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\noindent
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%{\it {\large version of \today}} \\[.3em] 
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\multicolumn{4}{l}{{\bf
                XIIIth International Workshop on Deep Inelastic Scattering, DIS05},
                April,~2005,~Madison} \\
%zz                 & Abstract:        & {\bf xxx,xxx}    &\\
%zz                 & Parallel Session & {\bf x,x}   &\\ 
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    www-h1.desy.de/h1/www/publications/conf/conf\_list.html}} \\[.2em]
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\begin{center}
  \Large
  {\bf 
   	Measurement of the Polarisation Dependence of the Total \boldmath{$e^{-}p$} Charged 
Current Cross Section}

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

\begin{abstract}

\noindent
Data taken with the H1 detector, for longitudinally polarised electrons
in left handed state in collision with
unpolarised protons at HERA, are used to measure the total charged
current cross section for $Q^2>400$\,GeV$^2$ and inelasticity $y<0.9$.
The polarisation dependence of the total charged current cross section
is compared with Standard Model expectations. 
%The data are used to
%obtain an extrapolated total charged current cross section for a fully
%left handed electron beam. This extrapolation is found to be
%consistent with the expectations of the Standard Model.


\noindent
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%\section{Results}

The integrated charged current (CC) cross section of longitudinally 
polarised electrons in collision with protons
is measured in the range $Q^2> 400$\,GeV$^2$ and $y<0.9$. 
The measurement of the cross section
is performed following the same analysis procedure as in~\cite{eplus0304} and
is based on the left handed data set taken recently by the H1 experiment
with an integrated luminosity of
$L = (17.75 \pm 0.21)$\,pb$^{-1}$ 
and an average polarisation of $P_e=(-25.40 \pm 0.44)\,\%$.
The value is:
\begin{eqnarray*}
\label{result}
\sigma_{CC} (P_e=         -0.25) & = & 66.42\,{\rm pb} \pm 2.39\,{\rm pb \,\,(stat)}  \pm 2.99\,{\rm pb \,\,(sys)}
\end{eqnarray*}
where the $1.2\%$ luminosity normalisation uncertainty is included in the
systematic error.
The polarisation uncertainty, which does not directly enter in the cross
section measurement, is shown in Fig.~\ref{fig:xscc}.

The measurement of the unpolarised CC cross section based on the
HERA-I data set with a luminosity of $16.4$~pb$^{-1}$ and
measured in the same phase space region is:
\begin{eqnarray*}
\label{resultunpol}
\sigma_{CC} (P_e=0) & = & 57.03\,{\rm pb} \pm 2.21 \,{\rm (stat)}  \pm 1.38 \,{\rm (sys)}
\end{eqnarray*}
where the systematic error also includes the normalisation uncertainty
of $1.8\%$.

The polarisation dependence of these cross sections is shown in 
Fig.~\ref{fig:xscc} in comparison with the Standard Model expectations
based on the H1 PDF 2000~\cite{h1pdf2000}. Also shown are 
the total cross sections and their polarisation dependence of 
the charged current interactions measured previously in positron-protron 
collisions~\cite{eplus0304}.


\begin{thebibliography}{99}

\bibitem{eplus0304}
H1 Collaboration, Contributed paper no. 756/758 to ICHEP04,
http://www-h1.desy.de/h1/www/publications/htmlsplit/H1prelim-04-141.long.html\,.

\bibitem{h1pdf2000}
H1 Collaboration (C. Adloff et al.), {\it Eur.\ Phys.\ J.} {\bf C30} (2003) 1.
\end{thebibliography}

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\begin{figure}[htb]
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\caption{Distribution of luminosity versus polarisation $P_e$ for data taken in 2005.}
\label{pol}
\end{figure}

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\begin{figure}[htb]
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\caption{
  Distributions of $E_e^{\prime}$ (a), $\theta_e$ (b), $Q^2$ (c) and 
  $P_{T,h}/P_{T,e}$ (d) of the NC data set.}
\label{lhnc}
\end{figure}

\begin{figure}[htb]
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\caption{
  Distributions of $Q^2_h$ (a), $P_{T,h}$ (b), $E_h-p_{z,h}$ (c) and 
  $x_h$ (d) of the CC data set.}
\label{lhcc}
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\caption{\label{fig:xscc}
  The dependence of the $e^+p$ and  $e^-p$ CC cross section with the lepton beam
  polarisation $P_e$ is shown. The data are compared to the prediction
  from the H1 PDF 2000 fit for polarised positrons (dashed line) and for polarised 
  electrons (full line) .
}
\label{xsec}
\end{figure}
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