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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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%Submitted to & \multicolumn{3}{r}{\footnotesize Electronic Access: {\it http://www-h1.desy.de/h1/www/publications/conf/conf\_list.html}} \\[.2em] \hline 
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Submitted to & & &
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\multicolumn{4}{l}{{\bf
                International Europhysics
                Conference on High Energy Physics},
                July~12,~2001,~Budapest} \\
 {\bf EPS 2001:} 
                 & Abstract:        & {\bf 804 }    &\\
                 & Session & {\bf 1}   &\\[.7em]
\multicolumn{4}{l}{{\bf
               XX International Symposium on Lepton and Photon Interactions}, 
               July~23,~2001,~Rome} \\ 
{\bf LP 2001:}  
                 & Abstract:        & {\bf 497} &\\
                 & Session & {\bf S08}   &\\ \hline
 & \multicolumn{3}{r}{\footnotesize {\it
    www-h1.desy.de/h1/www/publications/conf/conf\_list.html}} \\[.2em]
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\vspace*{2cm}

\begin{center}
  \Large
  {\bf 
    Radiative Charged Current Interactions at HERA
  }

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

\begin{abstract}

\noindent
A search for processes producing large missing transverse momentum in
conjunction with an energetic, isolated photon in $e^+p$ collisions is
reported. The data were collected at the HERA collider in the years
1994 to 2000, during which $27.5\mGEV$ positron beams were in
collision with $820$ and $920\mGEV$ proton beams. The data were
recorded with the H1 detector, and correspond to an integrated
luminosity of $100.9\,{\rm pb^{-1}}$. The data are presented, within
the context of the Standard Model, as the first measurement of the
cross section for radiative charged current interactions.
\end{abstract}

\end{titlepage}

\pagestyle{plain}

\section{Introduction}
Measurements of the inclusive cross sections for neutral current
($e^{+}p\rightarrow e^{+}X$) and charged current
($e^{+}p\rightarrow \bar{\nu} X$) processes\cite{HighQ2Inc} demonstrate
sensitivity to the partonic structure of the proton and to the
properties of the $\gamma$, $Z^0$ and $W^{\pm}$ propagators.  Charged
current interactions with final states containing an isolated,
energetic photon in addition to significant missing transverse
momentum (``radiative charged current interactions'') are sensitive to
the size of radiative corrections to the inclusive charged current
cross section. In the standard model the rate of such interactions
thus receives a contribution from the $WW\gamma$ triple boson vertex.
An anomalous rate of such interactions could be related to the
``anomalous couplings'', $\Delta \kappa$ and $\lambda$, related to the
magnetic dipole and electric quadrupole moments of the exchange
propagators respectively.  Non-zero values for $\Delta \kappa$
or$\lambda$ would be consistent with physics beyond the standard model
(BSM). Several putative BSM processes, for example the production and
subsequent decay of excited neutrinos, produce ``radiative charged
current'' final states. A failure of the standard model to predict the
rate or properties of such interactions would also call into question
the validity of the radiative corrections applied in the estimation of
the born cross sections for inclusive neutral and charged current
interactions.


This paper summarises the differences between this analysis and that
of the inclusive cross section measurements, and presents the first 
cross section measurement for radiative charged current interactions.

\section{Definition of the Cross Section\label{xsec}}
The events considered in this analysis are a subset of those selected
for the measurement of the inclusive charged current cross
section~\cite{HighQ2Inc}. An important variable is the transverse momentum
$P_T^{miss}$, defined
\begin{equation}
(P^{miss}_T)^2 = \left( \sum_i P_X^i\right)^2 + \left(\sum_i P_Y^i \right)^2
\end{equation}
where the sum is over all $i$ final state particles (excluding
neutrinos). The $x-y$ plane is perpendicular to the $z$ axis defined
by the direction of the proton beam.  A large value of $P^{miss}_T$,
indicating a large missing transverse momentum, is characteristic of
an energetic final state neutrino or antineutrino. The selection of
charged current events in this analysis is identical to that of
~\cite{HighQ2Inc} except that the data are restricted to the range
$P^{miss}_T>25\mGEV$.

Within this sample a search is performed for events containing one or
more isolated photons. Photons are required to have transverse
momentum greater than $3\mGEV$ and
$25^{\circ}<\theta_{\gamma}<145^{\circ}$. An isolation of at least
$0.5$ units in $\eta-\phi$ between the photon and the nearest jet with
$P_T>5\mGEV$ is required. Jets are defined according to the inclusive
$K_T$ algorithm such that all final state particles are included in a
jet.  The cross section is fully corrected for all effects arising
from finite efficiencies and resolutions such that it corresponds to
this kinematic region, summarised in table \ref{table}.

\section{Experimental Procedure}
The $e^{+}p$ data used in this analysis were collected in the years
between 1994 and 2000 and amount to a total integrated luminosity of
$100.9\,{\rm pb^{-1}}$. Data were collected with proton beams of both
$820\mGEV$ and $920\mGEV$. The luminosity weighted average centre of mass 
energy is $\sqrt{s}=313\mGEV$.

In addition to the selection requirements applied in the inclusive
charged current analysis~\cite{HighQ2Inc} and the requirement that
$P^{miss}_T>25\mGEV$, isolated photons are identified using three basic
properties.  First, they will produce compact clusters in the
electromagnetic section of the calorimeter. Second, they will not be
associated with a charged track in the tracking chambers. Third, they
will be isolated from other activity. The selection for isolated
photons requires that all of the following criteria are satisfied.

\begin{itemize} 
\item {\bf $P_T^{\gamma}> 3\mGEV$}. \newline $P_T^{\gamma}$ is the
  transverse momentum of the photon candidate.
\item {\bf $E^{\gamma}_{e.m.}/E^{\gamma}>0.95$}. \newline  
  $E^{\gamma}$ is the energy
  of the photon candidate. $E^{\gamma}_{e.m.}$ is the fraction of this
  energy in the electromagnetic section of the H1 LAr calorimeter. The
  calorimeter design is such that electromagnetic particles will usually
  deposit the majority of their energy in the electromagnetic section, whereas hadronic
  particles will usually deposit energy in both the electromagnetic and 
  hadronic sections.
\item {\bf $-225{\rm cm} < z_{impact} < 150{\rm cm}$}. \newline
  $z_{impact}$ is the 
  $z$ coordinate, defined with respect to the nominal interaction point, 
  of the photon candidate cluster centre of gravity. The event by event
  variation in the interaction vertex makes a cut on $z_{impact}$ preferable
  to a cut on $\theta$. This $z$ range corresponds approximately to the 
  range $25^{\circ}<\theta_{\gamma}<145^{\circ}$ for which the cross section
  is calculated.
\item {\bf $R_{\gamma-clus} > 0.5$ if $P_T^{clus}>0.5\mGEV$} \newline
  $R_{\gamma-clus}$ is  the separation in the $\eta-\phi$ plane between the
  photon candidate and the nearest cluster with transverse momentum
  $P_T^{clus}$ above $0.5\mGEV$.
\item {\bf $R_{\gamma-jet}>0.5$} \newline $R_{\gamma-jet}$ is the
  separation in the $\eta-\phi$ plane between the photon candidate and
  the nearest jet, defined according to the inclusive $K_T$ algorithm.
  This cut and the previous cut distinguish between genuine isolated
  electromagnetic particles from spurious candidates formed by an
  electromagnetic component of a hadronic shower or jet.
\item {\bf $R_{\gamma-track}>0.5$ if $P_T^{track}>0.8\mGEV$ and 
       $r_{CJC}>44\rm cm$. } \newline
  This cut rejects electromagnetic clusters associated with a charged 
  track. Only tracks with starting radii within the inner most central 
  drift chamber are considered as there is a significant probability that
  photons will convert into $e^{+}e^{-}$ pairs in the material between the 
  inner and outer drift chambers. 
\end{itemize}

The efficiency of this isolated photon selection is studied with the
aid of a Monte Carlo simulation of neutral and charged current events
produced by the DJANGO program in conjunction with the H1 simulation
and reconstruction software~\cite{HighQ2Inc}. The efficiency is found
to be between $70\%$ and $90\%$ with no strong variation as a function
of the position or transverse momentum of the photon candidate. The
fraction of events passing these cuts which do not contain an isolated
photon is estimated to be less than $1\%$. This background is found to be 
dominated by neutral current events in which the scattered lepton is
misidentified as a photon.

\section{Results}

A total of 17 events with missing transverse momentum and one or more
isolated photons are observed in the entire data sample, compared to
SM prediction of $16.14{\pm0.27}$, including an estimated background
of $0.16\pm0.03$ events. The properties of these events are summarised
in the distributions shown in figure \ref{plots}. The data are
everywhere in good agreement with the SM prediction.  The cross
section for $e^+p\rightarrow \nu\gamma X$ for $P_T^{miss}>25\mGEV$,
$P_T^{\gamma}>3\mGEV$, $25^{\circ}<\theta^{\gamma}<145^{\circ}$ and
$R_{\gamma-jet}>0.5$ is $\sigma_{data} = 0.208\pm0.066(stat) \pm0.062
(syst) {\rm pb}$ for an average $\sqrt{s}=313\mGEV$. The systematic
error includes all of the sources of uncertainty considered in the
inclusive charged current analysis and additional uncertainties
associated with the isolated photon selection procedure. The SM cross
section is estimated to be $\sigma_{django}=0.192\pm0.032{\rm pb}$
with the DJANGO Monte Carlo, in good agreement with the measurement.
These results are summarised in table \ref{table}. Further details 
of the analysis are described in ~\cite{anna}.

\section{Conclusions}
The first measurement of the cross section for the production of events 
with large missing transverse momentum and an isolated photon is presented.
The cross section for $e^+p\rightarrow \nu\gamma X$ for $P_T^{miss}>25\mGEV$,
$P_T^{\gamma}>3\mGEV$, $25^{\circ}<\theta^{\gamma}<145^{\circ}$ and
$R_{\gamma-jet}>0.5$ is found to be $\sigma_{data} = 0.208\pm0.066(stat)
\pm0.062 (syst) {\rm pb}$, in good agreement with the expectation of
the standard model. 


%
%   References for Contact Interaction paper
%
\begin{thebibliography}{99}

\bibitem{HighQ2Inc}
H1 Collab., C. Adloff et al., Eur. Phys. J. C19 (2001) 269-288 ,   12/00. 
\bibitem{anna} A. Burrage, PhD Thesis, University of Liverpool, 2000.
\end{thebibliography}


%\clearpage
\vspace{3cm}


\begin{table}[htb]
\begin{center}
\begin{tabular}{||c||}\hline
\hline
{\bf Cross Section for Radiative Charged Current}\\
{\small $p_t^{miss}>$25 \mGEV\hspace{0.2cm} $p_t^{\gamma}$$>3\mGEV$ \hspace{0.2cm} 2
5$^o$ $<$ $\theta^{\gamma}$ $<$ 145$^o$}\\ 
{\small $R_{jet - \gamma}$ $>$ 0.5 for $p_t^{jet} >$ $5 \mGEV$}\\
{ $e^+p$ at $\sqrt{s} = 313 \mGEV$} \hspace{1cm}{ H1
preliminary}\\
\hline
\hline
$\sigma_{data}$ =  0.208 $\pm$ 0.066 $\pm$ 0.048 pb\\
$\sigma_{django}$ =  0.192 $\pm$ 0.004 pb\\ 
\hline
\hline
\end{tabular}
\end{center}

\caption{Definition of the kinematic range for the cross section measurement of
radiative charge current events. The combined cross section for the entire
data sample is shown, together with the prediction from the DJANGO Monte Carlo
(see text). The uncertainties quoted for the data are statistical and
systematic in origin respectively. The uncertainty on the Monte Carlo 
prediction is purely statistical.}
\label{table}
\end{table}



\clearpage
%
\begin{figure}[p] 
  \begin{center}
    \epsfig{file=H1prelim-01-054.fig1.eps,width=16cm}
  \end{center}
  \caption{Distributions illustrating the properties (see text) of events with 
    missing transverse momentum and one or more isolated photons. The
    points are the data and the solid black line the standard model
    prediction. The solid red line is the estimated background from
    events which do not contain an isolated photon, which is dominated
    by neutral current processes in which the scattered lepton is
    misidentified as a photon.}
  \label{plots}
\end{figure} 

\end{document}

