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\title*{High $\mathbf{P_T}$ Leptons and W Production at HERA}
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\toctitle{High $\mathbf{P_T}$ Leptons and W Production at HERA}
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\titlerunning{High $\mathbf{P_T}$ Leptons and W Production at HERA}
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% to fit in the running head
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\author{Joachim Meyer}
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\authorrunning{Joachim Meyer}
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% please abbreviate author list for running head
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\institute{DESY, Hamburg, Germany}


\maketitle              % typesets the title of the contribution
%*****************************************************************************
\begin{abstract}
The H1 and ZEUS Collaborations have observed  events with high energy 
leptons and missing transverse momentum at the electron-proton collider HERA.
While some of these events can be explained by the expected properties of
W production with leptonic decay, three events with muons observed by H1 show properties atypical
for Standard Model processes.
\end{abstract}


\section{Introduction}
 In the history of high energy physics {\it leptons}
and {\it missing transverse momentum} have proven to be powerful signatures in searches for
new phenomena. 
In 1994, the H1 Collaboration has within a  modest integrated luminosity of
$ \sim 4 pb^{-1} $
observed an outstanding event  \cite{1994.h1}
featuring a high $P_T$ isolated muon, a high  $P_T$ hadronic system
and a large missing $P_T$.
Although the kinematics of the event was found to be compatible
with the production of an on-shell W decaying leptonically, the event was found  in
a region of phase space not likely to be populated by this process.
 
By now the luminosity accumulated at HERA in $e^+ p$ collisions at an energy of
$\sqrt{s} = 300$ GeV is an order a magnitude higher.
We report on
 dedicated searches \cite{ge.pub.h1highptl,zeuspap} 
 performed by  both HERA experiments
for
 events of such  topology, with either an isolated 
electron or muon. 
We also report on an analysis of most recent data accumulated in $e^- p$ collisions
in the years 1998-1999 at an energy of
$\sqrt{s} = 318$ GeV.


\section{Production of $W$ bosons in electron-proton collisions}
%and large missing $P_T$  \cite{ge.pub.h1highptl}. 
Within the Standard Model (SM), the dominant source for events 
with an isolated  high $P_T$ lepton
and large missing $P_T$ is the production of 
 $W$ bosons  with subsequent leptonic decay.
The lowest order diagrams for these processes 
($e p \rightarrow e W^{\pm} X , W^{\pm} \rightarrow \nu \ell^{\pm} $ )
are shown in
figure \ref{wprod.eps}.
%
\begin{figure}[htb]
\begin{center}
\includegraphics[width=.7\textwidth]{meyer.1.eps}
\end{center}
\caption[]{Parton level diagrams for the process $eq \rightarrow eql\nu$.}
\label{wprod.eps}
\end{figure}
%
From the MC simulation (using the program EPVEC \cite{ge.pub.wprod}) one expects 
 \begin{itemize}
\item a cross section $ \sim 50 fb^{-1}$   per charge state and leptonic
    decay channel
\item the cross section to increase towards low transverse momenta $P_T^X$ of the hadronic system
\item a Jacobian peak in the transverse mass of the lepton-neutrino system.
\end{itemize}
 
In EPVEC the cross section is calculated in leading order. Higher order QCD terms 
might enhance $W$-production especially 
at high $P_T^X$. NLO calculations, which were recently 
 made available \cite{spira1} for $W$ production processes induced by resolved photon 
interactions predict cross sections very close to the EPVEC numbers.
However, for the high  $P_T^X$ part of the cross section, which is dominated
by direct photon interactions, NLO calculations are not yet available.
 
W production at HERA also proceeds via the diagram in figure \ref{wprod.eps}e, i.e. the Triple Gauge
Boson Coupling. At HERA, photon exchange dominates over $Z$ exchange 
allowing for the study of the $\gamma W W $ vertex.  The $\gamma W W $ coupling 
is conventionally described  with two parameters labelled $\kappa$ and $\lambda$. In the Standard
Model they take the values $\kappa = 1 $ and $\lambda = 0$. Anomalous couplings may give 
rise to harder distributions in the transverse momentum of the $W$ and thus in $P_T^X$.
  



\section {The Data}
\subsection {H1 Analysis}
The analysis is based on  the Charged Current (CC)
event selection \cite{ge.pub.h1ccsel} 
including the following criteria (for details see \cite{ge.pub.h1highptl})
\begin{itemize}
\item calorimetric missing transverse momentum $  P_T^{calo} > 25 $ GeV 
\item  a well measured  track with $P_T > 10$ GeV  ({\it High $P_T$ track})
\item a reconstructed vertex in the interaction region
\item topological and timing filters against cosmic and halo muons
\item rejection of badly measured neutral current events
\end{itemize}
 For the  $e^+p$ data sample, corresponding to 36.5 $pb^{-1}$ this selection  
 leads to 124 events.

For this data sample the isolation of the high $P_T$ tracks with respect to jets or
other tracks in the event has been investigated.
The isolation is measured by the distance of the high $P_T$ track in the
$\eta-\phi$-plane (pseudorapidity-azimuthal angle-plane)
to its nearest neighbour track ($D_{track}$) and to the nearest hadron jet
($D_{jet}$) . Figure \ref{ge.fig.h1isol} shows the data sample in the 
$D_{track}$-$D_{jet}$-plane. 
%*******************************************************************************
\begin{figure}[b]
\begin{center}
\includegraphics[width=.5\textwidth]{meyer.2.eps}
\end{center}
\caption[]{Correlation between the distances $D_{jet}$ and $D_{track}$ (see text) to
the closest hadronic jet and track, for all high $P_T$ tracks.}
\label{ge.fig.h1isol}
\end{figure}
%******************************************************************************
The bulk of the 124 events are located at small values of
 both distances, as expected for genuine Charged Current events where the high $P_T$ track
 is associated with  the hadronic shower.
However, six events show a  high $P_T$ track 
 clearly isolated in the $D_{track}$-$D_{jet}$-plane. All  6 tracks are
 identified as leptons,
five are  muons (2 $\mu^+$, 2 $\mu^-$
and one $\mu$ of undetermined charge)
 and  one is an  $e^-$. The typical characteristics of these events can be
seen  in fig. \ref{muon2.ps}, 
where  one of the muon-events is shown   as an example.
%*******************************************************************************
\begin{figure}[t]
\begin{center}
\includegraphics[width=.8\textwidth]{meyer.3.eps}
\end{center}
\caption[]{Display of a H1 muon event. Shown are a longitudinal and a 
transverse view as well as the energy release as a function of azimuthal angle
$\phi$ and pseudorapidity $\eta$. }
\label{muon2.ps}
\end{figure}
%******************************************************************************
 Table \ref{kinematics} gives selected kinematic parameters of these six events.
 Although  not required in the selection also the muon events show a significant
 imbalance in the  total transverse momentum ($P_T^{miss}$).
 
 \begin{table}[t]
\begin{center}                
 \begin {tabular} {|l|c|c|c|c|c|c|}
 \hline  
[GeV] & {\bf ELECTRON} & {\bf MUON-1} & {\bf MUON-2} & {\bf MUON-3}  &
{\bf MUON-4} & {\bf MUON-5} \\ 
 \hline
 &&& &&&\\
$Q^l$& neg. &pos.&pos.&neg.&neg.&unmeas.\\ &&& &&&\\
  $P_T^l$&$37.6^{+1.3}_{-1.3}$  &  $23.4^{+7.5}_{-5.5} $ &$28.0^{+8.7}_{-5.4}$&
$38.6^{+12.0}_{-7.4}$&$81.5^{+75.2}_{-26.4}$&$ > 44$
\\ &&& &&&\\

$P_T^X$&$8.0\pm0.8$&$42.2\pm3.8$&$67.4\pm5.4$&$27.4\pm2.7$&$59.3\pm5.9$&$30.0\pm3.0$\\ &&& &&&\\


 $ P_T^{miss}$ &$30.6\pm 1.5$& $18.9^{+6.6}_{-8.3}$ &$43.2^{+6.1}_{-7.7}$&$42.1^{+10.1}_{-5.9}$&$29.4^{+71.8}_{-13.9}$&$>18$\\ &&& &&&\\



 $M_T^{l\nu}$ &$67.7\pm 2.7$&$3.0^{+1.5}_{-0.9}$ & $22.8^{+6.7}_{-4.2}$&$75.8^{+23.0}_{-14.0}$
&$94^{+157}_{-54}$&$>54$\\ &&& &&&\\

\hline
\end {tabular}
 \end{center}
\caption[]{Reconstructed event kinematics of the H1 events. Given are the charge $Q^l$ of the lepton, 
the transverse momenta of
the lepton $P_T^l$, of the hadronic system $P_T^X$, the total missing transverse momentum 
$ P_T^{miss}$ and the transverse lepton-neutrino
mass $M_T^{l\nu}$.  
In case of event MUON-5 $2 \sigma$ limits are quoted for the muon momentum 
and derived quantities.}
\label{kinematics}
\end{table}
 
  \begin{table}
\begin{center}
\begin{tabular}{|c|c|c|} \hline
 &  Electron Channel &  Muon Channel\\
 \hline \hline
Data & 0 $e^+$,1 $e^-$ & 5\\ \hline \hline
$W$ production & $ 1.65 \pm 0.47$  &$  0.53 \pm 0.11$ \\ \hline
$Z$ production &$0.01 \pm 0.01 $ & $ 0.01 \pm 0.01$\\ \hline
Charged Current & $0.02 \pm 0.01$ &  $ 0.01 \pm 0.01$ \\ \hline
Neutral Current & $ 0.51 \pm 0.10$ $e^+$, $0.02 \pm 0.01$ $e^-$  & $ 0.09 \pm 0.06 $ 
\\ \hline
Photoproduction &   $<0.02 $    & $<0.02$ \\ \hline
Heavy Quarks &  $<0.04$  & $<0.04$\\ \hline
Photon-Photon & $ 0.09\pm 0.03$ $e^+$, $0.04 \pm 0.01$ $e^-$    & $ 0.14
 ^{+0.14}_{-0.07} $
 \\
 \hline
\end{tabular}
\\
\caption{Observed and  predicted event rates (H1).
The  limits given correspond to 95\% confidence level.
Unless stated otherwise the quoted numbers refer to the summed
production of  both lepton charged states. }
\label{tableback}
\end{center}
\end{table}
 
 The  event rates from all Standard Model processes expected 
 to contribute to the signal are summarized in table \ref{tableback}. $W$ production 
 yields for both lepton channels the highest expected rate. Whereas in the electron channel
 the observed rate is well compatible with expectation, in the muon channel the observed five 
 events are to be compared with an expectation of $0.8 \pm 0.2$. 
  
 In order to compare the kinematic characteristics of the observed events with those
expected from $W$ - production
 a Monte Carlo simulation of 
$W$ - production was performed with 500 times the statistics used in the data
sample.
%*******************************************************************************
\begin{figure}[bth]
\begin{center}
\includegraphics[width=.9\textwidth]{meyer.4.eps}
\end{center}
\caption[]{Distribution of the H1-events in the $P_T^X$-$M_T^{l \nu}$ plane.
Figure a) shows the electron channel, figure b) the muon channel. The 1-$\sigma$
uncertainties
 on the measured kinematic parameters are indicated by the crosses.
(For event $\mu$5 the $2\sigma$ lower limit is shown for $M_T^{l \nu}$.)
The dominant SM contributions (dots for W production, open circles for $\gamma\gamma$
processes in the $\mu$ channel) are shown for an accumulated luminosity which is a
factor 500 higher than in the data. For the $\mu$ channel no significant contribution
is expected below $P_T^X=25$ GeV due to the event selection criteria.}
\label{ge.fig.h1wprod}
\end{figure}
%*****************************************************************************
Figure \ref{ge.fig.h1wprod} shows for the $e-$ and $\mu-$channel
 the simulated events in the
plane of hadronic transverse momentum $P_T^X$ and transverse mass $M_T^{l \nu}$,
together with the six events under consideration.
 Here
$M_T^{l \nu}$ is calculated from  the transverse momentum of the  charged lepton and a
neutrino, which is assumed to carry the  observed missing transverse momentum $P_T^{miss}$.
For $W$-production  one would expect $P_T^X$
to be low and the $M_T^{l \nu}$ distribution is expected to show  a Jacobian peak around the $W$-mass. The observed $
e^-$ events shows these characteristics.
Also two muon events are in  a region of phase space where $W$- events
are expected. In one of them (MUON-3) an additional positron is observed. Identifying this 
positron with the scattered positron, allows to constrain the kinematics yielding an
invariant muon-neutrino mass of $M = 82 ^{+19}_{-12} GeV$. 
The remaining three muon events (2 $\mu^+$ and $1 \mu^-$)
are unlikely to be explained by  $W$ production  or other SM processes considered.



%\clearpage

\subsection{ZEUS Analysis} 
 
The ZEUS collaboration has performed two analyses (for details see \cite{zeuspap})
using 47.7 $pb^{-1}$ of $e^+p$ data.

  One analysis searches for isolated tracks in events which are unbalanced 
  in transverse momentum.
The selection criteria  are very similar to those applied 
 in the H1 analysis. The main criteria are $P_T^{calo} > 20 $ GeV, an isolated 
 track with $P_T > 10 $ GeV and at least one hadronic jet with $E_T > 5$ GeV. 
  Three events pass the selection criteria, in all of them  the 
high $P_T$ track is identified as an $e^+$.
%Three events are observed in the electron channel
% (all 3 of positive charge) and zero events in the muon channel.
 The  observed  event yield agrees
 with the SM expectations of $3.5 \pm 0.7$  electron events and $2.0 \pm 0.4 $ muon 
 events, to which $W$ production contributes 0.9 and 0.4, respectively.
 
 In the other analysis ZEUS performed a dedicated measurement of the W 
 production cross section. Here no hadronic activity was required but an 
 electron or muon signature was requested in the selection.
 Three events were found in the electron channel (two in common with the first
 analysis) and zero events in the muon channel. 
 Fig. \ref{zeusnc} shows the display of one of the events. The imbalance in transverse 
 momentum is clearly visible.
\begin{figure}[htb]
\begin{center}
\includegraphics[width=.9\textwidth,bb=80 180 650 445]{meyer.5.eps}
\end{center}
\caption[]{Display of a ZEUS electron event. Shown are a longitudinal and a 
transverse view.} 
\label{zeusnc}
\end{figure}
 Table \ref{zeuskinematics} shows selected kinematic parameters of the 3  events.
  \begin{table}
\begin{center}                
 \begin {tabular} {|l|c|c|c|}
 \hline  
 [GeV]& {\bf e1} & {\bf e2} & {\bf e3}  \\ 
 \hline
 &&& \\
  $P_T^l$&$22.1 \pm 1.1$&$37.1 \pm 1.6$ & $48.8 \pm 2.0$
\\ &&& \\

$P_T^X$& $0.4 \pm 0.1$&$18.7 \pm 2.2$ & $19.0 \pm 2.5$\\ &&& \\


 $ P_T^{miss}$ &$21.7 \pm 1.1$&$32.9 \pm 1.4$ & $34.9 \pm 2.4$\\ &&& \\



 $M_T^{l\nu}$ &$43.7 \pm 1.6$&$68.2 \pm 2.2$ & $81.4\pm 3.2$\\
 &&& \\
\hline
\end {tabular}
 \end{center}
\caption[]{Reconstructed event kinematics of the three ZEUS events. Given are the transverse momenta of
the lepton $P_T^l$, the hadronic system $P_T^X$ ,the total event $ P_T^{miss}$ and the transverse lepton-neutrino
mass $M_T^{l\nu}$.}
\label{zeuskinematics}
\end{table}
 In fig.
 \ref{zeus.ptx_mt} the events are compared
with a MC simulation of W production. They are found to be well 
 compatible with expectation.     
\begin{figure}[htb]
\begin{center}
\includegraphics[width=.9\textwidth,bb=80 270 518 542]{meyer.6.eps}
\end{center}
\caption[]{Distribution of the three  $e^+$ events observed
by ZEUS
 in the $P_T^X$- $M_T^{l \nu}$ plane and in the $P_T^{e}$ - $P_T^{miss}$
plane,
compared with a Monte Carlo study of W production with a luminosity
of $ 50 fb^{-1}$. }
\label{zeus.ptx_mt}
\end{figure}
%****************************************************************************** 
The backgound in the event sample, mainly from CC processes, is estimated to be $1.1 \pm 0.3$
 events. Subtracting this background from the observed 3 events yields a cross section of 
 $\sigma(e^+p \rightarrow e^+W^{\pm} X ) = 0.9 ^{+1.0}_{-0.7}(stat) \pm 0.2(syst) $ pb.
 This result agrees well with the SM leading order expectation \cite{ge.pub.wprod} of
0.95 pb.  
 
 Best limits on anomalous couplings were obtained when considering only 
 the phase space region of higher values of $P_T^X$
 and combining the electron and muon channel. For $P_T^X > 20$ GeV
zero events were observed compared to a SM expectation of 1.2 events from $W$ and
$0.52 \pm 0.18$ events from other sources.  From this  an upper limit (95\% C.L.)
on the cross section of  $\sigma (P_T^X > 20 $GeV$) < 0.58 $ pb is derived which translates into  limits of
 \begin{center}
  $ -4.7 < \Delta \kappa < 1.5  \qquad \mbox{for} \quad \lambda = 0$ \\
  $-3.2 < \lambda < 3.2  \qquad   \mbox{for} \quad  \Delta \kappa = 0$
 \end{center}
on the anomalous  $WW\gamma$ couplings ($\Delta \kappa = \kappa -1 , \lambda$).
With the present statistics this result is not yet competitive with the limits
derived at the Tevatron and LEP, but will clearly improve with larger statistics.
 
 \section {Results from $e^-p$ HERA running}
 In the years 1998/1999 HERA was operated with electrons of 27.5 GeV colliding with
 protons of 920 GeV resulting in $\sqrt{s} = 318 $ GeV.  Both experiments 
applied the same analysis procedures 
 as explained above.
 
 ZEUS observed in a luminosity of $16  pb^{-1}$
 two events with isolated tracks, both being identified as 
 electrons ($e^-$). The result is consistent with the expectation of 
 $1.6 \pm 0.4$ events from SM processes, of which $0.8 \pm 0.4$ and $0.8 \pm 0.1$
 are in  the electron and muon channel, respectively. 
 Both events observed show a Neutral Current event
 topology where the missing transverse momentum $P_T^{miss}$ is in one 
 event due to a large energy leakage out of the main calorimeter 
and in the other event due to an energetic 
 muon associated to the hadronic shower.
 
 H1 analysed a data sample corresponding to $14  pb^{-1}$. No event was found
 fullfilling the selection criteria for the search for events with isolated tracks
 and $P_T^{miss}$. The SM expectation is $1.0 \pm 0.2$ events in the 
electron channel and $0.4 \pm 0.1 $ events  in the muon channel. 
 
 The good agreement between observation and SM expectation in both experiments
 implies that within the present statistical accuracy 
 there is no evidence of an excess of events with an isolated  lepton and
 missing $P_T$ in  $e^-p$  scattering at HERA.
  
 \section {Interpretation of the H1-Muon-Events \newline beyond the Standard Model}
 
  Considering the low probability
of the signal observed by H1 in the muon channel
  in $e^+p $ data  to be explained within the SM
it is worthwhile investigating 
  which processes beyond the SM could explain the observed events. 
  \begin{itemize}
  \item The interpretation of a 
lepto-quark produced by positron-quark fusion
   and decaying into a muon-quark system can be discarded because the measured event
  kinematics  is incompatible with a 2-body decay.
  \item In the hypothesis of a resonance decaying into a quark and an onshell  W
which decays leptonically, the escaping
  neutrino can be reconstructed using the W mass constraint. The resulting invariant
  mass of the system formed by the W and the measured hadronic system X is for the 
  events MUON-2 and MUON-4 within measurement errors found to be compatible with the 
  top mass. While the SM expectation for top production at HERA is unmeasurably small,    
  it could be significantly enhanced in dynamical models for fermion mass 
  generation \cite{fritzsch1}.
  \item Another  hypothesis  is the production of squarks in Supersymmetric Models
  with R-parity violation. Stop quark production ($e^+ d \rightarrow \tilde{t} $)
has been discussed by T. Kon et
 al. \cite{kon}. Events of the observed topology could be
  due to a decay $\tilde{t} \rightarrow W \tilde{b}$ with the sbottom quark decaying via 
  $ \tilde{b} \rightarrow d \nu$. This process would naturally produce events with 
  a high  $P_T$  lepton of positive charge, a high $P_T$ hadronic jet and significant 
  missing $P_T$. The kinematics of the muon events is found to be 
   compatible with a 
  scenario with a stop mass of 200 GeV and a sbottom mass of 100 GeV. 
 
  In order to investigate this hypothesis further an analysis has been 
  performed by H1 selecting events with at least two jets and missing transverse 
  momentum. In this class of events one would accept those stop decays in which the
  W decays hadronically. No events in excess of the SM expectation have been 
  observed. From this fact a 95\% upper limit on the expectation in the muon channel 
  of $N_{observed} 
  (W \rightarrow \mu \nu) < 0.36$ events 
  can be derived. This result  does not support the hypothesis that the three
  outstanding muon events could be due to this process.
   \end{itemize}
 \section {Summary and outlook}
  
  At the HERA electron proton collider events have been observed which
  feature a high $P_T$ charged lepton together with a significant imbalance
  in the overall event transverse momentum. Some of the observed events
  can be understood in terms of a production of on-shell $W$ bosons, decaying
  leptonically. This constitutes the first observation of this process in lepton hadron
  scattering. The cross section observed agrees with Standard Model expectations.
 
  In the H1 experiment three events have been observed in the muon channel, which
  are unlikely to be due to $W$ production or other 
  SM processes. The origin of
  these events will most probably only be clarified with much higher luminosities.
  The prospects to accumulate luminosities at least an order of magnitude 
  higher than available now, are very good, since in 2000 the HERA machine is
  undergoing a major luminosity upgrade.
 
 \section {Acknowledgements}
  
  I like to thank the organizers of the Ringberg workshop for providing a
  stimulating atmosphere for a very interesting workshop in a beautiful
  surrounding. 
    
 
%**************************************************************************
\begin{thebibliography}{8.}
\addcontentsline{toc}{section}{References}
\bibitem{1994.h1} H1 Collaboration, T. Ahmed et al. DESY Preprint 94-248 (1994)
\bibitem{ge.pub.h1highptl} H1 Collaboration, C.Adloff et al., Eur. Phys. J. 
 \textbf{C5},575 (1998)
\bibitem{zeuspap} ZEUS Collaboration, J. Breitweg et al, DESY Preprint 99-054 (1999)
\bibitem{ge.pub.wprod} U. Baur, J.A.M.Vermaseren, D.Zeppenfeld,
 Nucl. Phys. \textbf{ B375}, 3 (1992)
\bibitem{spira1} M. Spira, DESY Preprint 99-060 (1999)
\bibitem{ge.pub.h1ccsel} H1 Collaboration, C.Adloff et al., Z. Phys. \textbf {C67},
565 (1995), \\
 Phys. Lett. \textbf {B379}(1996), 319 (1996)
\bibitem {fritzsch1} H. Fritzsch, D. Holtmannsp\"otter, Phys.Lett. \textbf {B457},
186 (1999)
\bibitem{kon} T. Kon et al. Phys. Lett. \textbf{B376}, 227 (1996),\\
              T. Kon et al. Mod. Phys. Lett.  \textbf{A12}, 3143  (1997)


\end{thebibliography}



%\end{document}









