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\begin{document}

\pagestyle{empty}
\begin{titlepage}

\noindent
\begin{center}
\begin{small}
\begin{tabular}{llrr}
Submitted to & & &
\epsfig{file=/h1/www/images/H1logo_bw_small.epsi
,width=2.cm} \\[.2em] \hline
\multicolumn{4}{l}{{\bf
                XXII International Symposium on Lepton-Photon Interactions at High Energy},
                June~30,~2005,~Uppsala} \\
                 & Abstract:        & {\bf 398}    &\\
                 & Session: & {\bf QCD and hadron structure}   &\\ \hline
 & \multicolumn{3}{r}{\footnotesize {\it
    www-h1.desy.de/h1/www/publications/conf/conf\_list.html}} \\[.2em]
\end{tabular}
\end{small}
\end{center}
\vspace*{2cm}


\begin{center}
  \Large
  {\bf 
      Measurement of the Diffractive Cross Section in \\ 
      Charged Current Interactions at HERA
    }

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

\begin{abstract}

\noindent
A first differential measurement of charged current diffractive
interactions is presented using data taken by the H1 experiment
amounting to an integrated luminosity of 63 ${\rm pb^{-1}}$.  The
process $ep \rightarrow \nu XY$ is studied, where the $Y$ system is a
proton or proton remnant with $M_Y < $1.6 GeV and $|t| < $1.0 ${\rm
  GeV^2}$.  It is separated from the $X$ system by a large gap in
pseudorapidity.  Total and differential cross-sections are extracted
in the kinematic range $Q^2 >$ 200 ${\rm GeV^2}$, $y < 0.9$ and
$x_{I\!\!P} <$ 0.05 and compared to predictions from a model of
diffractive DIS in which the exchanged $W$ boson scatters from
diffractive parton densities extracted from fits to neutral current
data at lower $Q^2$.  The ratio of the diffractive charged current
cross-section to the inclusive charged current cross-section is also
measured.

\end{abstract}

\end{titlepage}

\pagestyle{plain}

\section{Introduction}
\label{intro}

Neutral Current Diffractive Deep-Inelastic Scattering (DDIS) has been
used to investigate the parton dynamics of diffractive exchanges
throughout the accessible kinematic range at {\sc Hera} \cite{eps,
  lowq2, hiq2}.  A LO QCD fit \cite{prn} based on the hard scattering
factorisation theorem for diffraction \cite{collins} has been made to
a subset of these data allowing the extraction of diffractive parton
densities.  In this fit it was necessary to make the assumption of
``Regge factorisation'', whereby the diffractive parton densities do
not change in shape as $\xpom$ and $t$ vary and their change in
normalisation is given by a parameterisation based on Reggeon flux
factors.  Both a leading `pomeron' contribution and a sub-leading
`reggeon' component are included in the fit, with different flux
factors and separately evolving parton densities.

A new measurement is presented here using $W$ bosons to probe the
structure of the diffractive exchange and to test the assumed parton
dynamics.  The process $ep \rightarrow \nu XY$ is studied, where the
presence of the diffractive exchange implies a large gap in rapidity
between the two hadronic final state systems.  Figure \ref{FIG:CCDDIS}
shows the diagram for the charged current DDIS process.

\begin{figure}[htbp]
\centering
\epsfig{file=H1prelim-04-115.fig1.eps,width=0.65\linewidth,clip=}
\caption{
  A schematic illustration of the charged current DDIS process at {\sc
    Hera}, $ep \rightarrow \nu XY$.  The positron couples to a virtual
  $W$ boson of virtuality $Q^2$ which interacts with the proton via a
  colour-singlet exchange, producing two distinct final state systems,
  $X$ and $Y$.  These two systems are separated by a large gap in
  rapidity if their masses are small compared with that of the full
  hadronic final state ($W$).}
\label{FIG:CCDDIS}
\end{figure}

Here, the standard charged current DIS variable definitions are used,
namely

\begin{equation}
Q^2=-q^2 \ ; \qquad y=\frac{P.q}{P.k} \ ; \qquad x=\frac{-q^2}{2P.q} \ ,
\end{equation}
determined by the four-momenta of the $W$ boson ($q$), the proton
($P$) and the incoming positron ($k$).  The additional diffractive
variables are defined as
\begin{equation}
\xpom=\frac{q.(P-p_Y)}{q.P} \ ; \qquad \beta=\frac{-q^2}{2q.(P-p_Y)} \ ; \qquad t=(P-p_Y)^2 \ ,
\end{equation}

where $p_Y$ is the four-momentum of the $Y$ system. Here, $\xpom$
corresponds to the fraction of the proton beam energy transferred to
the longitudinal momentum of the diffractive exchange, $\beta$ is the
fraction of the exchanged longitudinal momentum carried by the quark
coupling to the virtual $W$ boson and $t$ is the squared 4-momentum
transferred at the proton vertex.

In the analysis presented here, neither $t$, nor the mass $M_Y$ are
well measured as the $Y$ system is not detected. The measured
cross-section is corrected to the region
\begin{equation}
M_Y < 1.6\; \GeV  \ ; \qquad |t| < 1.0\; \GeVsq \ .
\label{eqn:myandt}
\end{equation}

The preliminary results presented here are based on high $Q^2$ data
collected with the H1 detector \cite{h1det} in $e^+p$ interactions at
$\sqrt{s}=(k+P) = 319 \;\GeV$ at {\sc Hera} in 1999 and 2000. The data
correspond to an integrated luminosity of $63\; \invpb$. Together with
the neutral current analyses \cite{eps, lowq2, hiq2} they complete the
H1 coverage of DDIS measurements for the first running period of the
{\sc Hera} machine.  These charged current data provide a test of the
factorisation schemes and other assumptions which have worked so well
for the neutral current data.  In particular, the charged current data
are sensitive to particular quark flavours from the diffractive parton
densities extracted from the analysis of the neutral current DDIS data
and thus have the potential to test the flavour decomposition of the
pomeron and the reggeon.


\section{Experimental Method}

\subsection{Selection Criteria and Kinematic Reconstruction}

The data used for the analysis are a subset of the high $Q^2$
inclusive charged current DIS sample studied in \cite{inchiq2}.
Charged current events are selected by requiring a missing transverse
momentum $P_T^{miss} > 12\; {\rm GeV}$.  The diffractive selection
requires a large gap in the pseudorapidity distribution of the final
state hadrons in the outgoing proton direction, signalling a colour
singlet exchange between the $W$ boson and the proton to produce two
well separated systems $X$ (contained in the main detector) and $Y$
(escaping unobserved into the beampipe).  The selection is based on an
absence of activity in the components of the H1 detector which are
sensitive to energy flow in the proton fragmentation region
\cite{eps}.

The reconstruction of the final state system $X$ uses an algorithm
which optimally combines tracking and calorimetric information without
double counting \cite{fixed}.  The mass of the $X$ system is
reconstructed as

\begin{equation}
M_X^2=(E^2 - p_x^2 - p_y^2 - p_z^2)_{h} \ .
\label{eqn:mxreccorr}
\end{equation}

Here, $(E, p_x, p_y, p_z)_{h}$ is the 4-vector of the overall
hadronic final state observed in the detector.  The inclusive DIS
kinematic variables are obtained from

\begin{equation}
y = \frac{E_h - p_{z,h}}{2E_e} \ ; \qquad Q^2 = \frac{P_{T,h}^2}{1-y} \ ; \qquad x = \frac{Q^2}{sy} \ ,
\label{eqn:defaultkinerec}
\end{equation}

where $E_h - p_{z,h}$ is the difference between the energy and the
longitudinal momentum of the $X$ system, $E_e$ is the positron beam
energy and $P_{T,h}$ is the transverse momentum of the $X$ system.

The diffractive kinematic variables are then reconstructed as

\begin{equation}
\beta = \frac{Q^2}{Q^2 + M_X^2} \ ; \qquad \xpom = \frac{x}{\beta} \ .
\label{eqn:diffkinerec}
\end{equation}

\subsection{Corrections to the Data}

The RAPGAP \cite{rapgap} Monte Carlo generator is used to describe the
DDIS process $ep \rightarrow \nu Xp$.  It is used to correct the data
for the effects of the detector acceptance and kinematic migrations
due to the finite detector resolution and imperfections in the
reconstruction.  RAPGAP uses diffractive parton densities extracted
from a leading order QCD fit, similar to that described in
section~\ref{intro}, but performed on earlier H1 data \cite{incl}. The
parton densities are convoluted with QCD matrix elements up to order
$\alpha_s$.  Further QCD radiation is simulated via an interface to
the ARIADNE \cite{ariadne} program, which is an implementation of the
Colour Dipole Model \cite{cdm,ariadne}.  As required by the data
\cite{incl}, a sub-leading exchange is also included, with parton
densities obtained from a parameterisation for the $\pi$-meson
\cite{pipdf}.  QED radiation is simulated via an interface to the
HERACLES \cite{heracl} program.

A factor $1.08 \pm 0.10$ is required to correct the data to the
measured range $\my < 1.6 \ {\rm GeV}$ and $|t| < 1 \ {\rm GeV^2}$.
This factor was evaluated using the DIFFVM \cite{diffvm} generator,
which simulates diffractive events both with intact final state
protons and with proton dissociation.
%equation \ref{eqn:myandt}.
Migrations into the measured range from very large $\xpom > 0.15$ or
large $\my > 5 \ {\rm GeV}$ values are estimated using the DJANGO
\cite{django} generator of non-diffractive charged current DIS. This
program is an interface between the HERACLES $ep$ event generator and
the ARIADNE program.

Corrections are made for several small background contributions to the
data.  The contamination from hard diffractive photoproduction
processes, in which mismeasurements lead to large fake missing
transverse momentum, is estimated using the RAPGAP program.  High
$Q^2$ neutral current background, entering the sample due to similar
mismeasurements, is estimated using DJANGO.  EPVEC \cite{epvec} is
used to simulate background from real heavy gauge boson ($W^{\pm},
Z^0$) production.  Comparisons of the full simulation with the
uncorrected data for several kinematic distributions can be seen in
figure \ref{FIG:contplots}.  The simulation gives a good description
of the data for all variables.

\subsection{Extraction of the Cross-Section}

The cross-section is corrected for the effects of background processes
and detector acceptance and migrations.  The effects of QED radiation
are ignored, which is reasonable given the statistical precision of
the data.  The acceptance, purity and stability\footnote{The purity
  (stability) of a bin is defined as the fraction of events
  reconstructed (generated) in a bin that were also generated
  (reconstructed) in that bin, according to the simulation.}  for each
quoted bin is required to be greater than 20 \% and is on average
greater than 50 \%.

A full analysis of the systematic uncertainties of the measurement was
performed.  The sources of systematic uncertainty associated with the
reconstruction of the final state hadrons are discussed in
\cite{inchiq2}. Those uncertainties particular to the diffractive
measurement are described in \cite{eps}.  The dominant systematic
uncertainties arise from the corrections for smearing about the $\my$
boundary of the measurement and the correction for smearing into the
sample from very large $\xpom$ as described using the DJANGO model.
The systematic error on the final cross-sections is approximately 20\%
on average and is small in comparison to the average statistical error
of approximately 45\%.

\section{Results}

\subsection{The Total Cross-Section and Ratio to the Inclusive}
\label{totsec}

The total charged current DDIS cross-section, measured for $Q^2 >
200\; {\rm GeV^2}, y < 0.9$ and $\xpom < 0.05$, is

\begin{equation}
\sigma_{CC}^{diff} = 0.42 \pm 0.13 \;(stat.) \pm 0.09 \;(sys.) \;{\rm pb}
\end{equation}

This measurement agrees very well with the prediction based on the
``H1 2002 fit'' to neutral current DDIS data as implemented in RAPGAP
of $\sigma_{CC}^{diff} = 0.43 \pm 0.01 \;(stat.)\;  {\rm pb}$.

The ratio of the diffractive charged current cross-section, measured
in the kinematic range above, to the inclusive charged current
cross-section $\sigma_{CC}^{inc}$, measured in the corresponding
kinematic range $Q^2 > 200 \;{\rm GeV^2}, y < 0.9$ and $x_{Bj} <
0.05$, is

\begin{equation}
\frac{\sigma_{CC}^{diff}}{\sigma_{CC}^{inc}} = 2.5 \pm 0.8 \;(stat.) \pm 0.6 \;(sys.)\; \%
\end{equation}


\subsection{The Differential Diffractive Charged Current Cross-Section}
\label{diffsec}

In figure \ref{fig1}, the diffractive charged current cross-section is
shown differentially in $\xpom$.  It is compared to the LO prediction
from the ``H1 2002 fit'' to neutral current DDIS data \cite{prn}.  The
sub-leading reggeon or ``meson'' contribution is also shown as a
dashed line and is large, as expected, in the highest $\xpom$ bin.
Within the the current limited statistical precision, the predictions
are consistent with the data

Figures \ref{fig2} and \ref{fig3} show the diffractive charged current
cross-section differentially in $Q^2$ and $\beta$, respectively.  The
prediciton of the fit is shown again with the contribution from the
meson.  Both differential cross-sections are described well by the
prediction.

\section{Conclusions}

A new measurement of charged current DDIS has been presented in the
kinematic range $Q^2 > 200\; {\rm GeV^2}, y < 0.9$ and $\xpom < 0.05$.
The results have been compared with predictions from a fit to lower
$Q^2$ neutral current DDIS data in which the partons are evolved to
higher $Q^2$ using the DGLAP equations.  Both the total diffractive
charged current cross-section and the $\xpom$, $Q^2$ and $\beta$
dependencies are well described by the predictions.


%
%   References
%
\begin{thebibliography}{99}

\bibitem{h1det} H1 Collaboration, I. Abt et al.,
Nucl. Instr. Meth. A386 (1997) 310 and 348.

\bibitem{eps} H1 Collaboration, \emph{Measurement of the Diffractive
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\bibitem{lowq2} H1 Collaboration, \emph{Measurement of the Diffractive
    Deep-Inelastic Scattering Cross Section at Low $Q^2$}, paper 981
  submitted to ICHEP2002, Amsterdam, Holland, July 2002.
  
\bibitem{hiq2} H1 Collaboration, \emph{Measurement of the Inclusive
    Cross Section for Diffractive Deep Inelastic Scattering at High $Q^2$},
  paper 090 submitted to EPS2003, Aachen, Germany, July 2003.
  
\bibitem{prn} H1 Collaboration,
\emph{Measurement and NLO DGLAP QCD Interpretation of Diffractive 
Deep-Inelastic Scattering at HERA}, paper 980 submitted to 
ICHEP2002, Amsterdam, Holland, July 2002.

\bibitem{collins} J. Collins,
Phys. Rev. D57 (1998) 3051 and erratum-ibid. D61 (2000) 019902.

\bibitem{inchiq2} H1 Collaboration, C. Adloff et al., Accepted by Eur.
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\bibitem{incl} H1 Collaboration, C. Adloff et al.,
Z. Phys. C76 (1997) 613.

\bibitem{fixed} H1 Collaboration, C. Adloff et al.,
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\bibitem{rapgap} H. Jung,
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\bibitem{heracl} A. Kwiatkowski, H. Speisberger, H. M$\ddot{\rm{o}}$hring,
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\bibitem{diffvm} B. List, A. Mastroberardino,
\emph{DIFFVM: A Monte Carlo Generator for diffractive processes in ep scattering}, in A. Doyle, G. Grindhammer, G. Ingelman, H. Jung (eds.): \emph{Monte Carlo Generators for HERA Physics}, DESY-PROC-1999-02 (1999) 396.

\bibitem{django} G. Schuler, H. Spiesberger, Proc. of the Workshop on Physics at HERA, Vol. 3, eds. W. Buchm$\ddot{\rm{u}}$ller, G. Ingelman, Hamburg, DESY (1992) 1419.

\bibitem{epvec}
U.~Baur, J.~A.~Vermaseren and D.~Zeppenfeld,
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Nucl.\ Phys.\ B {\bf 375} (1992) 3.
%%CITATION = NUPHA,B375,3;%%

\end{thebibliography}

\newpage

% plots 


\begin{figure}
\centering
\epsfig{file=H1prelim-04-115.fig2a.eps,width=0.49\linewidth}
\epsfig{file=H1prelim-04-115.fig2b.eps,width=0.49\linewidth}
\epsfig{file=H1prelim-04-115.fig2c.eps,width=0.49\linewidth}
\epsfig{file=H1prelim-04-115.fig2d.eps,width=0.49\linewidth}
\epsfig{file=H1prelim-04-115.fig2e.eps,width=0.49\linewidth}
\epsfig{file=H1prelim-04-115.fig2f.eps,width=0.49\linewidth}
\caption{
  Distributions of the uncorrected data are compared with the
  predictions of the RAPGAP CC DDIS simulation (dashed line), the
  total background simulation (dotted line) and the sum of both (solid
  line).}
\label{FIG:contplots}
\end{figure}


\begin{figure}
\centering
\epsfig{file=H1prelim-04-115.fig3.eps,width=1.0\linewidth}
\caption{
  The diffractive charged current cross-section differential in
  $\xpom$ plotted as a function of $\log(\xpom)$, compared with the
  prediction from the ``H1 2002 fit'' to neutral current DDIS data.
  Also shown is the sub-leading reggeon or ``meson'' contribution
  (dashed line).  }
\label{fig1}
\end{figure}

\begin{figure}
  \centering \epsfig{file=H1prelim-04-115.fig4.eps,width=1.0\linewidth}
\caption{
  The diffractive charged current cross-section differential in $Q^2$
  plotted as a function of $\log(Q^2)$, compared with the prediction
  from the ``H1 2002 fit'' to neutral current DDIS data.  Also shown
  is the sub-leading reggeon or ``meson'' contribution (dashed line).
  }
\label{fig2}
\end{figure}

\begin{figure}
\centering
\epsfig{file=H1prelim-04-115.fig5.eps,width=1.0\linewidth}
\caption{
  The diffractive charged current cross-section differential in
  $\beta$ plotted as a function of $\beta$, compared with the
  prediction from the ``H1 2002 fit'' to neutral current DDIS data.
  Also shown is the sub-leading reggeon or ``meson'' contribution
  (dashed line).  }
\label{fig3}
\end{figure}


\end{document}



