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\begin{titlepage}

\noindent
\begin{center}
%{\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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% \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}
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\vspace*{2cm}

\begin{center}
  \Large
  {\bf 
Neutral Current Interactions in $e^{\pm}p$ Scattering with Longitudinally Polarised Leptons}

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

\begin{abstract}

\noindent

The inclusive single differential cross section $d\sigma/dQ^2$ and the
reduced double differential cross section $\tilde{\sigma}(x,Q^2)$ are
presented for the neutral current process, $e^{\pm}p \rightarrow
e^{\pm} X$, in interactions with longitudinally polarised lepton beams
using the complete HERA-II data set. The cross sections are measured
in the region of large negative four-momentum transfer squared $Q^2
\geq 200$ GeV$^2$ and inelasticity $y<0.9$. The data are consistent
with the expected $Q^2$ dependence of polarised cross sections. The
data are compared to predictions of the Standard Model which is able
to provide a good description of the data. The polarisation asymmetry
is measured as a function of $Q^2$ and found to be in agreement with
expectation. The cross sections are combined with previously published
data from H1 to obtain the most precise unpolarised
measurements. These are used to extract the structure function
$xF_3^{\gamma Z}$.

% The inclusive single differential cross section ${\rm d}\sigma/{\rm
% d}Q^2$ and the reduced double differential cross section
% ${\tilde\sigma}(x,Q^2)$ are presented for the neutral current process,
% $e^{\pm}p\rightarrow e^{\pm} X$, in interactions with longitudinally
% polarised lepton beams. The cross sections are measured in the region
% of large negative four-momentum transfer squared, $Q^2 \geq 200\,{\rm
% GeV}^2$ and inelasticity, $y<0.9$. The data are consistent with the
% expected $Q^2$ dependence of polarised cross sections, albeit with the
% limited statistical precision of the data. The reduced cross section
% data are combined together with previously published unpolarised data
% to determine the structure function $x\tilde{F}_3$ with
% improved precision. The data are compared to predictions of the
% Standard Model which is able to provide a good description of the data.

\noindent
\end{abstract}


\end{titlepage}

\pagestyle{plain}

\section{Introduction} % 

HERA measurements of proton structure in neutral current (NC) deep
inelastic scattering (DIS) with polarised lepton beams are crucial to
the understanding of the detailed dynamics of QCD as well as allowing
the chiral structure of electroweak interactions to be simultaneously
probed at the highest energies. Previously published
measurements~\cite{h19497,h19899,h1hiq2,h1lowestq2,h1pdf2009} have already provided
unique constraints~\cite{h1hiq2,h1pdf2009,cteq,mstw} on the parton
densities functions (PDFs) of the proton as well as the axial and
vector couplings of the light quarks to the $Z^0$
boson~\cite{ewpaper}.

First neutral current (NC) cross section measurements of data taken in
the second phase of HERA operation with longitudinally polarised
leptons beams have been reported~\cite{h1dis06} for both electron and
positron scattering. The data presented here supercede those results,
now using the complete HERA-II data set, and are presented here in
detail.

In this paper measurements of the inclusive NC single
differential cross sections, ${\rm d}\sigma/{\rm d}Q^2$ and the
reduced cross section ${\tilde\sigma}(x,Q^2)$ are presented for $e^+p$
and $e^-p$ scattering. The data were taken with an incident lepton
beam energy of $27.5\,{\rm GeV}$, whilst the unpolarised proton beam
energy was $920\,{\rm GeV}$, yielding a centre-of-mass energy of
$\sqrt{s}=318\,{\rm GeV}$. Both data sets are further subdivided into
samples of left handed and right handed longitudinal polarisation,
$P_e=(N_R-N_L)/(N_R+N_L)$, where $N_R$ ($N_L$) is 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{The Neutral 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}

The generalised proton structure functions, $\tilde{F}_{2,3}$, may be
written as linear combinations of the hadronic structure functions
$F_{2}$, $F_{2,3}^{\gamma Z}$, and $F_{2,3}^{Z}$ containing
information on QCD parton dynamics as well as the EW couplings of the
quarks to the neutral vector bosons. The function $F_{2}$ is
associated to pure photon exchange terms, $F_{2,3}^{\gamma Z}$
correspond to photon-$Z^0$ interference and $F_{2,3}^{Z}$ correspond
to the pure $Z^0$ exchange terms. In addition the longitudinal
structure function $\tilde{F}_L$ may be similarly decomposed, however
this is important only at high $y$ and is expected to be negligible at
large $x$ (the familiar Bjorken $x$ variable) and $Q^2$. Neglecting
$\tilde{F}_{L}$, the linear combinations for arbitrarily polarised
$e^{\pm}p$ scattering are given by
\begin{eqnarray}
 \tilde{F}^{\pm}_2 = F_2 - (v_e \pm P_e a_e) \kappa  \frac{Q^2}{Q^2+M_Z^2}    F_2^{\gamma Z} 
            + (v_e^2+a_e^2 \pm P_e 2v_e a_e) \kappa^2 \left[\frac{Q^2}{Q^2+M_Z^2}\right]^2 F_2^Z \\
 x\tilde{F}^{\pm}_3 = -(a_e \pm P_e v_e)   \kappa    \frac{Q^2}{Q^2+M_Z^2}    xF_3^{\gamma Z} 
       + (2a_ev_e \pm P_e [v_e^2 + a_e^2] ) \kappa^2 \left[\frac{Q^2}{Q^2+M_Z^2}\right]^2 xF_3^Z 
\label{SF1}
\end{eqnarray}

Here $\kappa^{-1}=4\frac{M_W^2}{M_Z^2}(1-\frac{M_W^2}{M_Z^2})$
in the on-mass-shell scheme~\cite{oms} with $M_W$ and $M_Z$ the usual
weak vector boson masses. 
%The above expressions are related to the
%corresponding expressions for polarised positron scattering under the
%transformations $\tilde{F}_2^{L,R}(e^-p) \rightarrow
%\tilde{F}_2^{R,L}(e^+p)$ and 
%$x\tilde{F}_3^{L,R}(e^-p) \rightarrow x\tilde{F}_3^{R,L}(e^+p)$. For
%lepton beams with any polarisation the appropriate average of
%purely $L$ and $R$ structure functions is taken {\bf JOBBY!!!!}. 
For the first time
HERA is sensitive to the parity violating terms of the Standard Model,
namely those proportional to $P_e$ in eqs.~\ref{SF1} above.

In the quark parton model, the hadronic structure functions are
related to linear combinations of sums and differences of the quark
and anti-quark momentum distributions $xq(x,Q^2)$ and
$x\bar{q}(x,Q^2)$
\begin{eqnarray}
  \left[F_2,F_2^{\gamma Z},F_2^Z\right]  = x\sum_q [e_q^2,2e_qv_q,v_q^2+a_q^2](q+\bar{q}) \\
  \left[xF_3^{\gamma Z},xF3^Z \right] = 2x \sum_q[e_qa_q,v_qa_q](q-\bar{q})\,\,\,,
\label{SF2} 
\end{eqnarray} 
where $v_q$ and $a_q$ are the vector and axial-vector couplings of the light
quarks and $e_q$ is the charge of the quark of flavour $q$.

The differential cross section for $e^{\pm}$ scattering after
correction for QED radiative effects is then given by
\begin{equation}
\frac{\rm{d}^2\sigma^{\pm}_{NC}}{{\rm d}x{\rm d}Q^2}=
\frac{2\pi\alpha^2}{xQ^4}(Y_+\tilde{F}_2{\mp}Y_-x\tilde{F}_3-y^2\tilde{F}_L) \,\,\,,
\label{ncxsec} 
\end{equation} 
and the reduced cross section is defined by
\begin{equation}
\tilde{\sigma}^{\pm}(x,Q^2)\equiv
\frac{\rm{d}^2\sigma^{\pm}_{NC}}{{\rm d}x{\rm d}Q^2}\frac{xQ^4}{2\pi\alpha^2}\frac{1}{Y_+}\equiv
\tilde{F}_2{\mp}\frac{Y_-}{Y_+}x\tilde{F}_3-\frac{y^2}{Y_+}\tilde{F}_L \,\,\,.
\label{rxsec} 
\end{equation} 
The helicity dependence of the electroweak interactions is contained
within the terms $Y_{\pm}=1\pm(1-y^2)$ where $y$ characterises the
inelasticity of the interaction.

\section{Experimental Technique}
 
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}.

The $ep$ luminosity is determined by measuring the QED bremsstrahlung
($ep\rightarrow ep\gamma$) event rate by tagging the low angle
scattered lepton in a detector located at $z=-44$m adjacent to the
beam pipe.

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}(a) and (b) for the
$e^+$ and $e^-$ samples respectively.

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{h1hiq2} 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 candidate NC events follows closely that of the
previously published analysis of unpolarised data from
H1~\cite{h1hiq2} and is briefly described below.

NC events are characterised by an isolated high transverse momentum
lepton and a hadronic system opposite in azimuth to the scattered
lepton. Such events are triggered mainly using information from the
LAr calorimeter. The calorimeter has finely segmented geometry
allowing the selection of localised energy deposits in the
electromagnetic sections of the calorimeter. This selection is found
to be $100$\% efficient for leptons above $11$~GeV.

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,andrei}.

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, andrei}. The
hadronic calibration procedure is based on the double angle
reconstruction method~\cite{damethod} which uses the polar angles of
the scattered lepton and the hadronic final state to determine their
respective energies. The calibration procedure gives good agreement
between data and simulation within an estimated uncertainty of $2\%$
on the hadronic scale and between $1-3$\% on the electromagnetic
scale.

The NC kinematic quantities are determined using the $e\Sigma$
method~\cite{esigma} which uses information from the scattered lepton
and the hadronic final state optimising kinematic resolution and
minimising QED radiative corrections across the measured kinematic
plane.

\section{Measurement Procedure}

Candidate NC interactions are selected by requiring the scattered
lepton energy $E^{\prime}_e>11\,{\rm GeV}$, $Q^2_e > 133$~GeV$^2$ and
a reconstructed vertex within $35\,{\rm cm}$ in $z$ of the nominal
interaction point. Background from misidentified leptons is suppressed
by requiring a charged track to be associated to the lepton
candidate. Longitudinal energy-momentum conservation requires that
$E-P_z=2E_e$ where $E_e$ is the lepton beam energy and $E$ and $P_z$
are the usual components of the hadronic final state four-vector. By
requiring $E-P_z>35$~GeV the influence of radiative corrections is
considerably reduced which arises from initial state
bremmsstrahlung. This requirement further suppresses the contamination
from photoproduction background in which the the scattered lepton is
undetected in the backward beam pipe and a hadron is misidentified as a
lepton candidate.

The comparison of the data and the simulation (normalised to the
luminosity of the data) is shown in Fig.~\ref{nc} for the distribution
of scattered lepton energy $E_e^{\prime}$, the lepton polar angle
$\theta_e$, the reconstructed $Q^2_e$, and the transverse momentum
balance between the lepton and the hadronic final state,
$P_T^h/P_T^e$. The left and right handed samples are combined in these
figures. In all cases the simulation provides an accurate description
of the data and is used to correct for selection and resolution
effects.

The systematic uncertainties on the cross section measurements are
discussed briefly below (see \cite{bpthesis,andrei} 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
uncorrelated between the cross section measurements unless stated
otherwise.

\begin{itemize}

\item An uncertainty of $1\%~(z_{imp}<+20{\rm cm})$, $2\%~(+20{\rm
  cm}<z_{imp}<+100{\rm cm})$ and $3\%$ for $z_{imp}>+100{\rm cm})$ is
  assigned to the scale of the electromagnetic energy measured in the
  LAr calorimeter, where $z_{imp}$ is the z co-ordinate of the impact
  position of the scattered lepton in the LAr calorimeter. $0.5\%$ of
  this uncertainty is considered as a correlated component.
    
\item An uncertainty of $0.5\%$ for $\theta_e<100^{\circ}$ and $2\%$ for
  $\theta_e>100^{\circ}$ in the identification of the scattered
  electron or positron.

\item An uncertainty in the polar angle measurement of the scattered
  lepton is taken to be $2$~mrad for $\theta_e>120^{\circ}$ and
  $3$~mrad elsewhere.

\item An uncertainty of $2\%$ is assigned to the scale of the hadronic energy
  measured in the detector, of which $1\%$ is considered as a
  correlated component to the uncertainty. 
    
\item A $10\%$ correlated uncertainty is assigned to the amount of energy
  in the LAr calorimeter attributed to noise.
  
\item A $1$\% uncertainty on the trigger efficiency.
  
\item A $30\%$ correlated 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 combined uncertainty of finding an interaction vertex and
  associating a track to the scattered lepton is estimated to be
  $3\%$ for the $e^+p$ data and $2\%$ for the $e^-p$ data uncorrelated
  from point to point.

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

\item An error of $1\%$ 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 An uncertainty of $z$ dependence of the proton bunch
  structure is estimated to be $0.5\%$.

\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.

\item In addition, there is a global uncertainty of $2.1\%$
  on the luminosity measurement for both the $R$ and $L$ $e^{\pm}p$
  data samples.

\end{itemize}
%
The total systematic error is formed by adding the individual
uncertainties in quadrature.

\section{Results}

The measured cross sections $\frac{{\rm d}\sigma}{{\rm d}Q^2}$ for
$y<0.9$ are shown in Figs.~\ref{dsdq2ele} and~\ref{dsdq2pos} for
$e^+p$ and $e^-p$ scattering respectively. The data are measured in
the range $Q^2\geq 200$~GeV$^2$ up to $Q^2\simeq 20\,000$~GeV$^2$ over
which the cross sections fall by almost six orders of magnitude with
increasing $Q^2$. The cross sections are found to be similar at low
$Q^2$ for both lepton charges and polarisations, however at the
highest $Q^2$ differences are observed between the $e^+p$ and $e^-p$
cross sections arising from the structure function $x{\tilde
F}_3$. The data from both polarised samples are combined together and
corrected for the remaining residual polarisation to provide a
measurement of the unpolarised cross sections. These are shown in
Figs.~\ref{dsdq2eleunpol} and~\ref{dsdq2posunpol}.

The measured data are compared to the Standard Model expectation from
the H1 PDF 2009 fit~\cite{h1pdf2009} which provides an excellent
description of the $Q^2$ dependence of the data including
the difference between the $e^+p$ and $e^-p$ cross sections.

The comparisons of the measured unpolarised single differential cross
sections to various Standard Model predictions using different sets of
PDFs are shown in Figs.~\ref{dq2ratele} and~\ref{dq2ratpos}. It can be seen that
the H1 PDF 2009 expectations reproduce the shape of the steeply
falling cross sections very well for both $e^-p$ and $e^+p$
scattering. However, the prediction is approximately $3-4\%$ larger
than the measurements as shown in
Figs.~\ref{dq2ratele} and~\ref{dq2ratpos}(a). The total correlated normalisation
uncertainty is shown as dashed blue line on the inset figures and is
$\pm2.1\%$. Comparisons to Standard Model expectations using the
HERAPDF1.0 set of PDFs are shown in Figs.~\ref{dq2ratele} and~\ref{dq2ratpos}(b)
and are able to accurately describe both shape and normalisation of
the cross sections in $e^-p$ and $e^+p$ scattering. Also shown are the
predictions using the CTEQ6m PDFs which predict approximately $3-4\%$
smaller cross sections than are measured.  At the very highest $Q^2$
the $e^-p$ measurements have a tendency to overshoot the predictions
albeit with large statistical uncertainties.

In order to improve the statistical precision of the measurements
these cross sections are combined with previoulsy published HERA-I
measurements from H1~\cite{h19497,h19899,h1hiq2} using the statistical
combination procedure 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{dq2ratelefull} and~\ref{dq2ratposfull}
where again it can be seen that the expectation from H1 PDF 2009 is
approxmimately $2-3\%$ larger than the combined measurements and the
CTEQ6m PDFs predict a cross section approximately $2-3\%$ lower than
the measurements whereas the HERAPDF1.0 PDFs provide a very good
description of the shape and normalisation of the cross sections.

The Standard Model also predicts a difference in the cross section for
leptons with different helicity states arising from the chiral
structure of the neutral electroweak exchange. With longitudinally
polarised lepton beams in HERA-II such polarisation effects can be
tested, providing a direct measure of electroweak effects in the
neutral current cross sections. The polarisation asymmetry, $A$, is defined as

\begin{equation} 
\label{apm}
A = \frac{2}{P_R-P_L} \cdot \frac{\sigma^{\pm}(P_R) -\sigma^{\pm}(P_L)}
                          {\sigma^{\pm}(P_R) +\sigma^{\pm}(P_L)}\,\,\,.
\end{equation}

To a very good approximation $A$ measures the structure function ratio
\begin{equation}  \label{fgf}
        A^\pm
%        \simeq  \mp \kappa   a_e \frac{F_2^{\gamma Z}}{(F_2 + \kappa
%         a_e Y_- xF_3^{\gamma Z}/Y_+)}
         \simeq \mp  k a_e \frac{F_2^{\gamma Z}}{F_2}
\end{equation}
which is proportional to combinations $a_e v_q$ and is thus
a direct measure of parity violation. In positron scattering
$A$ is expected to be positive and about equal to $-A$ in electron scattering.
At large $x$  the asymmetry measures
the $d/u$ ratio of the valence quark distributions according to
\begin{equation} \label{doveru}
           A^\pm   \simeq  \pm  k \frac{1+d_v/u_v}{4+d_v/u_v}.
\end{equation}

The polarised single differential cross sections ${\rm d}\sigma/{\rm
d}Q^2$ from HERA-II are used to construct the asymmetry where it is
assumed that the correlated uncertainties of each measurement
cancel. The asymmetry is shown in Fig.~\ref{asymm} compared to the
Standard Model expectation from H1 PDF 2009. The magnitude of the
asymmetry is observed to increase with increasing $Q^2$ and is
negative in $e^-p$ and positive in $e+p$ scattering. The data are in
good agreement with the Standard Model expectation using H1 PDF 2009
and confirm the violation of parity in the neutral current channel.

The measurements are also presented as double differential reduced
cross sections, $\tilde{\sigma}_{NC}(x,Q^2)$ for $e^-p$ and $e^+p$
scattering in Figs.~\ref{xq2ele} and~\ref{xq2pos} respectively. The cross
sections are measured over the $Q^2$ range $150$ to $30\,000$ GeV$^2$
and over the $x$ range $0.0032$ to $0.65$. The cross sections have a
typical precision of $3\%$ for $Q^2<1\,000$~GeV$^2$ and are
statistically limited at higher $Q^2$. In $e^-p$ scattering the $L$
sample yeilds a cross section that is enhanced with respect to the $R$
sample whereas the reverse is true in $e^+p$ data. The H1 PDF 2009
prediction describes the $x$ dependance of the measured cross sections
well.

In Fig.~\ref{xq2unpol} the polarised reduced cross section
measurements are combined to produce an unpolarised measurement
corrected for the residual polarisation. These cross sections are
shown in Fig.~\ref{xq2unpol} for $e^{\pm}p$ scattering. At low $Q^2$
the two measurements are consistent with one another, however as the
$Q^2$ increases toward and beyond the Electroweak scale a clearly
increasing discrepancy between the $e^-p$ and $e^+p$ cross sections is
observed, consistent with the Standard Model expectation. Positron
scattering is suppressed with respect to electron scattering through
the increasing contribution of the structure function $x\tilde{F}_3$.

In order to improve precision the double differential cross section
measurements are combined with previously published measurements from
HERA-I~\cite{h19497,h19899,h1hiq2} using the same method as described
in~\cite{h1lowestq2}. The combined double differential cross sections
can be seen in Fig.~\ref{xq2unpolall} for the $Q^2$ range above
$150$~GeV$^2$. Again the, influence of $Z^0$ is clearly visible and is
shown for $Q^2>1\,000$~GeV$^2$ in Fig.\ref{xq2unpolhiq2}.

The structure functions $x{\tilde F}_3$ may be
obtained using the equation
\begin{eqnarray}
x{\tilde F}_3 = \frac{Y_+}{2Y_-}\left[\tilde{\sigma}^-(x,Q^2)-\tilde{\sigma}^+(x,Q^2)\right]
\label{extractxf3} 
\end{eqnarray} 

and is shown in Fig.~\ref{xf3} for all measured $x,~Q^2$ bins. In the context of the Standard Model it can be seen from
Eq.~\ref{SF1} that the dominant contribution to $x{\tilde F}_3$ arises
from the $\gamma Z$ interference term, since the pure $Z$ exchange
term is suppresed by an additional factor of $\kappa Q^2/(Q^2+M_Z^2)$
and, in the case of unpolarised scattering, the small vector coupling
$v_e$. Thus $x{\tilde F}_3^{\gamma Z}$ may be determined using the approximation
\begin{equation}
xF^{\gamma Z}_3 \simeq x{\tilde F}_3 \frac{(Q^2+M_Z^2)}{a_e \kappa Q^2}
\label{extractxf3gz} 
\end{equation} 
neglecting terms proportional to $v_e$. The data are shown in
Fig.~\ref{xf3gz} for the region of $x$ and $Q^2$ where the expected
sensitivity is larger than the normalisation uncertainty of the data.

This non-singlet structure
function has a weak $Q^2$ dependence and 
is also shown from the H1 PDF 2000 fit. Since the dependence
is weak, the data from each $Q^2$ are transformed to one $Q^2$ value at $1\,500$
GeV$^2$ and then averaged. The combination of extracted $xF^{\gamma
Z}_3$ data for all $Q^2$ values is shown in Fig.~\ref{xf3gz1500} and is
directly sensitive to the valence quark distributions. The Standard
Model prediction is also shown and found to be in excellent agreement
in both shape and magnitude with the data.

\section{Summary}
The NC cross sections ${\rm d}\sigma/{\rm d}Q^2$ have been measured
for $e^{\pm}p$ scattering with longitudinally polarised lepton beams
at HERA. The polarisation asymmetry is measured and data are found to
be consistent with the predicted behaviour of the polarised $ep$
scattering in the Standard Model. The cross sections are combined with
earlier published H1 measurements using the complete HERA data set.

The double differential NC cross sections
${\tilde\sigma}^{\pm}(x,Q^2)$ have been measured at high $Q^2$ for
$e^{\pm}p$ scattering. The data are combined with existing H1
measurements yielding H1 unpolarised cross section measurements using
the entire HERA I+II data set. An extraction of the structure
functions $x{\tilde F}_3$ and $xF_3^{\gamma Z}$ has been
performed. The data are in good agreement with expectation of the
Standard Model.

\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.

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\clearpage

%%%%%%%%%%%%%%%%%%%% 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-09-042.fig1a.eps,width=\textwidth}}
\put(-30,  0){\epsfig{file=H1prelim-09-042.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}

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


\clearpage

%%%%%%%%%%%%%%%%%%%% Fig.2: NC control plot %%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htb]
\begin{center}
\begin{picture}(90,200)(0,0)
\setlength{\unitlength}{1 mm}
\put(-15,100){\epsfig{file=H1prelim-09-042.fig2a.eps,height=10.5cm}}
\put(-15, -5){\epsfig{file=H1prelim-09-042.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)~$E_e^{\prime}$, (b,f)~$\theta_e$,
  (c,g)~$Q_e^2$ and (d,h)~$P_{T,h}/P_{T,e}$ shown in upper and lower
  plots for the selected events in the (a-d) $e^-p$ and (e-h) $e^+p$
  data sets. The Monte Carlo (MC) contributions from the neutral
  current (NC) process and the $ep$ background (bkg) processes are
  shown as open histograms with the latter contribution alone being
  shown as shaded histograms. In these plots the left and right handed
  samples are combined for each lepton charge.}
\label{nc}
\end{figure}

\clearpage

%%%%%%%%%%%%%%%%%%%% Fig.3: cross sections vs.Q2 e-  %%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htbp]
\begin{center}
\begin{picture}(90,200)(0,0)
\setlength{\unitlength}{1 mm}
\put(-30,100){\epsfig{file=H1prelim-09-042.fig3a.eps,width=\textwidth}}
\put(-30,-10){\epsfig{file=H1prelim-09-042.fig3b.eps,width=\textwidth}}
\put( 20,194){\bf (a)}
\put( 20, 85){\bf (b)}
\end{picture}
\end{center}
\caption{
The $Q^2$ dependence of the NC cross section ${\rm d}\sigma/{\rm
d}Q^2$ for $e^-p$ scattering with the (a) right handed $(R)$ and (b)
left handed $(L)$ polarisation data sets. The data (solid points) are
compared to the Standard Model prediction.
}
\label{dsdq2ele}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\clearpage

%%%%%%%%%%%%%%%%%%%% Fig.4: cross sections vs.Q2 e-  P=0 %%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htbp]
\begin{center}
\begin{picture}(90,100)(0,0)
\setlength{\unitlength}{1 mm}
\put(-30,0){\epsfig{file=H1prelim-09-042.fig4.eps,width=\textwidth}}
\end{picture}
\end{center}
\caption{
The $Q^2$ dependence of the NC cross section ${\rm d}\sigma/{\rm
d}Q^2$ for $e^-p$ unpolarised scattering. The data (solid points) are
compared to the Standard Model prediction.
}
\label{dsdq2eleunpol}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\clearpage

%%%%%%%%%%%%%%%%%%%% Fig.5: cross sections vs.Q2 e+ %%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htbp]
\begin{center}
\begin{picture}(90,200)(0,0)
\setlength{\unitlength}{1 mm}
\put(-30,100){\epsfig{file=H1prelim-09-042.fig5a.eps,width=\textwidth}}
\put(-30,-10){\epsfig{file=H1prelim-09-042.fig5b.eps,width=\textwidth}}
\put( 20,194){\bf (a)}
\put( 20, 85){\bf (b)}
\end{picture}
\end{center}
\caption{
The $Q^2$ dependence of the NC cross section ${\rm d}\sigma/{\rm
d}Q^2$ for $e^+p$ scattering with the (a) right handed $(R)$ and (b)
left handed $(L)$ polarisation data sets. The data (solid points) are
compared to the Standard Model prediction.
}
\label{dsdq2pos}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\clearpage

%%%%%%%%%%%%%%%%%%%% Fig.6: cross sections vs.Q2 e+  P=0 %%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htbp]
\begin{center}
\begin{picture}(90,100)(0,0)
\setlength{\unitlength}{1 mm}
\put(-30,0){\epsfig{file=H1prelim-09-042.fig6.eps,width=\textwidth}}
\end{picture}
\end{center}
\caption{
The $Q^2$ dependence of the NC cross section ${\rm d}\sigma/{\rm
d}Q^2$ for $e^+p$ unpolarised scattering. The data (solid points) are
compared to the Standard Model prediction.
}
\label{dsdq2posunpol}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


\clearpage



%%%%%%%%%%%%%%%%%%%% Fig.7: ds/dQ2 ratios e-  %%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htbp]
\begin{center}
\begin{picture}(90,200)(0,0)
\setlength{\unitlength}{1 mm}
\put(-30,100){\epsfig{file=H1prelim-09-042.fig7a.eps,width=\textwidth}}
\put(-30, 0) {\epsfig{file=H1prelim-09-042.fig7b.eps,width=\textwidth}}
\put( -3,190){\bf (a)}
\put( -3, 90){\bf (b)}
\end{picture}
\end{center}
\caption{
  The $Q^2$ dependences of the unpolarised NC cross section ratio
  ${\rm d}\sigma/{\rm d}Q^2$ for $e^-p$ scattering using PDFs obtained from (a) H1 PDF 2009 and (b) HERAPDF1.0.
  In addition the comparisons using CTEQ6m PDFs are also indicated. The data (solid points) are compared to the Standard
  Model prediction (green band).  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 on the inset
  figures.  }
\label{dq2ratele} 
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\clearpage


%%%%%%%%%%%%%%%%%%%% Fig.8: ds/dQ2 ratios e+  %%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htbp]
\begin{center}
\begin{picture}(90,200)(0,0)
\setlength{\unitlength}{1 mm}
\put(-30,100){\epsfig{file=H1prelim-09-042.fig8a.eps,width=\textwidth}}
\put(-30, 0) {\epsfig{file=H1prelim-09-042.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 unpolarised NC cross section ratio
  ${\rm d}\sigma/{\rm d}Q^2$ for $e^+p$ scattering using PDFs obtained from (a) H1 PDF 2009 and (b) HERAPDF1.0.
  In addition the comparisons using CTEQ6m PDFs are also indicated. The data (solid points) are compared to the Standard
  Model prediction (green band).  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 on the inset
  figures.  }
\label{dq2ratpos} 
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


\clearpage

%%%%%%%%%%%%%%%%%%%% Fig.9: ds/dQ2 e-  unpol HERA-I+II  %%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htbp]
\begin{center}
\begin{picture}(90,200)(0,0)
\setlength{\unitlength}{1 mm}
\put(-30,100){\epsfig{file=H1prelim-09-042.fig9a.eps,width=\textwidth}}
\put(-30, 0) {\epsfig{file=H1prelim-09-042.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 unpolarised combined HERA-I+II NC cross sections 
  ${\rm d}\sigma/{\rm d}Q^2$ for $e^-p$ scattering using PDFs obtained from (a) H1 PDF 2009 and (b) HERAPDF1.0.
  In addition the comparisons using CTEQ6m PDFs are also indicated. The data (solid points) are compared to the Standard
  Model prediction (green band).  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{dq2elefull} 
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\clearpage


%%%%%%%%%%%%%%%%%%%% Fig.10: ds/dQ2 e+  unpol HERA-I+II %%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htbp]
\begin{center}
\begin{picture}(90,200)(0,0)
\setlength{\unitlength}{1 mm}
\put(-30,100){\epsfig{file=H1prelim-09-042.fig10a.eps,width=\textwidth}}
\put(-30, 0) {\epsfig{file=H1prelim-09-042.fig10b.eps,width=\textwidth}}
\put( -3,190){\bf (a)}
\put( -3, 90){\bf (b)}
\end{picture}
\end{center}
\caption{
  The $Q^2$ dependences of the unpolarised combined HERA-I+II NC cross sections
  ${\rm d}\sigma/{\rm d}Q^2$ for $e^+p$ scattering using PDFs obtained from (a) H1 PDF 2009 and (b) HERAPDF1.0.
  In addition the comparisons using CTEQ6m PDFs are also indicated. The data (solid points) are compared to the Standard
  Model prediction (green band).  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{dq2posfull} 
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\clearpage


%%%%%%%%%%%%%%%%%%%% Fig.11: ds/dQ2 ratios e-  unpol HERA-I+II  %%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htbp]
\begin{center}
\begin{picture}(90,200)(0,0)
\setlength{\unitlength}{1 mm}
\put(-30,100){\epsfig{file=H1prelim-09-042.fig11a.eps,width=\textwidth}}
\put(-30, 0) {\epsfig{file=H1prelim-09-042.fig11b.eps,width=\textwidth}}
\put( -3,190){\bf (a)}
\put( -3, 90){\bf (b)}
\end{picture}
\end{center}
\caption{
  The $Q^2$ dependences of the unpolarised combined HERA-I+II NC cross section ratio
  ${\rm d}\sigma/{\rm d}Q^2$ for $e^-p$ scattering using PDFs obtained from (a) H1 PDF 2009 and (b) HERAPDF1.0.
  In addition the comparisons using CTEQ6m PDFs are also indicated. The data (solid points) are compared to the Standard
  Model prediction (green band).  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 on the inset
  figures.  }
\label{dq2ratelefull} 
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\clearpage


%%%%%%%%%%%%%%%%%%%% Fig.12: ds/dQ2 ratios e+  unpol HERA-I+II %%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htbp]
\begin{center}
\begin{picture}(90,200)(0,0)
\setlength{\unitlength}{1 mm}
\put(-30,100){\epsfig{file=H1prelim-09-042.fig12a.eps,width=\textwidth}}
\put(-30, 0) {\epsfig{file=H1prelim-09-042.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 unpolarised combined HERA-I+II NC cross section ratio
  ${\rm d}\sigma/{\rm d}Q^2$ for $e^+p$ scattering using PDFs obtained from (a) H1 PDF 2009 and (b) HERAPDF1.0.
  In addition the comparisons using CTEQ6m PDFs are also indicated. The data (solid points) are compared to the Standard
  Model prediction (green band).  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 on the inset
  figures.  }
\label{dq2ratposfull} 
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\clearpage


%%%%%%%%%%%%%%%%%%%% Fig.13: Asymmetry %%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htbp]
\begin{center}
\begin{picture}(90,110)(0,0)
\setlength{\unitlength}{1 mm}
\put(-35, -10){\epsfig{file=H1prelim-09-042.fig13.eps,width=\textwidth}}
\end{picture}
\end{center}
\caption{
  The $Q^2$ dependence of the polarisation asymmetry $A$, for $e^{+}p$
  (red circles) and $e^{-}p$ (blue squares). The data (solid points)
  are compared to the Standard Model prediction (full lines). 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{asymm} 
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\clearpage

%%%%%%%%%%%%%%%%%%%% Fig.14: Double diffl e- pol  %%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htbp]
\begin{center}
\begin{picture}(90,200)(0,0)
\setlength{\unitlength}{1 mm}
\put(-35, -10){\epsfig{file=H1prelim-09-042.fig14.eps,width=\textwidth}}
\end{picture}
\end{center}
\caption{
  The reduced cross section $\tilde{\sigma}_{NC}$ in $e^-p$ scattering
  for $R$ (filled sqaures) and $L$ (open circles) polarised
  samples. 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}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\clearpage

%%%%%%%%%%%%%%%%%%%% Fig.15: Double diffl e+ pol  %%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htbp]
\begin{center}
\begin{picture}(90,200)(0,0)
\setlength{\unitlength}{1 mm}
\put(-35, -10){\epsfig{file=H1prelim-09-042.fig15.eps,width=\textwidth}}
\end{picture}
\end{center}
\caption{
  The reduced cross section $\tilde{\sigma}_{NC}$ in $e^+p$ scattering
  for $R$ (filled sqaures) and $L$ (open circles) polarised
  samples. 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}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


\clearpage

%%%%%%%%%%%%%%%%%%%% Fig.16: Double diffl e+ & e-  Unpol HERA-II  %%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htbp]
\begin{center}
\begin{picture}(90,200)(0,0)
\setlength{\unitlength}{1 mm}
\put(-35, -10){\epsfig{file=H1prelim-09-042.fig16.eps,width=\textwidth}}
\end{picture}
\end{center}
\caption{
  The reduced cross section $\tilde{\sigma}_{NC}$ in unpolarised
  $e^{\pm}p$ scattering. 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{xq2unpol} 
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\clearpage

%%%%%%%%%%%%%%%%%%%% Fig.17: Double diffl e+ & e-  Unpol ALL HERA  %%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htbp]
\begin{center}
\begin{picture}(90,200)(0,0)
\setlength{\unitlength}{1 mm}
\put(-35, -10){\epsfig{file=H1prelim-09-042.fig17.eps,width=\textwidth}}
\end{picture}
\end{center}
\caption{
  The reduced cross section $\tilde{\sigma}_{NC}$ in unpolarised
  $e^{\pm}p$ scattering using the complete HERA I+II dataset. 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{xq2unpolall} 
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\clearpage

%%%%%%%%%%%%%%%%%%%% Fig.18: Double diffl e+ & e-  Unpol ALL HERA  High Q2 bins %%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htbp]
\begin{center}
\begin{picture}(90,150)(0,0)
\setlength{\unitlength}{1 mm}
\put(-35, -10){\epsfig{file=H1prelim-09-042.fig18.eps,width=\textwidth}}
\end{picture}
\end{center}
\caption{
  The reduced cross section $\tilde{\sigma}_{NC}$ in unpolarised
  $e^{\pm}p$ scattering using the complete HERA I+II dataset for $Q^2$
  above $1\,000$~GeV$^2$. 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{xq2unpolhiq2} 
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\clearpage

%%%%%%%%%%%%%%%%%%%% Fig.19: Double diffl xF3 all bins %%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htbp]
\begin{center}
\begin{picture}(90,150)(0,0)
\setlength{\unitlength}{1 mm}
\put(-35, -10){\epsfig{file=H1prelim-09-042.fig19.eps,width=\textwidth}}
\end{picture}
\end{center}
\caption{
  The structure function $x\tilde{F}_3$ evaluated using HERA-I and
  HERA-II data is shown (solid points) compared to the Standard Model
  expecation from H1 PDF 2009(solid curve). The inner error bars
  represent the statistical uncertainties and the outer error bars
  represent the total errors which includes the normalisation
  uncertainty.}
\label{xf3} 
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%%%%%%%%%%%%%%%%%%%% Fig.20: Double diffl xF3gZ all bins %%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htbp]
\begin{center}
\begin{picture}(90,150)(0,0)
\setlength{\unitlength}{1 mm}
\put(-35, -10){\epsfig{file=H1prelim-09-042.fig20.eps,width=\textwidth}}
\end{picture}
\end{center}
\caption{
  The structure function $xF_3^{\gamma Z}$ extracted from all HERA-I
  and HERA-II data (solid points) is shown together with the Standard
  Model expectation from H1 PDF 2009 (solid curve). The inner error bars
  represent the statistical uncertainties and the outer error bars
  represent the total errors which includes the normalisation
  uncertainty.}
\label{xf3gz} 
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


\clearpage

%%%%%%%%%%%%%%%%%%%% Fig.21: xF3gZ at Q2=1500 %%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htbp]
\begin{center}
\begin{picture}(90,150)(0,0)
\setlength{\unitlength}{1 mm}
\put(-35, -10){\epsfig{file=H1prelim-09-042.fig21.eps,width=\textwidth}}
\end{picture}
\end{center}
\caption{
  The structure function $xF_3^{\gamma Z}$ extracted from all HERA-I
  and HERA-II data (solid points) and transformed to
  $Q^2=1\,500$~GeV$^2$ is shown together with the Standard Model
  expectation from H1 PDF 2009 (solid curve) and HERAPDF 1.0 (shaded
  band). The inner error bars represent the statistical uncertainties
  and the outer error bars represent the total errors which includes
  the normalisation uncertainty.}
\label{xf3gz1500} 
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%



\end{document}


