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\begin{document}

\pagestyle{empty}
\begin{titlepage}

\noindent
% {\bf H-UM \& JS: version of \today} \\[.3em] 
Submitted to the 30th International Conference on 
High-Energy Physics ICHEP2000, \\ 
Osaka, Japan, July 2000


\vspace*{3cm}

\begin{center}
  \Large
  {\bf  W production in ep collisions at HERA}

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

\begin{abstract}
\noindent
A search for $W$ boson production in the process $ep \to eW X$, with
subsequent $W$ decay into electrons or muons, has been performed at
the electron-proton collider HERA using an integrated luminosity of
13.6 pb$^{-1}$ in $e^-p$ scattering and 81.6 pb$^{-1}$ in $e^+p$
scattering. The analysis has been tuned to maximise the acceptance of
$W$ boson production, and reject other Standard Model processes. In
$e^-p$ interactions no events are observed, consistent with the
expectation of the Standard Model in this low luminosity sample. In
the $e^+p$ data 14 events are seen in the electron and muon channel
compared to an expectation of 8.2 $\pm$ 2.0 dominated by W production
(6.4 $\pm$ 1.9). The excess above the expectation is mainly due to
events with transverse momentum of the hadronic system greater than 25
GeV where 9 events are found compared to 2.3 $\pm$ 0.6 expected. Four of
these events are observed in the latest data sample, presented for the
first time here.

\end{abstract}

\vfill
\begin{flushleft}
  {\bf Abstract: 974 } \\
  {\bf Parallel session: 11, 3} \\
  {\bf Plenary talk: 11, 7~b} 
\end{flushleft}

\end{titlepage}

\pagestyle{plain}

\section{Introduction}
\label{sec:intro}

The HERA collaborations have previously reported \cite{isol,wzeus} the
observation of events with high $P_T$ isolated leptons and missing
transverse momentum in $e^{+}p$ collisions during the period 1994-7.
A further search for such events in $e^{-}p$ collisions during the
period 1998-9 is reported in \cite{isonew}.  Such events can be
interpreted as leptonic $W$ decay. In the $e^{+}p$ data sample H1 has
reported \cite{isol} one $e^-$ event and 5 $\mu^{\pm}$ events compared
to expectations from the Standard Model of 2.4$\pm$0.5 and 0.8$\pm$0.2
for the $e^{\pm}$ and $\mu^{\pm}$ decay channels respectively, which
are dominated by $W$ production. For the same data taking period ZEUS
has reported \cite{wzeus} 3 (0) $e^{+}$ ($\mu^{\pm}$) events compared
to an expectation of 2.1 (0.8) $W$ events and $1.1\pm0.3$
($0.7\pm0.2$) background events for the $e^{\pm}$ ($\mu^{\pm}$) decay
channel.

An extended analysis, developed to preferentially select W decays, has
also been presented in \cite{wstanf}. In this paper we present the
results of a similar search for $W$ production using the 36.5
pb$^{-1}$ of $e^+p$ data (1994-7), the 13.6 pb$^{-1}$ of $e^-p$ data
(1998-9) and the most recent 45.0 pb$^{-1}$ of $e^+p$ data
(1999-2000). The analysis has been further developed to maximise the
acceptance of $W$ boson production in the processes $e^{\pm}p\to
e^{\pm}WX$, $W\to e \nu$ or $W\to \mu \nu$.

This paper is organised as follows. Section \ref{sec:monte} describes
the Standard Model processes that contribute to the signal and to the
background.  Section \ref{sec:exper} describes the H1 detector and
experimental conditions. Section \ref{sec:lephad} outlines the lepton
identification criteria and the hadronic reconstruction methods. The
selection requirements and the results for the electron\footnote{In
  this paper ``electron'' refers generically to both electrons and
  positrons.  Where distinction is required the terms $e^-$ and $e^+$
  are used.}  and muon decay channels are described in sections
\ref{sec:lepsel} and \ref{sec:results}. Section \ref{sec:kinem}
discusses the kinematics of the selected events.  The paper is
summarised in section \ref{sec:summary}. A comparison between the
H1 and ZEUS analyses is made in appendix~\ref{sec:zeuscomp}.

\section{Standard Model Processes} 
\label{sec:monte}


In this section the processes within the Standard Model that are
expected to contribute to signal and background are outlined.  These
processes are described in detail in \cite{isol}.

\begin{itemize}
\item {$W$ production}
  
  The generator EPVEC \cite{epvec}, which uses leading order QCD
  calculations, was used to estimate the Standard Model expectation
  for $W$ production. The total W production cross section amounts to
  1.1 pb for electron-proton cms energy $\sqrt{s}=300$ GeV and 1.3 pb
  for $\sqrt{s}=318$ GeV. Final state parton showers are simulated
  using the PYTHIA framework \cite{epvecmcw}. An error of 30\% is
  quoted for this cross section calculation.  This is due mainly to
  uncertainties in the photon parton density functions and the scale
  at which the calculation is performed.

\item {Charged Current (CC) processes : $ep\to\nu X$}
  
  A CC DIS event can mimic the topology of leptonic $W$ decay events
  if a particle in the hadronic final state is misinterpreted as a
  candidate lepton from $W$ decay.  The generator DJANGO \cite{django}
  was used to calculate this contribution. Studies of CC events where
  a candidate electron, passing loose selection requirements, is found
  show that events of this kind are described by the expectation
  within a systematic error of 30\% (see section~\ref{sec:lephad}).

\item {Neutral Current (NC) processes : $ep\to eX$} 
  
  The scattered electron in a NC DIS event can be misinterpreted as
  the lepton from $W$ decay, but the missing transverse momentum can
  only be produced by fluctuations in the shower or detector response
  to the final state particles, or by limited geometrical acceptance.
  The generator DJANGO \cite{django} was used to calculate this
  contribution. The generator PYTHIA \cite{pythia} was used to
  calculate the QCD photoproduction process $\gamma p\to X$.
  Production of heavy flavours is included in DJANGO and PYTHIA.
  \cite{aroma}. Studies of NC events with reconstructed missing
  transverse momentum show that events of this kind are described by
  the expectation within a systematic error of 30\% (see
  section~\ref{sec:lephad}).

  
\item {Lepton pair production in two photon ($\gamma\gamma$)
    interactions}
 
  Inelastic lepton pair production can mimic the topology of $W$
  events if one lepton escapes detection, and measurement error causes
  apparent missing momentum. The generator LPAIR \cite{lpair} was used
  to calculate this contribution. Studies of events with two
  identified leptons show that events of this kind are described by
  the expectation within a systematic error of 75\%.


\end{itemize}

In order to determine acceptances and background contributions for the
selected events, the detector response to events produced by the above
programs is simulated in detail using a program based on
GEANT~\cite{GEANT}. The simulated events are then subjected to the
same reconstruction and analysis chain as the real data.

\section{Experimental Conditions} 
\label{sec:exper}

A detailed description of the H1 detector can be found in
\cite{h1det}. Only those components of particular importance to this
analysis are described here.


The inner tracking system consisting of central and
forward\footnote{The forward direction and the positive $z$-axis are
  taken to be that of the proton beam direction.} tracking detectors
consisting of drift chambers are used to measure the charged particle
trajectories and to determine the interaction vertex.  A magnetic
field of 1.15 Tesla allows the measurement of the particle transverse
momenta.

Electromagnetic and hadronic final state particles are absorbed in a
highly segmented calorimeter \cite{calo}, which is 5 to 8 interaction
lengths deep depending on the polar angle of the particle.

The calorimeter is surrounded by a superconducting coil and an iron
yoke instrumented with streamer tubes. Tracks of penetrating charged
particles, such as muons, which escape the calorimeter are
reconstructed from their hit pattern in the streamer tubes with an
efficiency of greater than $90\%$.

In the forward region of the detector two sets of three drift chamber
layers (the forward muon system) detect muons. Also in the forward
direction, around the beam-pipe, is the plug calorimeter which
measures hadronic showers.

The LAr calorimeter is the main trigger for high transverse energy
events. The trigger efficiency is $\approx 98\%$ for events with an
electron which has transverse momentum above 10 GeV. For events with
high missing transverse momentum, determined from an imbalance in
energy measured in the calorimeter, $P^{calo}_{T}$, the efficiency is
$98\%$ when $P^{calo}_{T}>25$~GeV and is $50\%$ when $P^{calo}_{T} =
12 $~GeV \cite{eplus}.

\section{Lepton identification and Hadronic Reconstruction}
\label{sec:lephad}

An electron candidate is defined by the presence of a compact and
isolated electromagnetic cluster of energy in the LAr calorimeter,
associated with a track having a distance of closest approach to the
cluster of less than 12 cm. Electrons found in regions between
calorimeter modules containing large amounts of inactive material are
excluded \cite{eplus}. The energy of the electron candidate is
measured from the calorimeter cluster.

Muons are identified by requiring tracks in the instrumented iron, the
forward muon system, the inner tracking system or any combination.
Muon candidates formed from inner tracks alone must be associated with
a pattern typical of a minimum ionising particle in the LAr
calorimeter. All candidates with a inner track link are required to
have transverse momentum $>1$ GeV and candidates formed solely by a
track in the instrumented iron are rejected for $\theta<25^\circ$.

A stronger muon identification is required to select muon candidates
from $W$ decay. If the muon candidate is not associated with a forward
muon track it must have an inner track link and either a track segment
or an energy deposit in the instrumented iron. The energy of the muon
candidate is measured from the curvature of the track in the inner
tracking system.

The hadronic final state is measured by combining calorimeter energy
deposits with low momentum tracks as described in \cite{eplus}. The
calibration of the final hadronic energy scale is made by comparing
the transverse momentum of the precisely measured positron to that of
the hadronic final state in a large NC event sample. The ratio of
these two measurements is used to correct the hadronic energy
measurement as a function of the hadronic polar angle.

\section{Selection of Electron and Muon {\boldmath $W$} Decays}
\label{sec:lepsel}

Multiple cut requirements must be imposed to remove the large
background arising from NC, CC, $\gamma p$ and $\gamma\gamma$
interactions, whilst maintaining a good acceptance of W decay events.
These are listed in tables \ref{cutsa} and \ref{cutsb} and are defined
in terms of the quantities described below.

\begin{itemize}
\item $P^{calo}_{T}$, the missing transverse momentum measured in the
  calorimeter.
\item $P^{miss}_{T}$, the total missing transverse momentum 
  reconstructed from calorimeters and track detectors.
\item $P^l_T$, the transverse momentum of an identified muon or electron.
\item $P^X_T$, the transverse momentum of the hadronic system, defined
as all reconstructed particles apart from identified isolated leptons.
\item $\theta_l$, the polar angle of the muon or electron, where
  $\theta_l=0^o$ is defined as the direction of the incoming proton
  beam.
\item $\delta_{miss}=2E_{e}-\sum E_i(1-\cos \theta_i)$, where $E_i$
  and $\theta_i$ denote the energy and polar angle of each detected
  particle in the event and $E_e$ is the electron beam energy. For an
  event where only longitudinal momentum in the proton direction is
  undetected $\delta_{miss}=0$.
\item $\Delta \phi_{l-X}$, the difference in azimuthal angle between
  the lepton and the vector that balances the vector of the hadronic
  final state $X$. NC events typically have low values of $\Delta
  \phi_{l-X}$.
\item $V_{ap}/V_{p}$, a measure of the isotropy of the event.  It is
  defined as the ratio of the anti-parallel to parallel components of
  the measured calorimetric transverse momentum, with respect to the
  direction of the missing transverse momentum~\cite{eplus}.  Events
  with one or more particles, that do not deposit much energy in the
  calorimeter ($\mu$, $\nu$), generally have low values of
  $V_{ap}/V_{p}$.
\item ${\zeta}^{2}_{l}=4 E^{l}E_e \cos^2 \theta_l/2$, where $E^l$ is
  the energy of the final state lepton. For NC events, where the
  scattered electron is misinterpreted as a decay lepton from the $W$,
  ${\zeta}^{2}_{l}$ is equal to the four momentum transfer squared
  $Q^2$. Since the NC cross section falls steeply with $Q^2$, these
  events generally have small values of ${\zeta}^{2}_{l}$. Conversely,
  leptons from $W$ decay generally have high values of ${\zeta}^{2}_{l}$.
\item $E_{cone}$, the energy contained within a cone of radius 1 in
  $\eta$-$\phi$ space around the electron, that is not associated to
  the electron.
\end{itemize}

The isolation of high-$P_{T}$ tracks with respect to other tracks in
the event or with respect to jets, is quantified using:
\begin{itemize}
\item their distance $D_{jet}$ to the closest hadronic jet in the
  pseudorapidity-azimuth plane ($\eta$ - $\phi$), defined by
  $D_{jet}=\sqrt{(\Delta\eta_{track-jet})^{2}
    +(\Delta\phi_{track-jet})^{2}}$ (for this purpose jets are
  reconstructed using an inclusive $k_T$ algorithm \cite{kt1,kt2} with
  $R<1$ and $E^{min}_{T}=5$~GeV). If there is no jet in the event,
  $D_{jet}$ is defined with respect to the polar and azimuthal angle
  of the hadronic final state $X$.
\item their distance $D_{track}$ to the closest track in $\eta$ -
  $\phi$, defined in an analogous way to $D_{jet}$, where all tracks
  with a polar angle greater than $5^{o}$ are considered.
\end{itemize}

The dominant background source in the electron decay channel arises
from NC events which have significant $P_{T}^{calo}$ due to
fluctuations in the measurement of the final state particles. To
reduce this background, events with NC topology (isotropic and with
the lepton and hadronic system diametrically opposite in the
transverse (azimuthal) plane) are rejected. For low values of
$P_{T}^{calo}$, where the NC background is largest, the requirement on
$\zeta^{2}_l$ is tightened. A further requirement that the lepton
candidate be isolated from the hadronic final state is imposed to
reject CC events.  Events which have in addition to the isolated
electron one or more isolated muons are not considered in the electron
channel, but may contribute in the muon channel.

The dominant backgrounds in the muon channel are due to the inelastic
two photon process $ep\to e\mu^+\mu^-X$ and photoproduction events
which contain a muon. The final sample is selected by rejecting
isotropic events and events where more than one muon is observed.
Elastic lepton pair production is suppressed by rejecting events which
have low track multiplicities and where the muon is found to be
opposite in azimuth to the hadron system.

To verify that the backgrounds that contribute to the two channels are
well understood, event samples are defined according to less stringent
criteria. For the electron channel these criteria are those shown in
table \ref{cutsa}, but requiring $\zeta^2>500$ GeV$^2$ and the
$\frac{V_{ap}}{V_p}$ cut from table \ref{cutsb}. For the muon channel
these criteria are also those shown in table \ref{cutsa}, lowering the
$P_T^{\mu}$ threshold to 5 GeV, dropping the $P_T^{miss}$ requirement,
but also requiring the $\frac{V_{ap}}{V_p}<$ cut from table
\ref{cutsb}. Only events with at least one isolated muon satisfying
the stronger selection requiremants (see section \ref{sec:lepsel}) are
allowed in the muon sample. The events thus selected in the $e^+p$
data sample are shown in figure \ref{fig:econ} for the electron decay
channel and figure \ref{fig:mcon} for the muon decay channel.  Also
included in the figures are the Standard Model expectation and the
expectation from $W$ production alone. The electron channel is
dominated by NC events and the muon channel is dominated by the two
photon process $\gamma\gamma\to\mu^+\mu^-$. All quantities that are
used for the final selection cuts are found to be well described in
both shape and normalisation by the Standard Model expectation.
Similar agreement between the data and simulation is obtained for the
$e^-p$ data sample.

Further studies of individual background processes have also been
performed. On example is a subset of the muon sample described above,
defined by requiring at least two isolated muons, at least one of
which satisfies the stronger selection requirements. This sample is
shown in figure \ref{fig:studies}(a,b). The expectation is dominated
by the two photon process $\gamma\gamma\to\mu^+\mu^-$. The data sample
is shown to be well described in both shape and normalisation by the
Standard Model expectation.


A second sample was selected from CC events\cite{eplus}, with the additional
requirement that the electron finder (see section \ref{sec:lephad})
found a candidate electron. This sample is shown in figure
\ref{fig:studies}(c,d). The expectation is dominated by radiative CC
events or CC events where a final state particle fakes an electron
cluster. The data sample is shown to be well described in both shape
and normalisation by the Standard Model expectation.

Following the selection criteria described above, the efficiencies as a
function of $P_T^X$ are shown in table \ref{acc}. These efficiencies
were calculated using the EPVEC generator for $W$ production.  The
overall efficiency to select $W \to e \nu$ events is $44\%$ and to
select $W \to \mu \nu$ events is $15\%$. The difference in efficiency
between the two channels is due to the cut on $P_{T}^{calo}$ which
acts as a cut on $P_{T}^{X}$ because the muon deposits little energy
in the calorimeter. There is thus little efficiency in the muon decay
channel for $P_{T}^{X}<12$~GeV. For values of $P_{T}^{X}>12$~GeV the
efficiencies of the two decay channels are comparable.

\begin{table}[t]
\begin{center}
\begin{tabular}{|c||c|} \hline
 Variable  & Requirement\\ \hline
\hline                                                   
$P_T^l$ & $ >$ 10 GeV\\
\hline
$\theta_l$ & $5^o<\theta_l<145^o$\\
\hline
$P_T^{Calo}$ & $>$ 12 GeV\\
\hline
$D_{jet}$ & $>$ 1.0\\
\hline
$P_T^{miss}$ & $>$ 12 GeV\\
\hline
\end{tabular}
\end{center}
\caption{Selection requirements common to both decay channels}
\label{cutsa}
\end{table}

\begin{table}[h]
\begin{center}
\begin{tabular}{|c||c|c|} \hline
 Variable  & Electron  & Muon \\ \hline
\hline
$\zeta^2$ & $>500$ GeV$^2$ & - \\
          & $>5000$ GeV$^2$ for $P_T^{Calo} <$ 25 GeV & -\\
\hline
$\frac{V_{ap}}{V_p}$ & $<$ 0.5 ($<$ 0.15 for $P_T^e <$ 25 GeV) & $<$ 0.4 ($<$ 0.15 for $P_T^{Calo} <$ 25 GeV)\\
\hline
$D_{track}$ & $>$ 0.5 for $\theta_e \ge 45^o$ &  $>$ 0.5 \\
            & $>$ 0.5 for $\frac{E_{cone}}{E^l}>$ 0.05 &  \\
\hline                                                   
$P_T^X$ &  -  &$>$ 12 GeV\\ 
\hline
$\Delta\phi_{e-X}$ & $>$ 20$^o$ & $>$ 10$^o$ for $\le$ 2 central tracks\\
\hline
\# isolated $\mu$ & 0 & 1\\
\hline
$\delta_{miss}$ & $ >$ 5 GeV $^+$ & - \\
\hline
\end{tabular}
\begin{flushright}
  $^+$ if only one $e$ candidate is detected, which has the same charge as the beam
  lepton.
\end{flushright}
\end{center}
\caption{Selection requirements specific to each decay channel}
\label{cutsb}
\end{table}



\section{Results}
\label{sec:results}

For the $e^-p$ data sample no events are observed in either the
electron or muon channels. This compares to the Standard Model
expectations of 1.46 $\pm$ 0.30 events in the electron channel and 0.32
$\pm$ 0.09 in the muon channel.


In the $e^+p$ data sample after all selection requirements 6 candidate
events are observed in the $W \to e\nu$ channel compared to 4.72 $\pm$
1.42 expected from $W$ production and 1.43 $\pm$ 0.35 from background
sources.

One of the candidate events in the electron decay channel is observed
to contain an $e^-$. This event was first reported and discussed in
\cite{isol}.  Three of the other candidate events contain an $e^+$.
The charges of the electrons in the remaining two events are
unmeasured since the electrons are produced at low polar angles and
they shower in material in the tracking detectors.

For the $e^+p$ data sample in the $W \to \mu\nu$ channel 8 candidate
events are observed compared to 1.65 $\pm$ 0.50 expected from $W$
production and 0.37 $\pm$ 0.20 from other Standard Model sources.
Five of the muon events observed in the $e^+p$ data sample are those
first reported and discussed in \cite{isol}. Five of the events have
positively charged muon, 2 have negative muons and one is not
determined.



\section{Event kinematics}
\label{sec:kinem}

Distributions of the selected events in lepton polar angle,
acoplanarity, transverse mass and $P_T^X$ are shown in figure
\ref{fig:emfinal}. The figure shows the electron and muon decay
channels combined. Also included is the expectation of the Standard
Model. The events are generally found at low values of lepton polar
angle and evenly distributed in acoplanarity in agreement with the
expectation. The reduction in the expectation at low and high
acoplanarity is due to the selection cuts.  The events are distributed
in a Jacobian peak associated to the nominal W mass, as expected from
W production. At $P_T^X <$ 25 GeV there is good agreement between the
expectation and the observed events. At higher values of $P_T^X$ the
data lie above the expectation.

The scattered positron is tagged in three of the events, allowing the
lepton-neutrino mass to be reconstructed, under the assumption that
there is only one neutrino in the final state and there is no initial
state QED radiation. All three events yield masses that are consistent
with the $W$ mass, having values of $82^{+19}_{-12}$, $71^{+10}_{-11}$
and $77^{+22}_{-15}$ GeV. 

The transverse mass and the transverse momentum of the hadronic system
of the selected events are compared to W production in
figure~\ref{fig:ptxmlnu}. Four muon events and three electron events
have high $P_T^X$, atypical of Standard Model W production.  Among
those, three muon events have been observed in the 1994-7 data and
discussed in~\cite{isol}. The kinematics of the new events with
$P_T^X>25$~GeV are detailed in table~\ref{evkin}.  Event displays of
the tagged W candidate in the electron channel and of the new high
$P_T^X$ muon event are presented in figures \ref{fig:edisplay} and
\ref{fig:mudisplay}.

The significance of missing transverse momentum and acoplanarity has
been studied with data using a sample of NC events having similar
transverse momentum and lepton polar angle to the $W$ candidates
selected. The transverse momentum is reconstructed using the
calorimetric deposit for comparison with the electron events and using
the electron track momentum for comparison with the muon candidates.
The deviations from zero in the $P_T^{miss}$ and acoplanarity plane
for NC events quantify the experimental smearing. The distribution of
this sample is presented in figure~\ref{fig:dphi_ptmis}. This study
clearly shows that the observed acoplanarities and missing momenta in
the W candidates are inconsistent with a measurement error and
confirms the existence of a non-detected particle in those events.


Details of the dependence of the event rate for the $e^+p$ data sample
as a function of the transverse momentum of the hadronic final state,
$P_{T}^{X}$, are given in table \ref{etab1} and \ref{mtab1} for the
electron and muon channels. The combined results for the electron and
muon decay channels are given in table \ref{emtab}.  At
$P_{T}^{X}<25$~GeV 5 $W$ candidates are seen in agreement with the
expectation from the Standard Model.  At $P_{T}^{X}>25$ GeV 9 events
are seen 6 of which are seen at $P_{T}^{X}>40$ GeV where the expection
for Standard Model $W$ production is very low.



\section{Summary}
\label{sec:summary}


A search for $W$ production events ($ep\to eWX$, $W\to l \nu$) has
been performed on an $e^+p$ data sample corresponding to an integrated
luminosity of 81.6 pb$^{-1}$ and on an $e^-p$ data sample
corresponding to an integrated luminosity of 13.6 pb$^{-1}$.  The
selection has been optimised to increase the acceptance of $W$
production events and it extends to lower values of hadronic
transverse momentum $P_{T}^{X}$ than have been previously published.

No events are observed in the $e^-p$ data, consistent with the
expectations of 1.46 $\pm$ 0.30 and 0.32 $\pm$ 0.09 for the electron
and muon decay channels respectively in this low luminosity data
sample.  Fourteen events are found in the $e^+p$ data sample which are
kinematically consistent with $W$ production, 6 in the electron decay
channel and 8 in the muon decay channel.  One electron event and 5 of
the muon events were first reported and discussed in \cite{isol}.  The
expected rates from the Standard Model are 6.14 $\pm$ 1.46 and 2.01
$\pm$ 0.54 for the electron and muon decay channels respectively in
the $e^+p$ data sample. 

The rate of $W$ production in both decay channels is consistent with
the expected rate at low values of $P_T^X$. At $P_T^X>$ 25 GeV,
however, the 9 observed events exceed the Standard Model prediction of
2.26 $\pm$ 0.57.

\section*{Acknowledgements}

We are grateful to the HERA machine group whose outstanding efforts
have made and continue to make this experiment possible.  We thank the
engineers and technicians for their work in constructing and now
maintaining the H1 detector, our funding agencies for financial
support, the DESY technical staff for continual assistance, and the
DESY directorate for the hospitality which they extend to the non DESY
members of the collaboration.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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HERA'', paper \# 157s submitted to EPS99 Tampere. 
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HERA'', prepared for th 9th International Symposium on Lepton and Photon Interactions at High Energies, Stanford, USA, August 1999.
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U.Baur, J.A.M. Vermaseren, D.Zeppenfeld,  \Journal{\NPB}{375}{1992}{3}. 
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DJANGO 6.2; G.A. Schuler and H. Spiesberger, Proc. of the Workshop Physics at 
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Vol. 3 p.1419.
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T. Sj\"ostrand, Comput. Phys. Commun. {\bf 82} (1994) 74.
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S. Baranov et al., Proc. of the Workshop Physics at HERA, W. Buchm\"uller and 
G. Ingelman (Editors), (October 1991, DESY-Hamburg) Vol. 3 p.1478; 
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\bibitem{GEANT} R. Brun et al., GEANT3 User's Guide,
  CERN-DD/EE-84-1 (1987).  
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 H1 Collab., I. Abt et al., \Journal{\NIMA}{386}{1997}{310} and {348}.
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H1 Calorimeter Group, B. Andrieu et al., \Journal{\NIMA}{336}{1993}{460}.
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\end{thebibliography}

\newpage
\begin{table}[ht]
\begin{center}
\begin{tabular}{|c||c|c|} \hline
 & \multicolumn{2}{c|}{Efficiency}\\ \hline
  & $e$ & $\mu$\\ \hline
\hline
$P_T^X>0$~GeV  & 0.44 & 0.15 \\ \hline
$P_T^X>12$~GeV & 0.40 & 0.39 \\ \hline
$P_T^X>25$~GeV & 0.39 & 0.49 \\ \hline
$P_T^X>40$~GeV & 0.39 & 0.53 \\ \hline
\end{tabular}
\end{center}
\caption{Efficiencies of the final selection for $W$ decay in the electron and 
muon channels as a function of $P_T^X$. These efficiencies were calculated 
with the EPVEC generator.}
\label{acc}
\end{table}

\begin{table}[htbp]
\begin{center}
\begin{tabular}{|c||c|c|c|c| }
\hline
Event      & R248207  & R252020 & R268338  &  R266336      \\
           & E32134   & E30485  & E70014   &  E4126        \\
           & $e^+$    & $e^+$   & $e^+$    &  $\mu^+$      \\ \hline
 $P_T^{l}$ / GeV    & $32\pm1$  & $25\pm2$ & $28\pm1$   &   $21\pm3$    \\
 $P_T^{calo}$ / GeV & $42\pm4$  & $39\pm4$ & $57\pm5$   &   $53\pm3 $   \\
 $P_T^{X}$ / GeV    & $41\pm3$  & $43\pm4$ & $39\pm4$   &   $50\pm3 $   \\
 $P_T^{miss}$ / GeV & $43\pm5$  & $42\pm4$ & $57\pm5$   &   $66\pm7 $   \\
 $M^T_{l\nu}$ / GeV & $63\pm4$  & $51\pm4$ & $76\pm5$   &   $72\pm8 $   \\
 $M_{l \nu}$ / GeV    &           & $77^{+21}_{-14}$&     &               \\ 
\hline
\end{tabular}
\caption{ New events at high $P_T^X>25$ GeV. }
\label{evkin}
\end{center}
\end{table}

\begin{table}[htbp]
\begin{center}
\begin{tabular}{|c||c|c||c|c|} \hline
          Electron & H1 Preliminary Data & SM expectation & $W$ & Other SM processes\\ \hline
\hline  
 $P_{T}^{X}>0$~GeV  & 6 & 6.14 $\pm$ 1.46  & 4.72 $\pm$ 1.42  & 1.43 $\pm$ 0.35 \\
\hline  
 $P_{T}^{X}>12$~GeV & 4 & 2.06 $\pm$ 0.51  & 1.65 $\pm$ 0.50  & 0.41 $\pm$ 0.14  \\
\hline
 $P_{T}^{X}>25$~GeV & 3 & 1.05 $\pm$ 0.27  & 0.83 $\pm$ 0.25  & 0.23 $\pm$ 0.10  \\
\hline
 $P_{T}^{X}>40$~GeV & 2 & 0.33 $\pm$ 0.10  & 0.31 $\pm$ 0.09  & 0.01 $\pm$ 0.01  \\
\hline
\end{tabular}
\end{center}
\caption{Observed and predicted event rates in the electron decay channel for all $e^+p$ data.}
\label{etab1}        
\begin{center}
\begin{tabular}{|c||c|c||c|c|} \hline
              Muon & H1 Preliminary Data & SM expectation & $W$ & Other SM processes\\ \hline
\hline  
 $P_{T}^{X}>12$~GeV & 8 & 2.01 $\pm$ 0.54  & 1.65 $\pm$ 0.50  & 0.37 $\pm$ 0.20  \\
\hline
 $P_{T}^{X}>25$~GeV & 6 & 1.21 $\pm$ 0.32  & 1.01 $\pm$ 0.30  & 0.20 $\pm$ 0.10  \\
\hline
 $P_{T}^{X}>40$~GeV & 4 & 0.46 $\pm$ 0.13  & 0.43 $\pm$ 0.13  & 0.04 $\pm$ 0.03  \\
\hline
\end{tabular}
\end{center}
\caption{Observed and predicted event rates in the muon decay channel for all $e^+p$ data.}
\label{mtab1}        
\end{table}

\begin{table}[ht]
\begin{center}
\begin{tabular}{|c||c|c||c|c|} \hline

       Electron and Muon & H1 Prelim. Data & SM expectation & $W$ & Other SM processes\\ \hline
\hline  
 $P_{T}^{X}>0$~GeV  & 14 & 8.16 $\pm$ 1.97  & 6.36 $\pm$ 1.91 & 1.80 $\pm$ 0.46 \\
\hline  
 $P_{T}^{X}>12$~GeV & 12 & 4.07 $\pm$ 1.03  & 3.30 $\pm$ 0.99  & 0.77 $\pm$ 0.27  \\
\hline
 $P_{T}^{X}>25$~GeV & 9  & 2.26 $\pm$ 0.57  & 1.83 $\pm$ 0.55  & 0.43 $\pm$ 0.15  \\
\hline
 $P_{T}^{X}>40$~GeV & 6  & 0.79 $\pm$ 0.22  & 0.74 $\pm$ 0.22  & 0.05 $\pm$ 0.03  \\
\hline
\end{tabular}
\end{center}
\caption{Observed and predicted event rates in the electron and muon decay channels combined for all $e^+p$ data. Only the electron channel contributes for
$P_{T}^{X}<12$ GeV}
\label{emtab}        
\end{table}


\begin{figure}[ht]
\setlength{\unitlength}{1cm}
\begin{picture}(12.0,7.0)
\put(0.,0.0)
{\epsfig{file=/x02/usr/malden/plots/94_00/econ_9400_ptcal.eps,width=7.0cm}}
\put(8.0,0.0)
{\epsfig{file=/x02/usr/malden/plots/94_00/econ_9400_ptx.eps,width=7.0cm}}
\end{picture}
\begin{picture}(12.0,7.0)
\put(0.,0.0)
{\epsfig{file=/x02/usr/malden/plots/94_00/econ_9400_acop.eps,width=7.0cm}}
\put(8.0,0.0)
{\epsfig{file=/x02/usr/malden/plots/94_00/econ_9400_dtrack.eps,width=7.0cm}}
\end{picture}
\begin{picture}(12.0,7.0)
\put(0.,0.0)
{\epsfig{file=/x02/usr/malden/plots/94_00/econ_9400_q2e.eps,width=7.0cm}}
\put(8.0,0.0)
{\epsfig{file=/x02/usr/malden/plots/94_00/econ_9400_dmiss.eps,width=7.0cm}}
\end{picture}
\caption{A comparison of the $e^+p$ data selected with the loose requirements 
  in the electron decay channel compared to the combined Standard
  Model expectation (open histogram). The total error on the Standard
  Model expectation is given by the shaded band. The $W$ production
  component of the Standard Model expectation is given by the shaded
  histogram.}
\label{fig:econ} 
\end{figure}

\begin{figure}[ht]
\setlength{\unitlength}{1cm}
\begin{picture}(12.0,7.0)
\put(0.,0.0)
{\epsfig{file=/x02/usr/malden/plots/94_00/mcon_9400_thmu.eps,width=7.0cm}}
\put(8.0,0.0)
{\epsfig{file=/x02/usr/malden/plots/94_00/mcon_9400_ptmu.eps,width=7.0cm}}
\end{picture}
\begin{picture}(12.0,7.0)
\put(0.,0.0)
{\epsfig{file=/x02/usr/malden/plots/94_00/mcon_9400_acop.eps,width=7.0cm}}
\put(8.0,0.0)
{\epsfig{file=/x02/usr/malden/plots/94_00/mcon_9400_ptmiss.eps,width=7.0cm}}
\end{picture}
\begin{picture}(12.0,7.0)
\put(0.,0.0)
{\epsfig{file=/x02/usr/malden/plots/94_00/mcon_9400_ptcal.eps,width=7.0cm}}
\put(8.0,0.0)
{\epsfig{file=/x02/usr/malden/plots/94_00/mcon_9400_ptx.eps,width=7.0cm}}
\end{picture}
\caption{A comparison of the $e^+p$ data selected with the loose requirements in the muon decay channel compared to the combined Standard Model expectation (open histogram). The total
  error on the Standard Model expectation is given by the shaded band.
  The $W$ production component of the Standard Model expectation is
  given by the shaded histogram.}
\label{fig:mcon} 
\end{figure}

\begin{figure}[ht]
\setlength{\unitlength}{1cm}
\begin{picture}(12.0,7.0)
\put(0.,0.0)
{\epsfig{file=/x02/usr/malden/plots/94_00/mcon_lpair_9400_thmu.eps,width=7.0cm}}
\put(8.0,0.0)
{\epsfig{file=/x02/usr/malden/plots/94_00/mcon_lpair_9400_ptx.eps,width=7.0cm}}
\large
\put(5.5,5.0){(a)}
\put(13.0,5.0){(b)}
\end{picture}
\begin{picture}(12.0,7.0)
\put(0.,0.0)
{\epsfig{file=/x02/usr/malden/plots/94_00/cc_study_pte.eps,width=7.0cm}}
\put(8.0,0.0)
{\epsfig{file=/x02/usr/malden/plots/94_00/cc_study_theta.eps,width=7.0cm}}
\large
\put(5.5,5.0){(c)}
\put(13.0,5.0){(d)}
\end{picture}
\caption{Comparison of a $\gamma\gamma\to\mu^+\mu^-$ sample ((a) and (b)) and a charged current ( + candidate electron) sample ((c) and (d)) with the Standard Model expectation. The error on the Standard Model expectation is given by the shaded band.} 
\label{fig:studies} 
\end{figure}

\begin{figure}[ht]
  \setlength{\unitlength}{1cm}
\begin{picture}(12.0,7.0)
\put(0.,0.0)
{\epsfig{file=/x02/usr/malden/plots/94_00/emharsh_9400_theta.eps,width=7.0cm}}
\put(8.0,0.0)
{\epsfig{file=/x02/usr/malden/plots/94_00/emharsh_9400_acop.eps,width=7.0cm}}
\end{picture}
\begin{picture}(12.0,7.0)
\put(0.,0.0)
{\epsfig{file=/x02/usr/malden/plots/94_00/emharsh_9400_mt.eps,width=7.0cm}}
\put(8.0,0.0)
{\epsfig{file=/x02/usr/malden/plots/94_00/emharsh_9400_ptx.eps,width=7.0cm}}
\end{picture}
\caption{A comparison of the final $e^+p$ data selection in the electron and muon decay channels combined compared to the combined Standard Model expectation (open histogram).  The total error on the Standard Model expectation is given by the shaded band. The $W$
  production component of the Standard Model expectation is given by
  the shaded histogram.}
\label{fig:emfinal} 
\end{figure}

\begin{figure}[ht]
\setlength{\unitlength}{1cm}
  {\epsfig{file=/x02/usr/malden/plots/94_00/2D_ptx_MT.eps,width=18.0cm}}    
  \caption{A comparison of the final data sample in each decay channel, showing the distribution in $P_T^X$ and $M_T^{l\nu}$. The smaller dots represent the distribution of Standard Model W Monte Carlo events with a luminosity 500 times that of the data sample.}
\label{fig:ptxmlnu} 
\end{figure}

\begin{figure}[ht]
\setlength{\unitlength}{1cm}
{\epsfig{file=/x02/usr/malden/plots/94_00/2D_acop_ptmiss.eps,width=18.0cm}}    
  \caption{A comparison of the final data sample in each decay channel, showing the distribution in $\Delta\phi_{l-X}$ and $P_T^{miss}$. The dots represent the distribution of  NC data events.}
\label{fig:dphi_ptmis} 
\end{figure}

\begin{center}
  \begin{figure}[ht]
    \setlength{\unitlength}{1cm}
    \begin{picture}(12.0,10.0)
      \put(2.0,0.0)
      {\epsfig{file=/x02/usr/malden/plots/94_00/R252020.E30485.ps,bbllx=10pt,bblly=85pt,bburx=585pt,bbury=770pt,width=10.0cm,angle=90}}    
    \end{picture}
    \caption{Event display of the tagged $W$ candidiate in the electron channel}
    \label{fig:edisplay} 
  \end{figure}
  
  \begin{figure}[ht]
    \setlength{\unitlength}{1cm}
    \begin{picture}(12.0,10.0)
      \put(2.0,0.0)
      {\epsfig{file=/x02/usr/malden/plots/94_00/R266336.E4126.ps,bbllx=10pt,bblly=85pt,bburx=585pt,bbury=770pt,width=10.0cm,angle=90}}    
    \end{picture}
    \caption{Event display of the new high $P_T^X$ muon event}
    \label{fig:mudisplay} 
  \end{figure}
\end{center}
\begin{appendix}
\section{Comparison with ZEUS}
\label{sec:zeuscomp}
ZEUS have also performed a search for events with missing transverse
momentum and an isolated high $P_T$ lepton \cite{wzeus}. No excess of
events above the Standard Model expectation at high $P_T^X$ was
observed. Recently ZEUS have performed a search for $P_T^X>$ 25 GeV
with additional cuts to enhance the $W$ component of the selected
events \cite{zeusosaka}. The ZEUS selection is very similar to that of
H1 (described in section \ref{sec:lepsel}) apart from the angular
range, which is smaller in the ZEUS analysis. To facilitate comparison
between the two experiments, H1 have repeated their analysis, with the
additional requirement that 0.3$<\theta_{lepton}<$2.0 radians, which
is approximately the ZEUS angular range. The results are shown in
table \ref{h1zeus}. All events for $P_T^X>$ 25 GeV that are found
with the standard analysis are also found with the restricted angular
range. The Standard Model expectation is reduced by 20-25\%.


\begin{table}[ht]
\begin{center}
\begin{tabular}{|c||c|c|c|c|} \hline
              Electron & H1 Preliminary Data & SM expectation & $W$ & Other SM processes\\ \hline
\hline
 $P_{T}^{X}>25$~GeV & 3 & 0.84 $\pm$ 0.22  & 0.67 $\pm$ 0.20  & 0.16 $\pm$ 0.09  \\
\hline
 $P_{T}^{X}>40$~GeV & 2 & 0.27 $\pm$ 0.08  & 0.26 $\pm$ 0.08  & 0.01 $\pm$ 0.01  \\
\hline
\end{tabular}
\begin{tabular}{|c||c|c|c|c|} \hline
              Muon & H1 Preliminary Data & SM expectation & $W$ & Other SM processes\\ \hline
\hline
 $P_{T}^{X}>25$~GeV & 6 & 0.94 $\pm$ 0.26  & 0.78 $\pm$ 0.23  & 0.16 $\pm$ 0.10  \\
\hline
 $P_{T}^{X}>40$~GeV & 4 & 0.35 $\pm$ 0.10  & 0.33 $\pm$ 0.10  & 0.02 $\pm$ 0.01  \\
\hline
\end{tabular}
\end{center}
\caption{Observed and predicted event rates in the electron and muon decay channel for all $e^+p$ data, with the angular range restricted to 0.3$<\theta_{lepton}<$2.0 radians.}
\label{h1zeus}        
\end{table}
\end{appendix}
\end{document}
