb  was measured. 
 
\begin{figure}[h]
  \begin{center}
    \epsfig{file=H1prelim-02-051.fig1.eps,width=3.2 cm}
\caption{Example of a feynman diagram for  $\gamma \gamma \longrightarrow \mu \mu$.}
  \end{center}
\end{figure}

\begin{figure}[h]
  \begin{center}
    \epsfig{file=H1prelim-02-051.fig2a.eps,width=4 cm}
    \epsfig{file=H1prelim-02-051.fig2b.eps,width=4 cm}
    \caption{Example of feynman diagrams for  $\gamma \longrightarrow \mu \mu$.}
  \end{center}
\end{figure}
\begin{figure}[h]
  \begin{center}
    \epsfig{file=H1prelim-02-051.fig3.eps,width=4 cm}
\caption{Example of a feynman diagram for  $Z^{0}$-production.}
  \end{center}
\end{figure}

\newpage

\begin{thebibliography}{99}
%\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{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{Ishikawa:1993qr}
T.~Ishikawa, T.~Kaneko, K.~Kato, S.~Kawabata, Y.~Shimizu and H.~Tanaka [MINAMI-TATEYA group Collaboration],
% ``GRACE manual: Automatic generation of tree amplitudes in Standard Models: Version 1.0,''
KEK-92-19.
%
\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-internal note (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;%%


\end{thebibliography}

% \input{figures}




\newpage
%\section{Differential Cross Sections} 
\begin{figure}[h]
  \begin{center}
    \epsfig{file=H1prelim-02-051.fig4.eps,width=14 cm}
    \caption{Invariant mass of di-muons in comparison to the SM 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 figure).}
\label{fig:invariantmass}
  \end{center}
\end{figure}
%
\begin{figure}[h]
  \begin{center}
    \epsfig{file=H1prelim-02-051.fig5.eps,width=14cm}
    \caption{Invariant mass of di-muons (fine binning, logarithmic y axis). For details see figure \ref{fig:invariantmass}.}
  \end{center}
\end{figure}
%
\begin{figure}[h]
  \begin{center}
   \epsfig{file=H1prelim-02-051.fig6.eps,width=14cm}
   \caption{Transverse Momentum of the muons. For details see first figure. }
 \end{center}
\end{figure}
%
\begin{figure}[h]
  \begin{center}
    \epsfig{file=H1prelim-02-051.fig7.eps,width=14cm}
\caption{Hadronic transverse momentum distribution in di-muon events. For details see  figure \ref{fig:invariantmass}.}
 \end{center}
\end{figure}
%
\begin{figure}[h]
  \begin{center}
    \epsfig{file=H1prelim-02-051.fig8.eps,width=14cm}
\caption{Invariant mass of the $\gamma$-proton system for di-muon events. For details see figure \ref{fig:invariantmass}. }
 \end{center}
\end{figure}
%
\begin{figure}[h]
  \begin{center}
    \epsfig{file=H1prelim-02-051.fig9.eps,width=14cm}
    \caption{Invariant mass  of inelastic produced muon pairs.}
 \end{center}
\end{figure}
\begin{figure}[h]
  \begin{center}
    \epsfig{file=H1prelim-02-051.fig10.eps,width=14cm}
    \caption{Invariant mass  of elastic  produced muon pairs.}
 \end{center}
\end{figure}
\begin{figure}[h]
  \begin{center}
    \epsfig{file=H1prelim-02-051.fig11.eps,width=14cm}
    \caption{Uncorrected distribution of the missing transverse  momentum of di-muon events. }
 \end{center}
\end{figure}

\begin{figure}[h]
\epsfig{file=H1prelim-02-051.figev1.ps,bbllx=53 pt,bblly=324 pt,bburx=495pt,bbury=760pt,angle=90,width=7.55 cm,clip=}  
\hspace{0.25 cm}
 \epsfig{file=H1prelim-02-051.figev2.ps,bbllx=118 pt,bblly=325 pt,bburx=418pt,bbury=650pt,angle=90,width=8 cm,clip=}  
    \caption{Event display of the event  with the highest invariant mass  of the muon pair ($M_{|mu,\mu} =  80$~GeV) (left figure) and an event display of the di-muon event with the highest transverse momentum of the hadronic final state ($P_{t}^{X}=47$~GeV) (right figure). } 
\end{figure}



\begin{table}[htbp]
  \begin{center}
    \begin{tabular}[h]{|l|l|}
\hline
$\sigma_{tot}$ & (46.5 $\pm$1.3 $\pm$ 4.7)~pb \\  \hline
$\sigma_{tot}^{inel}$& (20.8 $\pm$0.9 $\pm$ 3.3)~pb \\  \hline
    \end{tabular}
    \caption{Total cross sections for di-muon pair production and the total cross section for inelastic di-muon production.}
    \label{tab:totcross}
  \end{center}
\end{table}
\newpage


 

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