%================================================================
% LaTeX file with preferred layout for the contributed papers to
% the ICHEP Conference 98 in Vancouver
% process with:  latex hep98.tex
%                dvips -D600 hep98
%================================================================
\RequirePackage{lineno}
\documentclass[12pt]{article}
\usepackage{epsfig}
\usepackage{amsmath}
\usepackage{hhline}
\usepackage{amssymb}
\usepackage{times}
\usepackage{color}

\renewcommand{\topfraction}{1.0}
\renewcommand{\bottomfraction}{1.0}
\renewcommand{\textfraction}{0.0}
\newlength{\dinwidth}
\newlength{\dinmargin}
\setlength{\dinwidth}{21.0cm}
\textheight23.5cm \textwidth16.0cm
\setlength{\dinmargin}{\dinwidth}
\setlength{\unitlength}{1mm}
\addtolength{\dinmargin}{-\textwidth}
\setlength{\dinmargin}{0.5\dinmargin}
\oddsidemargin -1.0in
\addtolength{\oddsidemargin}{\dinmargin}
\setlength{\evensidemargin}{\oddsidemargin}
\setlength{\marginparwidth}{0.9\dinmargin}
\marginparsep 8pt \marginparpush 5pt
\topmargin -42pt
\headheight 12pt
\headsep 30pt \footskip 24pt
\parskip 3mm plus 2mm minus 2mm
\setlength{\parindent}{0.0cm} 
\newcommand{\picob}{\mbox{{\rm ~pb}}}
\newcommand{\QQ}  {\mbox{${Q^2}$}}

%===============================title page=============================

% Some useful tex commands
%
\def\GeV{\hbox{$\;\hbox{\rm GeV}$}}
\def\MeV{\hbox{$\;\hbox{\rm MeV}$}}
\def\TeV{\hbox{$\;\hbox{\rm TeV}$}}

\newcommand{\pb}{\rm pb}
\newcommand{\cm}{\rm cm}
\newcommand{\hdick}{\noalign{\hrule height1.4pt}}

\begin{document}
%%%%\linenumbers
\pagestyle{empty}
\begin{titlepage}

\noindent
\begin{center}
%{\it {\large version of \today}} \\[.3em] 
\begin{small}
\begin{tabular}{llrr}
%Submitted to & \multicolumn{3}{r}{\footnotesize Electronic Access: {\it http://www-h1.desy.de/h1/www/publications/conf/conf\_list.html}} \\[.2em] \hline 
%Submitted to & \multicolumn{3}{r}{\footnotesize {\it www-h1.desy.de/h1/www/publications/conf/conf\_list.html}} \\[.2em] \hline 
Submitted to & & &
% \epsfig{file=/h1/www/images/H1logo_bw_small.epsi,width=2.cm} \\[.2em] \hline
\epsfig{file=H1logo_bw_small.epsi,width=2.cm} \\[.2em] \hline
% \multicolumn{4}{l}{{\bf
%                 33rd International Conference on High Energy Physics, ICHEP06},
%                 July.~26-Aug.2,~2006,~Moscow} \\
%                  & Abstract:        & {\bf }    &\\
%                  & Parallel Session & {\bf Electroweak}   &\\ \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 
   Charged current interactions in $ep$ scattering at HERA with longitudinally 
   polarised lepton beams}

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

\begin{abstract}

\noindent
Data taken with $e^{\pm}$ beams of different longitudinal polarisation
states in collision with unpolarised protons at HERA are used to
measure the total cross sections of the charged current process,
$e^{\pm} p\rightarrow \nu X$, for negative four-momentum transfer
squared $Q^2 > 400\,{\rm GeV}^2$ and inelasticity $y<0.9$. Together
with the corresponding cross section obtained from the previously
published unpolarised data, the polarisation dependence of the charged
current cross section is measured and found to be in agreement with
the Standard Model prediction. The data are also used to measure the
single and double differential reduced cross sections $d\sigma/dQ^2$
and $\tilde{\sigma}(x,Q^2)$ using the complete HERA-II data set. 

\noindent
\end{abstract}


\end{titlepage}

\pagestyle{plain}

\section{Introduction}
%
%The $ep$ collider HERA has been running in the second phase (HERA-II) 
%since autumn 2003 with a longitudinally polarised positron or electron beam.
%The first $e^+p$ data collected by the H1 and ZEUS experiments have been
%published recently~\cite{h105,zeus06}.
%The $e^-p$ data are being taken and part of the data has been analysed with 
%the preliminary results reported~\cite{h1dis06}.

Measurements of deep
inelastic scattering (DIS) with polarised leptons on protons allow the
parton distribution functions (PDFs) of the proton to be further
constrained through polarisation asymmetries~\cite{klein} and specific
tests of the electroweak (EW) parts of the Standard Model to be
performed~\cite{ewpaper,ewheraproc}.  In particular, the measurements
presented here extend the tests of the ${\rm V}-{\rm A}$ structure of
charged current interactions from low $Q^2$~\cite{charm} into the high
$Q^2$ regime, where $Q^2$ is the negative four-momentum transfer
squared.

At HERA DIS proceeding via charged currents (CC), \mbox{$ep\rightarrow \nu X$},
and neutral currents (NC), \mbox{$ep \rightarrow eX$}, can be measured 
accurately~\cite{h1lowq2,h1hiq2,h1lowestq2,h1pdf2009}. 
The polarisation dependence of the CC and NC cross sections is
fixed within the Standard Model framework. Specifically, the Standard
Model predicts, from the absence of right handed charged currents, that the
CC $e^-p$ cross section is directly proportional to the fraction of left
handed electrons in the beam.

In this paper measurements of the charged current cross sections,
$\sigma^{\rm tot}_{\rm CC}$, $d\sigma/dQ^2$ and the reduced double
differential cross section $\tilde{\sigma}(x,Q^2)$ are reported for
two values of longitudinal polarisation, $P_e=(N_R-N_L)/(N_R+N_L)$,
with $N_R$ ($N_L$) being the number of right (left) handed leptons in
the beam. The corresponding data sets are termed the $R$ and $L$ data
sets respectively. The corresponding luminosity and longitudinal
lepton beam polarisation is given in Tab.~\ref{lumi} below.
\begin{table}[h]
  \begin{center}
    \begin{tabular}{|r|c|c|}
\hline
 & $R$ & $L$\\
\hline
$e^-p$ & $\mathcal{L}=45.9$~pb$^{-1}$ & $\mathcal{L}=103.2$~pb$^{-1}$ \\
       & $P_e=(+36.9\pm 2.3)\%$ & $P_e=(-26.1\pm 1.0)\%$ \\
\hline
$e^+p$ & $\mathcal{L}=98.1$~pb$^{-1}$ & $\mathcal{L}=81.9$~pb$^{-1}$ \\
       & $P_e=(+32.5\pm 1.2)\%$ & $P_e=(-37.6\pm 1.4)\%$ \\
\hline
\end{tabular}
\caption{
Table of integrated luminosities, $\mathcal{L}$, and luminosity weighted
longitudinal polarisation, $P_e$ for the data sets presented here.}
\label{lumi}
\end{center}
\end{table}


\section{Charged Current Cross Section}
%
The measured double differential CC cross section for collisions of polarised 
electrons with unpolarised protons, corrected for QED radiative
effects, may be expressed as
%
%\vspace{-6mm}
\begin{equation}
\frac{{\rm d}^2\sigma^{\pm}_{\rm CC}}{{\rm d}x {\rm d}\QQ} = (1-P_e)
 \frac{G_F^2}{4\pi x } \left[\frac{M_W^2}{M_W^2+Q^2} \right]^2
\left(Y_+W^{\pm}_2-Y_ \mp xW^{\pm}_3 -y^2W^{\pm}_L \right ) \cdot (1+\delta^{\rm CC}_{\rm weak})\,,
\label{Scc}
\end{equation}
where $x$ is the Bjorken $x$ variable and $y$ characterises the
inelasticity of the interaction. The Fermi constant $G_F$ is
defined~\cite{hector} using the weak boson masses.  Other quantities
in Eq.(\ref{Scc}) include $M_W$, the mass of the $W$ boson,
$W^{\pm}_2$, $xW^{\pm}_3$ and $W^{\pm}_L$, CC structure functions for
$e^{\pm}p$ scattering, and $\delta^{\rm CC}_{\rm weak}$, the weak
radiative corrections.  The helicity dependences of the weak
interaction are contained in $Y_\pm=1\pm(1-y)^2$. In the quark parton
model (QPM), where $W^{\pm}_L\equiv 0$, the structure functions
$W^{\pm}_2$ and $xW^{\pm}_3$ may be expressed as the
sum and difference of the quark and anti-quark momentum distributions,
$xq(x,Q^2)$ and $x\overline{q}(x,Q^2)$:
\begin{eqnarray}
W^-_2  &=& x(u+c+\overline{d}+\overline{s})\,, W^+_2  = x(\overline{u}+\overline{c}+ d + s )\,,\\
xW^-_3 &=& x(u+c-\overline{d}-\overline{s})\,, xW^+_3 = x(d + s - \overline{u} - \overline{c}) 
\end{eqnarray}
The total cross section, $\sigma^{\rm tot}_{\rm CC}$, is defined as
the integrated cross section in the kinematic region $Q^2>400\,{\rm
GeV}^2$ and $y<0.9$.  From Eq.(\ref{Scc}) it can be seen that the
cross section has a linear dependence on the polarisation of the
electron beam $P_e$. For a fully right handed electron beam, $P_e=1$,
or a fully left handed positron beam the cross section is identically
zero in the Standard Model.

\section{Experimental Technique}
 
At HERA transverse polarisation of the lepton beam arises naturally
through synchrotron radiation via the Sokolov-Ternov
effect~\cite{spin}. In $2000$ a pair of spin rotators was installed in
the beamline on either side of the H1 detector, allowing transversely
polarised leptons to be rotated into longitudinally polarised states and
back again. The degree of polarisation is constant around the HERA
ring and is continuously measured using two independent polarimeters
LPOL~\cite{lpol} and TPOL~\cite{tpol}.  The polarimeters are situated
in beamline sections in which the beam leptons have longitudinal and
transverse polarisations respectively.  Both measurements rely on an
asymmetry in the energy spectrum of left and right handed circularly
polarised photons undergoing Compton scattering with the lepton
beam. The TPOL measurement uses in addition a spatial asymmetry. The
LPOL polarimeter measurements are used when available and TPOL
measurements otherwise. The polarisation profile weighted by the luminosity 
values is shown in Fig.~\ref{profile_pol}.

The H1 detector components most relevant to this analysis are the
liquid argon (LAr) calorimeter, which measures the positions and
energies of charged and neutral particles over the polar\footnote{The
polar angle $\theta$ is defined with respect to the positive $z$
axis, the direction of the incident proton beam.} angular range
$4^\circ<\theta<154^\circ$, and the inner tracking detectors, which
measure the angles and momenta of charged particles over the range
$7^\circ<\theta<165^\circ$. A full description of the detector can be
found in~\cite{h1det}.

Simulated DIS events are used in order to determine acceptance corrections.
DIS processes are generated using the DJANGO~\cite{django} Monte Carlo (MC)
simulation program, which is based on LEPTO~\cite{lepto} for 
the hard interaction and HERACLES~\cite{heracles} for single photon
emission and virtual EW corrections.
LEPTO combines ${\cal O}(\alpha_s)$ matrix elements with higher order QCD
effects using the colour dipole model as implemented in ARIADNE~\cite{cdm}.
The JETSET program~\cite{jetset} is used to simulate 
the hadronisation process.  
In the event generation the DIS cross section is calculated using the 
H1 PDF $2009$~\cite{h1pdf2009} parametrisation for the proton PDFs.

The dominant $ep$ background contribution arises from photoproduction
processes. These are simulated using the PYTHIA~\cite{pythia} MC with
leading order PDFs for the proton taken from CTEQ~\cite{cteq5}
and for the photon from GRV~\cite{ggrv}. Further backgrounds from NC
DIS, QED-Compton scattering, lepton pair production, prompt photon
production and heavy gauge boson ($W^{\pm},Z^0$) production are also
simulated; their final contribution to the analysis sample is small. Further
details are given in~\cite{h1hiq2}.

The detector response to events produced by the generation
programs is simulated in detail using a program based on
GEANT~\cite{GEANT}. These simulated events are then subjected to the
same reconstruction and analysis chain as the data.

The selection of CC interactions follows closely that
of the previously published analysis of unpolarised data from H1~\cite{h1hiq2}
and is briefly described below.  
The CC events are characterised as having large unbalanced
transverse momentum, $P_{T,h}$, attributed to the undetected neutrino.
The quantity $P_{T,h}$ is determined from
$P_{T,h} = \sqrt{(\sum_i{p_{x,i}})^2+(\sum_i{p_{y,i}})^2}$, where
the summation is performed
over all particles of the hadronic final state. 
The hadronic final state particles are reconstructed using a combination of 
tracks and calorimeter deposits in an energy flow algorithm that avoids double
counting~\cite{bpthesis}.  

The CC kinematic quantities are determined from the hadonic final
state~\cite{jb} using the relations
\begin{equation}
   y_{h} = \frac{E_h-p_{z,h}}{ 2 \ E_e }\,,
   \hspace*{2cm}
   Q^2_{h} = \frac{P_{T,h}^2}{ 1-y_{h}}\,,
   \hspace*{2cm}
    x_h=\frac{Q^2_h} {s \ y_h}\,,
\end{equation}
where $E_h-p_{z,h}\equiv \sum_i (E_i-p_{z,i})$ and $E_e$ is the incident 
electron beam energy.

NC interactions are also studied as they provide an accurate and high
statistics data sample with which to check the detector response.  The
selection of NC interactions is based mainly on the requirement of an
identified scattered electron in the LAr calorimeter, with an energy
$E^\prime_e>11\,{\rm GeV}$.  The NC sample is used to carry out an
{\it in-situ} calibration of the electromagnetic and hadronic energy
scales of the LAr calorimeter using the method described
in~\cite{h1hiq2, bpthesis, adilthesis, ringaile}. The hadronic
calibration procedure is based on the balance of the transverse energy
of the electrons with that of the hadronic final state.  The
calibration procedure gives good agreement between data and simulation
within an estimated uncertainty of $2\%$ on the hadronic scale.

In addition, NC events are used for studies of systematic
uncertainties in the charged current analysis.  The data are processed
such that all information from the scattered electron is suppressed,
providing the so-called {\it pseudo-CC}
sample~\cite{bpthesis,adilthesis,ringaile,biljana}. This sample mimics CC
interactions allowing trigger and selection efficiencies to be checked
with high statistical precision and independently of the MC simulation.

\section{Measurement Procedure}

Candidate CC interactions are selected by requiring $P_{T,h}>12\,{\rm
GeV}$ and a reconstructed vertex within $35\,{\rm cm}$ in $z$ of the
nominal interaction point. In order to ensure high efficiency of the
trigger and good kinematic resolution the analysis is further
restricted to the domain of 
$0.03<y_h<0.85$.  The $ep$ background is dominantly due to
photoproduction events, in which the scattered electron escapes
undetected in the backward direction and transverse momentum
is missing due to fluctuations in the detector response or
undetected particles. This background is suppressed exploiting the
correlation between $P_{T,h}$ and the ratio $V_{ap}/V_p$ of 
transverse energy flow
anti-parallel and parallel to the hadronic final state transverse
momentum vector~\cite{bpthesis,adilthesis,ringaile}.
The suppression cuts are different for the $R$ and $L$ data sets as the
relative photoproduction contributions differ in the two samples.  The
residual $ep$ background is negligible for most of the measured
kinematic domain.  The simulation is used to estimate this
contribution, which is subtracted statistically from the CC data
sample. Non-$ep$ background is rejected by searching for
typical cosmic ray and beam-induced background event
topologies~\cite{bpthesis,adilthesis,ringaile}. 

The $Q^2_h$, $P_{T,h}$, $E_h-p_{z,h}$ and $x_h$ distributions of the
selected events are shown in Figs.\,\ref{conte-} and \,\ref{conte+}for the $L$ (upper) and
$R$ (lower) samples.  The simulation provides a good description of
the data. The contribution of background photoproduction processes is
small and has the largest influence at low $P_{T,h}$.

Events with $Q^2_h> 400\,{\rm GeV}^2$ are used to measure the cross
sections, which correspond to the kinematic region $Q^2>400\,{\rm
GeV}^2$ and $y<0.9$ and thus are corrected for the effects of the
analysis cuts.  The correction factor is calculated to be $1.07$ using
the H1 PDF $2009$ parametrisation.

The systematic uncertainties on the cross section measurements are
discussed briefly below (see \cite{bpthesis,adilthesis,ringaile} and
references therein for more details). Positive and negative variations
of one standard deviation of each error source are found to yield
errors which are symmetric to a good approximation. The systematic
uncertainties of each source are taken to be fully correlated between
the cross section measurements unless stated otherwise.

\begin{itemize}
\item An uncertainty of $2\%$ is assigned to the scale of the hadronic energy
  measured in the LAr calorimeter, of which $1\%$ is considered as a
  correlated component to the uncertainty. This results in a total
  uncertainty of $1.3\%$ on the cross section measurements.
    
\item A $10\%$ uncertainty is assigned to the amount of energy
  in the LAr calorimeter attributed to noise, which gives rise to a
  systematic error of $0.3\%$ on the cross section measurements.
  
\item The variation of cuts against photoproduction on 
  $V_{ap}/V_p$ and $P_{T,h}$ has an effect on the cross sections of
  $0.6\%$.
  
\item A $30\%$ uncertainty on the subtracted $ep$ background is determined from a comparison of
  data and simulation after relaxing the anti-photoproduction cuts,
  such that the sample is dominated by photoproduction events.
  
\item The non-$ep$ background finders introduce an inefficiency for 
  CC events. The associated uncertainty is estimated using pseudo-CC
  data and found to depend on $y$. The uncertainty is $2\%$ for
  $y<0.1$ and $1\%$ for $y>0.1$.

\item A $y$-dependent error is assigned to the vertex finding efficiency: 
An uncertainty of $1\%$ is applied
  for $y>0.15$ , $4\%$ for $0.15>y>0.06$, and $15\%$ for
  $y<0.06$. This yields an uncertainty of $\simeq 2\%$ on the total
  cross section measurements.

\item An uncertainty of $0.5\%$ accounts for the
  dependence of the acceptance correction on the PDFs used in the 
  MC simulation.

\item A $1.8\%$ uncertainty on the trigger efficiency is determined
  based on the pseudo-CC data sample. The uncorrelated component of
  this uncertainty is $1\%$.

\item An error of $0.8\%$ is estimated for
  the QED radiative corrections. This accounts for missing
  contributions in the simulation of the lowest order QED effects and
  for the uncertainty on the higher order QED and EW corrections.

\item In addition, there is a global uncertainty of $2.1\%$
 on the luminosity measurement for both the $R$ and $L$ data samples,
 of which $0.5\%$ is considered as correlated.

\item The relative uncertainty in the measurement of the lepton
  beam polarisation is taken to be $1.6\%$ for the LPOL and $3.5\%$
  for the TPOL~\cite{Lorenzon}, yielding a total relative polarisation
  uncertainty in the $e^+p$ sample of $1.2\%$ for the $R$ data set and
  $1.4\%$ for the $L$ data set. For the $e^-p$ data a relative
  uncertainty of $2.3\%$ for the $R$ data set and $1.0\%$ for the $L$
  data set is obtained. These uncertainties are not included in the
  error bars of the data points.

\end{itemize}
%
The total systematic error is formed by adding the individual
uncertainties in quadrature and amounts to about $4\%$ on
the total cross section measurements.

\section{Results}

The measured integrated CC cross sections are quoted in the range
$Q^2> 400\,{\rm GeV}^2$ and $y<0.9$ and are given in Tab.~\ref{cctot}
and shown in Figs.~\ref{sigtot1} and~\ref{sigtot2}.  The measurement
of the unpolarised total cross section in the same phase space based
on HERA-I data is also given. This measurement follows identically the
procedure described in~\cite{h1e-} but with the $Q^2$ cut adopted in
this analysis. The systematic uncertainties of this unpolarised
measurement are taken to be the same as in~\cite{h1hiq2}, with the
exception of the QED radiative correction uncertainty, which has been
reduced from $3\%$ to $0.8\%$. The measurements are compared to
expectations of the Standard Model using the H1 PDF $2009$
parametrisation. The uncertainty on the Standard Model expectations
combines the uncertainties from experimental data used in the H1 PDF
$2009$ fit as well as model uncertainties~\cite{h1pdf2009}.

The data exhibit a clear linear polarisation dependence of the cross
sections which is maximal for left handed $e^-p$ scattering and right
handed $e^+p$ scattering demonstrating the parity violation of purely
weak charged current interactions. 


\begin{table}[h]
  \begin{center}
    \begin{tabular}{|l|r|c|c|}
\hline
&  $P_e \,\,(\%)$ & $\sigma^{\rm tot}_{\rm CC} \,\,({\rm pb})$ &  SM expectation $({\rm pb})$\\
\hline
       & $+36.9$ & $36.3 \pm 1.1_{\rm stat} \pm 1.0_{\rm sys}$ & $37.3^{+1.0}_{-0.8}$ \\
$e^-p$ & $  0.0$ & $57.0 \pm 2.2_{\rm stat} \pm 1.4_{\rm sys}$ & $59.2^{+1.6}_{-1.3}$ \\
       & $-26.1$ & $71.0 \pm 1.1_{\rm stat} \pm 2.0_{\rm sys}$ & $74.5^{+2.0}_{-1.6}$ \\
\hline
       & $+32.5$ & $39.2 \pm 0.8_{\rm stat} \pm 1.4_{\rm sys}$ & $37.8^{+1.1}_{-0.8}$ \\
$e^+p$ & $  0.0$ & $28.4 \pm 0.8_{\rm stat} \pm 0.8_{\rm sys}$ & $28.5^{+0.9}_{-0.3}$ \\
       & $-37.6$ & $17.8 \pm 0.6_{\rm stat} \pm 0.6_{\rm sys}$ & $17.8^{+0.5}_{-0.3}$ \\
\hline
\end{tabular} 
\caption{ Measured cross section values for
    $\sigma^{\rm tot}_{\rm CC}$ in the region
    $Q^2> 400\,{\rm GeV}^2$ and $y<0.9$ compared to the Standard Model
    (SM) expectation from H1 PDF 2009.}
\label{cctot}
\end{center}
\end{table}
% period   sigma            stats         tot
% e-LH : 70.978209     1.479     3.117
% e-RH: 36.261408     3.105     4.164
% e+LH: 17.834243     3.376     4.778
% e+RH: 39.209233     2.075     4.043

% H1PDF2009 expectations: Here they are:
% e-LH: 74.545586 + 2.7352 - 2.2018 (%)
% e-RH: 37.325401 + 2.7347 - 2.2014
% e+LH: 17.798948 + 2.9652 - 1.2386
% e+RH: 37.804802 + 2.9662 - 1.2377
% e- (P=0) : 59.1542 + 2.7334 - 2.2025
% e+ (P=0): 28.5352 + 2.9671 - 1.2364

% A linear fit to the polarisation dependence of the measured cross
% sections is performed taking into account the correlated systematic
% uncertainties between the measurements and is shown in Fig.~\ref{xsec}.
% The fit provides a reasonable description of the data with a
% $\chi^2=0.8$ for one degree of freedom. The result of the fit 
% extrapolated to the point $P_e=1$ yields a fully right handed charged current
% cross section of
% %
% %\vspace{-6mm}
% \begin{equation}
% \label{result}
% \sigma^{\rm tot}_{\rm CC} (P_e=1)= -0.9 \pm 2.9_{\rm stat}  \pm 1.9_{\rm sys} 
% \pm 2.9_{\rm pol}\,\, {\rm pb}\,,
% \end{equation}
% where the quoted errors correspond to the statistical (stat),
% experimental (sys) and polarisation-related (pol) systematic
% uncertainties.  This extrapolated cross section is consistent with the
% Standard Model prediction of a vanishing cross section and corresponds
% to an upper limit on $\sigma^{\rm tot}_{\rm CC} (P_e=1)$ of $8.0\,{\rm pb}$ 
% at $95\%$ confidence level (CL), as derived according to~\cite{feldman}. 
% This result excludes the existence of charged currents involving
% right handed fermions mediated by a boson of mass below $186\,{\rm GeV}$ at $95\%$\,CL,
% assuming Standard Model couplings and a massless right handed $\nu_e$.


%It is also possible to fit the measured cross sections by constraining the
%cross section at $P_e=-1$ to zero. This yields a cross section at
%$P_e=0$ of $27.5\pm 0.6_{\rm stat} \pm 0.9_{\rm sys}\,{\rm pb}$ with a
%$\chi^2/{\rm dof}=3.5$ and a negligible error due to the uncertainty
%on the polarisation measurement. The fitted value agrees well with the
%Standard Model expectation of $26.3\pm 0.4\,{\rm pb}$.

Measurements of the single differential cross sections ${\rm
d}\sigma/{\rm d}Q^2$ have also be made for the $L$ and $R$ samples in
$e^{\pm}p$ scattering. These are shown in Figs.~\ref{dsdq2elepol}
and~\ref{dsdq2pospol} compared to the Standard Model expectation based
on the PDFs from H1 PDF 2009. The cross sections are observed to fall
with increasing $Q^2$ and have a more rapid decrease for
$Q^2>~2\,000$~GeV$^2$. In the context of the Standard Model this is
understood to arise from the falling parton densities as $Q^2$ (and
hence also $x$) increases. Close to the Electroweak scale the
influence of the heavy $W^{\pm}$ propagator $(\sim
[M^2_W/(Q^2+M^2_W)]^2)$ causes a further suppression of the cross
section.

The performance of the Standard Model in being able to describe these
cross section measurements is better seen in Figs.~\ref{dq2ratele}
and~\ref{dq2ratpos} where the ratio of the measured cross sections to
the Standard Model expectations using the H1 PDF 2009 partons is
shown. Also visible is the ratio using the HERAPDF1.0 partons. The
Standard Model provides a good description of the measured cross
sections in both shape and normalisation, although it is noted that
the $e^-p$ $L$ data lie systematically below the prediction by about
$2-3\%$ (where the normalisation uncertainty is $\pm2.1\%$). The data
are in better agreement with the HERAPDF1.0 expectation.

The charged current cross section is largest for $e^-p$ left polarised
scattering ($P_e<0$) and with the given integrated luminosity these
measured cross section have a precision which is approximately
balanced between the statistical and systematic uncertainties. In all
other samples the data are limited by their statistical
uncertainty. This uncertainty can be reduced by combining the $L$ and
$R$ samples into an effective unpolarised data set (correcting for the
small residual polarisation). The resulting cross sections are then
combined with previously published H1 measurements of the unpolarised
cross sections~\cite{h19497,h1e-,h1hiq2}. The method of combination is
described in detail in~\cite{h1lowestq2}. This method forms a model
independant average from several measurements of the same cross
section taking into account the systematic uncertainties correlated
across the data sets. The final combined cross sections make use of
the complete HERA dataset collected by H1 and amounts to a total
luminosity of $165.5$~pb$^{-1}$ for $e^-p$ scattering and
$280.8$~pb$^{-1}$ for $e^+p$ scattering. The combined cross sections
are shown in Figs.~\ref{dq2elefull} and~\ref{dq2posfull} where again
it can be seen that the expectation from H1 PDF 2009 proveds an
excellent description of the data. The cross section ratios to the
Standard Model expectation using the H1 PDF 2009 partons are shown in
Fig.~\ref{dq2ratfull}.

In order to obtain the best sensitivity to the PDFs the double
differential reduced cross sections $\sigma^{\rm tot}_{\rm CC}$ are
measured for each of the four data sets, $e^{\pm}p$ for the $R$ and
$L$ polarised samples. The cross sections are shown in
Figs.~\ref{xq2ele} and~\ref{xq2pos} for electron scattering and
positron scattering respectively. 

These data are combined into an effective unpolarised measurement afer
correcting for the residual polarisation, and then further combined
with unpolarised measurements from HERA-I as described earlier. These
measurements using the complete HERA-I+II data sets are shown in
Figs.~\ref{xq2elefull} and~\ref{xq2posfull} for electron and positron
scattering respectively. The expectation to the Standard Model using H1
PDF 2009 is shown as the shaded band.

The leading order quark and anti-quark contributions to the reduced
cross sections are shown for the electron and positron scattering data
in Figs.~\ref{xq2elefullq} and~\ref{xq2posfullq} rspectively. In the
former case the cross section is everywhere dominated by the up-type
quark contributions from $u$ and $c$. This is due to the small sea
quark contribution at high $x$ and the $(1-y)^2$ helicity suppression
of anti-quarks at low $x$. However, in the case of positron scattering
this helicity suppression factor affects the down-type quarks at low
$x$. At high $x$ the large $d$ valence distribution is unsuppressed,
thus $CC$ measurements in $e^+p$ can provide stringent constraints on
the high $x$ $d$ valence PDF.

In Fig.~\ref{nccc} the $Q^2$ dependance of the cross section
measurements from H1 and ZEUS are shown for unpolarised charged lepton
scattering in both the neutral and charged current channels. The
HERAPDF 1.0 fit is compared to the data and shows good agreement
across the range of the measurements.

\section{Summary}

Measurements of polarised $e^{\pm}p$ charged current cross sections
$\sigma^{\rm tot}_{\rm CC}$, $d\sigma/dQ^2$ and
$\tilde{\sigma}(x,Q^2)$ using the complete HERA-II data set have been
reported. The results are based on data collected from collisions of
unpolarised protons with polarised electron and positron beams in left
and right helicity states. The polarisation dependence of the charged
current cross section has thus been established at HERA both in $e^+p$
and in $e^-p$ collisions, extending previous tests of the chiral
structure of the charged current interaction into the region of large,
space-like $Q^2$. The data are found to be consistent with the
Standard Model axiomatic absence of right handed charged currents.

The statistical uncertainty of the differential measurements is
reduced by combining the HERA-I and HERA-II data to yield unpolarised
differential cross sections with a total luminosity of
$165.5$~pb$^{-1}$ for $e^-p$ scattering and $280.8$~pb$^{-1}$ for
$e^+p$ scattering.


\section*{Acknowledgements}

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

\newpage
\begin{thebibliography}{99}

%\bibitem {h105}
%A.~Aktas {\it et al.}  [H1 Collaboration],
%%``First measurement of charged current cross sections at HERA with
%%longitudinally polarised positrons,''
%Phys.\ Lett.\ B {\bf 634} (2006) 173
%[hep-ex/0512060].
%%%CITATION = HEP-EX 0512060;%%

%\bibitem{zeus06}
%S.~Chekanov {\it et al.}  [ZEUS Collaboration],
%%``Measurement of high-Q**2 deep inelastic scattering cross sections with a
%%longitudinally polarised positron beam at HERA,''
%hep-ex/0602026.
%%%CITATION = HEP-EX 0602026;%%

%\bibitem{h1dis06}
%B. Antunovic, ``Charged current in polarised $e^\pm p$ collisions at HERA-II'',
%presented at DIS 2006 on behalf of the H1 Collaboration.

\bibitem {klein}
%\cite{Klein:vs}
M.~Klein and T.~Riemann,
%``Electroweak Interactions Probing The Nucleon Structure,''
Z.\ Phys.\ C {\bf 24} (1984) 151.
%%CITATION = ZEPYA,C24,151;%%


\bibitem {ewpaper}
A.~Aktas {\it et al.}  [H1 Collaboration],
%`` A Determination of Electroweak Parameters at HERA''
Phys.\ Lett. B {\bf 632} (2006) 35 
[hep-ex/0507080].
%%CITATION = HEP-EX 0507080;%%

\bibitem {ewheraproc}
R.~Beyer {\it et al.}, Proceedings of the Workshop ``Future Physics at HERA'', 
vol.\ 1,
eds. W.~Buchm\"uller, G.~Ingelman, A.~De~Roeck and R. Klanner, DESY (1996) 142;\\
R.~Cashmore {\it et al.}, ibid., 163.

\bibitem{charm}
%\cite{Jonker:1979md}
  M.~Jonker {\it et al.} [CHARM Collaboration],
  %``Polarization Of Positive Muons Produced In High-Energy Anti-Neutrino
  %Interactions,''
  Phys.\ Lett.\ B {\bf 86} (1979) 229.
  %%CITATION = PHLTA,B86,229;%%
%\cite{Adloff:2000qk}


\bibitem{h1lowq2}
  C.~Adloff {\it et al.}  [H1 Collaboration],
  %``Deep-inelastic inclusive e p scattering at low x and a determination of
  %alpha(s),''
  Eur.\ Phys.\ J.\ C {\bf 21} (2001) 33
  [hep-ex/0012053].
  %%CITATION = HEP-EX 0012053;%%

\bibitem{h1hiq2}
C.~Adloff {\it et al.}  [H1 Collaboration],
%``Measurement and QCD Analysis of Neutral and Charged Current Cross Sections 
% at HERA''
Eur.\ Phys.\ J.\ C {\bf 30} (2003) 1
[hep-ex/0304003].
%%CITATION = HEP-EX 0304003;%%

\bibitem{h1lowestq2}
  H.~Collaboration,
  %``Measurement of the Inclusive ep Scattering Cross Section at Low Q^2 and x
  %at HERA,''
  Eur.\ Phys.\ J.\  C {\bf 63} (2009) 625
  [arXiv:0904.0929 [hep-ex]].
  %%CITATION = EPHJA,C63,625;%%

\bibitem{h1pdf2009}
  F.~D.~Aaron {\it et al.}  [H1 Collaboration],
  %``A Precision Measurement of the Inclusive ep Scattering Cross Section at
  %HERA,''
  Eur.\ Phys.\ J.\  C {\bf 64} (2009) 561
  [arXiv:0904.3513 [hep-ex]].
  %%CITATION = EPHJA,C64,561;%%

%\cite{Arbuzov:1995id}
\bibitem{hector}
  A.~Arbuzov, D.Y.~Bardin, J.~Bluemlein, L.~Kalinovskaya and T.~Riemann,
  %``HECTOR 1.00 - A program for the calculation of QED, QCD and electroweak
  %corrections to ep and lN deep inelastic neutral and charged current
  %scattering,''
  Comput.\ Phys.\ Commun.\  {\bf 94}, 128 (1996)
  [hep-ph/9511434].
  %%CITATION = HEP-PH 9511434;%%

\bibitem{spin}
 A.A.~Sokolov and I.M.~Ternov, Sov.\ Phys.\ Dokl.\ {\bf 8} No. 12 (1964) 1203.
 
\bibitem{lpol}
 M.~Beckmann {\it et al.}, Nucl.\ Instrum.\ Meth.\ A {\bf 479} (2002) 334.

\bibitem{tpol}
 D.P.~Barber {\it et al.}, Nucl.\ Instrum.\ Meth.\ A {\bf 329} (1993) 79.
 
\bibitem{h1det}
% H1 Collaboration, I.~Abt {\it et al.}, Nucl.\ Instr.\ Meth.\ A386 (1997)
% 310 and 348.  -> No, 310 & 397
I.~Abt {\it et al.}  [H1 Collaboration],
%``The H1 detector at HERA,''
Nucl.\ Instrum.\ Meth.\ A {\bf 386} (1997) 310 and 348; \\
%%CITATION = NUIMA,A386,310;%%
%
R.D.~Appuhn {\it et al.}  [H1 SPACAL Group],
%``The H1 lead/scintillating-fibre calorimeter,''
Nucl.\ Instrum.\ Meth.\ A {\bf 386} (1997) 397.
%%CITATION = NUIMA,A386,397;%%

\bibitem{django}
  G.A.~Schuler and H.~Spiesberger, 
  Proceedings of the Workshop ``Physics at HERA'', \\vol.\ 3,
  eds. W.~Buchm\"uller, G.~Ingelman, DESY (1992) 1419.

\bibitem{lepto} 
  G.~Ingelman, Proceedings of the Workshop ``Physics at HERA'', vol.\ 3,\\
  eds. W.~Buchm\"uller, G.~Ingelman, DESY (1992) 1366.   
  
\bibitem{heracles}   
%\cite{Kwiatkowski:1990es}
A.~Kwiatkowski, H.~Spiesberger and H.-J.~M\"ohring,
%``Heracles: An Event Generator For E P Interactions At Hera Energies Including Radiative Processes: Version 1.0,''
Comput.\ Phys.\ Commun.\  {\bf 69} (1992) 155.
%%CITATION = CPHCB,69,155;%%

\bibitem{cdm}
%\cite{Lonnblad:1992tz}
L.~L\"onnblad,
%``ARIADNE version 4: A Program for simulation of QCD cascades implementing the color dipole model,''
Comput.\ Phys.\ Commun.\  {\bf 71} (1992) 15.
%%CITATION = CPHCB,71,15;%%

\bibitem{jetset}  
%\cite{Sjostrand:1986hx}
T.~Sj\"ostrand and M.~Bengtsson,
%``The Lund Monte Carlo For Jet Fragmentation And E+ E- Physics: Jetset Version 6.3: An Update,''
Comput.\ Phys.\ Commun.\  {\bf 43} (1987) 367.
%%CITATION = CPHCB,43,367;%%

\bibitem{pythia} 
%\cite{Sjostrand:1993yb}
T.~Sj\"ostrand,
%``High-energy physics event generation with PYTHIA 5.7 and JETSET 7.4,''
Comput.\ Phys.\ Commun.\  {\bf 82} (1994) 74.
%%CITATION = CPHCB,82,74;%%

\bibitem{cteq5} 
H.L.~Lai {\it et al.}  [CTEQ Collaboration],
%``Global {QCD} analysis of parton structure of the nucleon: CTEQ5 parton
%distributions,''
Eur.\ Phys.\ J.\ C {\bf 12} (2000) 375
[hep-ph/9903282].
%%CITATION = HEP-PH 9903282;%%

\bibitem{ggrv} 
%\cite{Gluck:1991jc}
M.~Gl\"uck, E.~Reya and A.~Vogt,
%``Photonic parton distributions,''
Phys.\ Rev.\ D {\bf 46} (1992) 1973.
%%CITATION = PHRVA,D46,1973;%%

\bibitem{GEANT} R. Brun {\it et al.}, GEANT3 User's Guide,
  CERN-DD/EE-84-1 (1987).  

\bibitem{bpthesis}
B.~Portheault, Ph.D.\ thesis (March 2005), LAL 05-05 (IN2P3/CNRS), 
Universit\'e de Paris-Sud XI, Orsay, available at 
http://www-h1.desy.de/publications/theses\_list.html.

\bibitem{jb}
A.~Blondel and F.~Jacquet, Proceedings of the Study of an $ep$ Facility for 
Europe,\\ ed.\ U.~Amaldi, DESY (1979) 391.

\bibitem{adilthesis}
A.~Aktas, Ph.D.\ thesis (August 2005), Hamburg University, available at 
http://www-h1.desy.de/publications/theses\_list.html.

\bibitem{ringaile}
R.~Pla\v{c}akyt\.{e}, Ph.D. thesis (June 2006) , Max-Planck-Institut f\"ur Physik, Munich, will be available at 
http://www-h1.desy.de/publications/theses\_list.html.

\bibitem{biljana}
B.~Antunovic, Ph.D.\ thesis (September 2007), Max-Planck-Institut f\"ur Physik, Munich, will be available at 
http://www-h1.desy.de/publications/theses\_list.html.

%\cite{Lorenzon:1997pq}
\bibitem{Lorenzon}
W.~Lorenzon [HERMES Collaboration],
%``Beam polarimetry at HERA,''
DESY-HERMES-97-68,
%\href{http://www.slac.stanford.edu/spires/find/hep/www?r=desy-hermes-97-68}{SPIRES entry}
{\it 7th International Workshop on Polarized Gas Targets and
Polarized Beams}, Urbana, IL, 18-22 Aug 1997;\\
F.~Corriveau {\it et al.}  [TPOL Polarimeter Group],
``A Calibration of the HERA Transverse Polarimeter for the 2003/2004 Data'', 
available at http://www.desy.de/{\small $\sim$}pol2000/documents/documents.html.

\bibitem{h1e-}
C.~Adloff {\it et al.}  [H1 Collaboration],
%``Measurement of neutral and charged current cross sections in electron  proton
%collisions at high Q**2,''
Eur.\ Phys.\ J.\ C {\bf 19} (2001) 269
[hep-ex/0012052].
%%CITATION = HEP-EX 0012052;%%

\bibitem{feldman}
  G.J.~Feldman and R.D.~Cousins,
  %``A Unified approach to the classical statistical analysis of small
  %signals,''
  Phys.\ Rev.\ D {\bf 57} (1998) 3873
  [physics/9711021].
  %%CITATION = PHYS-ICS 9711021;%%

\bibitem{h19497}
  C.~Adloff {\it et al.}  [H1 Collaboration],
  % ``Measurement of neutral and charged current cross-sections in positron
  % proton collisions at large momentum transfer,''
  Eur.\ Phys.\ J.\ C {\bf 13}, 609 (2000)
  [arXiv:hep-ex/9908059].
  %%CITATION = HEP-EX 9908059;%%

\end{thebibliography}

\newpage
%%%%%%%%%%%%%%%%%%%% Fig.1: Polarisation profile %%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htb]
\begin{center}
\begin{picture}(90,220)(0,0)
\setlength{\unitlength}{1 mm}
\put(-30,110){\epsfig{file=H1prelim-09-041.fig1a.eps,width=\textwidth}}
\put(-30,  0){\epsfig{file=H1prelim-09-041.fig1b.eps,width=\textwidth}}
\put( -5,200){\bf (a)}
\put( -5,85){\bf (b)}
\end{picture}
\end{center}
\caption{
  The polarisation profile weighted by the luminosity values for the
  (a) $e^-p$ data and (b) $e^+p$ data. The $L (R)$ sample corresponds to distribution having
  negative (positive) polarisation values.}
\label{profile_pol}
\end{figure}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%%%%%%%%%%%%%%%%%%%% Fig.2: CC control plots e- %%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htb]
\begin{center}
\begin{picture}(90,200)(0,0)
\setlength{\unitlength}{1 mm}
\put(-15,100){\epsfig{file=H1prelim-09-041.fig2a.eps,height=10.5cm}}
\put(-15, -5){\epsfig{file=H1prelim-09-041.fig2b.eps,height=10.5cm}}
\put( 35,199){\bf (a)}
\put( 90,199){\bf (b)}
\put( 35,148){\bf (c)}
\put( 90,148){\bf (d)}
%
\put( 35, 94){\bf (e)}
\put( 90, 94){\bf (f)}
\put( 35, 43){\bf (g)}
\put( 90, 43){\bf (h)}
%
\end{picture}
\end{center}
\caption{
  Distributions of (a,e)~$\log_{10}{Q^2_h}$, (b,f)~$P_{T,h}$,
  (c,g)~$E-P_Z$ and (d,h)~$\log_{10}{x_h}$ shown in upper and lower
  plots for the selected events in the (a-d) $e^-p$ $L$ and (e-h)
  $e^-p$ $R$ data sets. The Monte Carlo (MC) contributions from the
  charged current (CC) process and the $ep$ background (bkg) processes
  are shown as the full line, the total uncertainty is represented by
  the shaded band. The contribution from the $ep$ background is shown
  as the lower shaded histogram.}
\label{nc}
\end{figure}

\clearpage

%%%%%%%%%%%%%%%%%%%% Fig.3: CC control plots e+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htb]
\begin{center}
\begin{picture}(90,200)(0,0)
\setlength{\unitlength}{1 mm}
\put(-15,100){\epsfig{file=H1prelim-09-041.fig3a.eps,height=10.5cm}}
\put(-15, -5){\epsfig{file=H1prelim-09-041.fig3b.eps,height=10.5cm}}
\put( 35,199){\bf (a)}
\put( 90,199){\bf (b)}
\put( 35,148){\bf (c)}
\put( 90,148){\bf (d)}
%
\put( 35, 94){\bf (e)}
\put( 90, 94){\bf (f)}
\put( 35, 43){\bf (g)}
\put( 90, 43){\bf (h)}
%
\end{picture}
\end{center}
\caption{
  Distributions of (a,e)~$\log_{10}{Q^2_h}$, (b,f)~$P_{T,h}$,
  (c,g)~$E-P_Z$ and (d,h)~$\log_{10}{x_h}$ shown in upper and lower
  plots for the selected events in the (a-d) $e^-p$ $L$ and (e-h)
  $e^+p$ $R$ data sets. The Monte Carlo (MC) contributions from the
  charged current (CC) process and the $ep$ background (bkg) processes
  are shown as the full line, the total uncertainty is represented by
  the shaded band. The contribution from the $ep$ background is shown
  as the lower shaded histogram.}
\label{conte+}
\end{figure}

\clearpage

%%%%%%%%%%%%%%%%%%%% Fig.4: cross sections vs. Pe H1pdf2009 %%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htb]
\begin{center}
\begin{picture}(90,150)(0,0)
\setlength{\unitlength}{1 mm}
\put(-30,  0){\epsfig{file=H1prelim-09-041.fig4.eps,width=\textwidth}}
\end{picture}
\end{center}
\caption{
  The dependence of the $e^\pm p$ CC cross section on the lepton beam
  polarisation $P_e$. The inner and outer error bars represent
  respectively the statistical and total errors. The uncertainties on
  the polarisation measurement are smaller than the symbol size.  The
  data are compared to the Standard Model prediction based on the H1
  PDF $2009$ parametrisation (dark shaded band). The light shaded band
  corresponds to the resulting one-sigma contour of a linear fit to
  the data shown as the central line.}
\label{sigtot1}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%% Fig.5: cross sections vs. Pe HERAPDF1.0 %%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htb]
\begin{center}
\begin{picture}(90,150)(0,0)
\setlength{\unitlength}{1 mm}
\put(-30,  0){\epsfig{file=H1prelim-09-041.fig5.eps,width=\textwidth}}
\end{picture}
\end{center}
\caption{
  The dependence of the $e^\pm p$ CC cross section on the lepton beam
  polarisation $P_e$. The inner and outer error bars represent
  respectively the statistical and total errors. The uncertainties on
  the polarisation measurement are smaller than the symbol size.  The
  data are compared to the Standard Model prediction based on the
  HERAPDF 1.0 parametrisation (dark shaded band). The light shaded
  band corresponds to the resulting one-sigma contour of a linear fit
  to the data shown as the central line.}
\label{sigtot2}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\clearpage
%%%%%%%%%%%%%%%%%%%% Fig.6: ds/dQ2 e- pol  %%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htb]
\begin{center}
\begin{picture}(90,200)(0,0)
\setlength{\unitlength}{1 mm}
\put(-15,100){\epsfig{file=H1prelim-09-041.fig6a.eps,height=10.5cm}}
\put(-15, -5){\epsfig{file=H1prelim-09-041.fig6b.eps,height=10.5cm}}
\put( 35,199){\bf (a)}
\put( 35, 94){\bf (b)}
%
\end{picture}
\end{center}

\caption{
  The $Q^2$ dependences of the CC cross section $d\sigma/dQ^2$, shown
  for the $e^-p$ data (solid points) using the $L$ (a) and $R$ (b)
  polarised samples.  The results are compared with the corresponding
  Standard Model expectations determined from the H1 PDF 2000 fit. The
  inner and outer error bars represent respectively the statistical
  and total errors.}
\label{dsdq2elepol}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\clearpage
%%%%%%%%%%%%%%%%%%%% Fig.7: ds/dQ2 e+ pol  %%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htb]
\begin{center}
\begin{picture}(90,200)(0,0)
\setlength{\unitlength}{1 mm}
\put(-15,100){\epsfig{file=H1prelim-09-041.fig7a.eps,height=10.5cm}}
\put(-15, -5){\epsfig{file=H1prelim-09-041.fig7b.eps,height=10.5cm}}
\put( 35,199){\bf (a)}
\put( 35, 94){\bf (b)}
%
\end{picture}
\end{center}

\caption{
  The $Q^2$ dependences of the CC cross section $d\sigma/dQ^2$, shown
  for the $e^+p$ data (solid points) using the $L$ (a) and $R$ (b)
  polarised samples.  The results are compared with the corresponding
  Standard Model expectations determined from the H1 PDF 2000 fit. The
  inner and outer error bars represent respectively the statistical
  and total errors.}
\label{dsdq2pospol}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%%%%%%%%%%%%%%%%%%%% Fig.8: ds/dQ2 ratios e- L&R  %%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htbp]
\begin{center}
\begin{picture}(90,200)(0,0)
\setlength{\unitlength}{1 mm}
\put(-30,100){\epsfig{file=H1prelim-09-041.fig8a.eps,width=\textwidth}}
\put(-30, 0) {\epsfig{file=H1prelim-09-041.fig8b.eps,width=\textwidth}}
\put( -3,190){\bf (a)}
\put( -3, 90){\bf (b)}
\end{picture}
\end{center}
\caption{
  The $Q^2$ dependences of the CC cross section ratio ${\rm
  d}\sigma/{\rm d}Q^2$ for $e^-p$ scattering using the $L$ (a) and $R$
  (b) polarised data samples, to the Standard Model expectation
  obtained from H1 PDF 2009 (green band). In addition the ratio using
  the expectation from HERAPDF1.0 is also shown (dashed line). The
  inner error bars represent the statistical uncertainties and the
  outer error bars represent the total errors. The normalisation
  uncertainty is not included in the error bars and is instead
  represented by the blue dashed lines.}
\label{dq2ratele} 
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%%%%%%%%%%%%%%%%%%%% Fig.9: ds/dQ2 ratios e+ L&R  %%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htbp]
\begin{center}
\begin{picture}(90,200)(0,0)
\setlength{\unitlength}{1 mm}
\put(-30,100){\epsfig{file=H1prelim-09-041.fig9a.eps,width=\textwidth}}
\put(-30, 0) {\epsfig{file=H1prelim-09-041.fig9b.eps,width=\textwidth}}
\put( -3,190){\bf (a)}
\put( -3, 90){\bf (b)}
\end{picture}
\end{center}
\caption{
  The $Q^2$ dependences of the CC cross section ratio ${\rm
  d}\sigma/{\rm d}Q^2$ for $e^+p$ scattering using the $L$ (a) and $R$
  (b) polarised data samples, to the Standard Model expectation
  obtained from H1 PDF 2009 (green band). In addition the ratio using
  the expectation from HERAPDF1.0 is also shown (dashed line). The
  inner error bars represent the statistical uncertainties and the
  outer error bars represent the total errors. The normalisation
  uncertainty is not included in the error bars and is instead
  represented by the blue dashed lines.}
\label{dq2ratpos} 
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%







%%%%%%%%%%%%%%%%%%%% Fig.10: cross section ds/dQ2 e- HERA-I+II %%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htb]
\begin{center}
\begin{picture}(90,150)(0,0)
\setlength{\unitlength}{1 mm}
\put(-30,  0){\epsfig{file=H1prelim-09-041.fig10.eps,width=\textwidth}}
\end{picture}
\end{center}
\caption{
  The $Q^2$ dependence of the unpolarised CC cross section
  $d\sigma/dQ^2$, shown for the $e^-p$ data (solid points) using the
  complete HERA-I+II data set.  The results are compared with the
  corresponding Standard Model expectations determined from the H1 PDF
  2000 fit. The inner and outer error bars represent respectively the
  statistical and total errors.}
\label{dq2elefull}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%%%%%%%%%%%%%%%%%%%% Fig.11: cross section ds/dQ2 e+ HERA-I+II %%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htb]
\begin{center}
\begin{picture}(90,150)(0,0)
\setlength{\unitlength}{1 mm}
\put(-30,  0){\epsfig{file=H1prelim-09-041.fig11.eps,width=\textwidth}}
\end{picture}
\end{center}
\caption{
  The $Q^2$ dependence of the unpolarised CC cross section
  $d\sigma/dQ^2$, shown for the $e^+p$ data (solid points) using the
  complete HERA-I+II data set.  The results are compared with the
  corresponding Standard Model expectations determined from the H1 PDF
  2000 fit. The inner and outer error bars represent respectively the
  statistical and total errors.}
\label{dq2posfull}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%% Fig.12: ds/dQ2 ratios e- L&R  %%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htbp]
\begin{center}
\begin{picture}(90,200)(0,0)
\setlength{\unitlength}{1 mm}
\put(-30,100){\epsfig{file=H1prelim-09-041.fig12a.eps,width=\textwidth}}
\put(-30, 0) {\epsfig{file=H1prelim-09-041.fig12b.eps,width=\textwidth}}
\put( -3,190){\bf (a)}
\put( -3, 90){\bf (b)}
\end{picture}
\end{center}
\caption{
  The $Q^2$ dependences of the CC cross section ratio ${\rm
  d}\sigma/{\rm d}Q^2$ for $e^-p$ scattering (a) and $e^+p$ scattering
  (b) polarised data samples, to the Standard Model expectation
  obtained from H1 PDF 2009 (green band). The measurements use the
  complete HERA-I+II data set. In addition the ratio using the
  expectation from HERAPDF1.0 is also shown (dashed line). The inner
  error bars represent the statistical uncertainties and the outer
  error bars represent the total errors. The normalisation uncertainty
  is not included in the error bars and is instead represented by the
  blue dashed lines.}
\label{dq2ratfull} 
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%% Fig.13: Double diffl e- L & R  %%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htbp]
\begin{center}
\begin{picture}(90,200)(0,0)
\setlength{\unitlength}{1 mm}
\put(-35, -10){\epsfig{file=H1prelim-09-041.fig13.eps,width=\textwidth}}
\end{picture}
\end{center}
\caption{
  The reduced cross section $\tilde{\sigma}_{CC}$ in polarised $e^-p$
  scattering using the $L$ (solid points) and $R$ (open points) data
  sets. The data are compared to the Standard Model prediction from H1
  PDF 2009. The inner error bars represent the statistical
  uncertainties and the outer error bars represent the total
  errors. The normalisation uncertainty is not included in the error
  bars.}
\label{xq2ele} 
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%% Fig.14: Double diffl e+ L & R  %%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htbp]
\begin{center}
\begin{picture}(90,200)(0,0)
\setlength{\unitlength}{1 mm}
\put(-35, -10){\epsfig{file=H1prelim-09-041.fig14.eps,width=\textwidth}}
\end{picture}
\end{center}
\caption{
  The reduced cross section $\tilde{\sigma}_{CC}$ in polarised $e^+p$
  scattering using the $L$ (solid points) and $R$ (open points) data
  sets. The data are compared to the Standard Model prediction from H1
  PDF 2009. The inner error bars represent the statistical
  uncertainties and the outer error bars represent the total
  errors. The normalisation uncertainty is not included in the error
  bars.}
\label{xq2pos} 
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%%%%%%%%%%%%%%%%%%%% Fig.15: Double diffl e- P=0  %%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htbp]
\begin{center}
\begin{picture}(90,200)(0,0)
\setlength{\unitlength}{1 mm}
\put(-35, -10){\epsfig{file=H1prelim-09-041.fig15.eps,width=\textwidth}}
\end{picture}
\end{center}
\caption{
  The reduced cross section $\tilde{\sigma}_{CC}$ in unpolarised
  $e^-p$ scattering using the complete HERA-I+II data sets. The data
  are compared to the Standard Model prediction from H1 PDF 2009. The
  inner error bars represent the statistical uncertainties and the
  outer error bars represent the total errors. The normalisation
  uncertainty is not included in the error bars.}
\label{xq2elefull} 
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%% Fig.16: Double diffl e+ P=0  %%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htbp]
\begin{center}
\begin{picture}(90,200)(0,0)
\setlength{\unitlength}{1 mm}
\put(-35, -10){\epsfig{file=H1prelim-09-041.fig16.eps,width=\textwidth}}
\end{picture}
\end{center}
\caption{
  The reduced cross section $\tilde{\sigma}_{CC}$ in unpolarised
  $e^+p$ scattering using the complete HERA-I+II data sets. The data
  are compared to the Standard Model prediction from H1 PDF 2009. The
  inner error bars represent the statistical uncertainties and the
  outer error bars represent the total errors. The normalisation
  uncertainty is not included in the error bars.}
\label{xq2posfull} 
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%% Fig.17: Double diffl e- P=0  & quarks %%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htbp]
\begin{center}
\begin{picture}(90,200)(0,0)
\setlength{\unitlength}{1 mm}
\put(-35, -10){\epsfig{file=H1prelim-09-041.fig17.eps,width=\textwidth}}
\end{picture}
\end{center}
\caption{
  The reduced cross section $\tilde{\sigma}_{CC}$ in unpolarised
  $e^-p$ scattering using the complete HERA-I+II data sets. The data
  are compared to the Standard Model prediction from H1 PDF 2009. The
  inner error bars represent the statistical uncertainties and the
  outer error bars represent the total errors. The normalisation
  uncertainty is not included in the error bars. The separate
  contributions from quarks and anti-quarks are shown as the dashed
  and dashed-dotted curves.}
\label{xq2elefullq} 
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%% Fig.18: Double diffl e+ P=0  & quarks %%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htbp]
\begin{center}
\begin{picture}(90,200)(0,0)
\setlength{\unitlength}{1 mm}
\put(-35, -10){\epsfig{file=H1prelim-09-041.fig18.eps,width=\textwidth}}
\end{picture}
\end{center}
\caption{
  The reduced cross section $\tilde{\sigma}_{CC}$ in unpolarised
  $e^+p$ scattering using the complete HERA-I+II data sets. The data
  are compared to the Standard Model prediction from H1 PDF 2009. The
  inner error bars represent the statistical uncertainties and the
  outer error bars represent the total errors. The normalisation
  uncertainty is not included in the error bars. The separate
  contributions from quarks and anti-quarks are shown as the dashed
  and dashed-dotted curves.}
\label{xq2posfullq} 
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%% Fig.19: NC & CC ds/dQ2 e+/e-  %%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htbp]
\begin{center}
\begin{picture}(90,200)(0,0)
\setlength{\unitlength}{1 mm}
\put(-35, -10){\epsfig{file=H1prelim-09-041.fig19.eps,width=\textwidth}}
\end{picture}
\end{center}
\caption{
  The $Q^2$ dependence of the unpolarised NC and CC cross sections
  $d\sigma/dQ^2$, shown for the $e^+p$ (open points) and $e^-p$ (solid
  points) scattering data from the H1 and ZEUS collaborations. The
  results are compared with the corresponding Standard Model
  expectations determined from the HERAPDF 1.0 fit. The inner and
  outer error bars represent respectively the statistical and total
  errors.}
\label{nccc} 
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%



\end{document}


