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\begin{document}

\pagestyle{empty}
\begin{titlepage}

\noindent
% {\bf H-UM \& JS: version of \today} \\[.3em] 
Submitted to the 30th International Conference on 
High-Energy Physics ICHEP2000, \\ 
Osaka, Japan, July 2000


\vspace*{3cm}

\begin{center}
  \Large
  {\bf 
    Inclusive Measurement of Deep Inelastic Scattering at high
    {\boldmath $Q^2$} in Positron-Proton Collisions at HERA }

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

\begin{abstract}

\noindent
  The inclusive $e^+ p$~single and double differential cross-sections
  for neutral and charged current processes are measured with the H1
  detector at HERA. The data were
  taken in 1999 and 2000 at a centre-of-mass energy of $\sqrt{s}=320$
  GeV and and correspond to an integrated
  luminosity of $45.9 \ {\rm pb}^{-1}$. 
  The cross-sections are measured in the range of
  four-momentum transfer squared $Q^2$ between $150$ and $30\,000$
  GeV$^2$, and Bjorken $x$ between $0.0032$ and $0.65$.
  These are compared to previous H1 results based on $35.6 \pb^{-1}$
  of data taken in 1994 to 1997 at $\sqrt{s} = 300$ GeV.
  The new measurements are found to be fully consistent with previous
  ones and well described by next-to-leading order QCD fits in the
  framework of the Standard Model. 
\end{abstract}


\vfill
\begin{flushleft}
  {\bf Abstract: 975 } \\
  {\bf Parallel session: 7b} \\
  {\bf Plenary talk: 11 } 
\end{flushleft}

\end{titlepage}

\pagestyle{plain}

\section{Introduction}

\noindent
Inclusive Deep Inelastic Scattering (DIS) cross-sections are 
sensitive to the proton structure and QCD dynamics.
Since 1992 the experiments H1 and ZEUS have used the colliding
lepton--proton beams of the HERA accelerator to extend considerably the
phase space of such measurements into new kinematic regions of large
four-momentum transfer squared, $Q^2$, and small $x$, where $x$ is the
Bjorken scaling variable. The large integrated luminosity collected by
the experiments has allowed measurements to be made in the very high
$Q^2$ range up to $30\,000$ GeV$^2$. In this region where $Q^2 \simeq
M_Z^2$ or $M_W^2$, the $Z^0$ and $W^{\pm}$ boson masses squared, the effects of the
electroweak sector of the Standard Model can be tested in DIS. In addition
signals of new physics beyond the Standard Model may be expected to
arise at the highest $Q^2$ where the smallest distance scales of proton
structure are probed.

Both contributions to DIS, neutral current (NC) interactions,
\mbox{$ep \rightarrow eX$}, and charged current (CC) interactions,
\mbox{$ep \rightarrow \nu X$} can be measured at HERA and give
complementary information on the QCD and electroweak parts of the
Standard Model. The cross-sections are defined in terms of two of the
kinematic variables $Q^2$, $x$, and $y$, where $y$ quantifies the
inelasticity of the interaction.
%\begin{equation}
%Q^2 = -q^2\equiv(k-k')^2
%\hspace*{1.1cm}
%x  = \frac{Q^2} {2 p \cdot q}
%\hspace*{1.1cm}
%y = \frac{p \cdot q} {p \cdot k},
%\hspace*{1.1cm}
%s \equiv (p+k)^2 = Q^2/xy
%\end{equation}
%where $k (k^{'})$ and $p$ are the four-momenta of the incident
%(scattered) lepton and proton, and where the proton and lepton rest
%masses are neglected. 
%The quantity $-Q^2$ is the four-momentum
%transfer squared, $x$ is the Bjorken scaling variable, $y$ specifies
%the inelasticity, and $\sqrt{s}$ is the $ep$ centre-of-mass energy of
%the $ep$ interaction. 

%Measurements by the fixed target experiments
%span the $x$ range $0.01$ to $0.9$ and up to a maximum $Q^2$ of $250$
%\Gevv.  Previous measurements by the HERA experiments, H1 and ZEUS,
%extend to lower values of $x \approx\ 10^{-5}$ at low $Q^2$, and at
%higher $x$ to $Q^2$ of $5000$ \Gevv~\cite{H194,ZEUS94}. 

%The measurements presented in this paper extend the $Q^2$ range to
%$30\,000$ \Gevv.
%high four-momentum transfer
%squared, $Q^2$, and low Bjorken $x$. 

Measurements of the NC and CC cross-sections in $e^+p$ scattering 
have been made by H1 and ZEUS based on the data taken in 1994 to 
1997 \cite{h1hiq2,zeushiq2} when the $ep$
centre-of-mass energy $\sqrt{s}$ was about $300$ GeV. 
Here new $e^+p$ NC and CC
cross-section measurements based on data taken at an increased
centre-of-mass energy of $320$ GeV in 1999 and 2000 are
presented \footnote{The increase in centre-of-mass energy is due to an
increase in the proton beam energy from $E_p=820$ GeV to $920$ GeV in
1998}. The luminosity of this data set is $45.9$ pb$^{-1}$.

The new data are compared to those from 1994-1997. In particular the region
of high $Q^2$ is interesting since a slight excess of NC events 
over the Standard
Model expectation was observed in 1994 to 1996 for $Q^2 > 15\,000$
GeV$^2$ \cite{h1exc,zeusexc}. The NC and CC cross-sections in 1999-2000
are combined with the data from 1994-1997 taking into account the difference 
in centre-of-mass energy. The measurements are compared to the Standard Model
expectations. 

%This paper is divided into 5 sections. In section 2 the data and
%event selection are described. The calibration procedure
%is given in section 3, and the cross-section measurements and
%comparisons are presented in section 4. In section 5 the paper is
%summarised.


\section{Neutral and Charged Current Cross-Sections}

The NC cross-section for the process $e^+p\rightarrow e^+X$
with unpolarised beams is given by
%
\begin{eqnarray}
\label{Snc1}
%\left(
\frac{{\rm d}^2\sigma_{NC}}{{\rm d}x\;{\rm d}\QQ}
%\right)_{Born}
& = & \frac{2\pi \alpha^2}{xQ^4}    
%\left(\frac{1}{\QQ}\right)^2  \hspace*{0.2cm} 
%\phi_{NC}^{\pm}(x,Q^2) 
%\left[Y_+ \Ftwo (x,\QQ ) \pm Y_{-}x\Fz (x,\QQ )-y^2 \FL (x,\QQ )\right] 
\left[Y_+ \Ftwo - Y_{-}x\Fz -y^2 \FL \right]\;\;\;, 
%(1+\delta_{NC}^{qed})
%+\delta_{NC}^{weak}).
\end{eqnarray}
%where
%\begin{eqnarray}
%\label{Snc}
%\phi_{NC}^{\pm}(x,Q^2) & = & 
%Y_+ \Ftwo (x,\QQ ) \pm Y_{-}x\Fz (x,\QQ )-y^2 \FL (x,\QQ ) .
%\end{eqnarray}
%
where $\alpha$ is the fine structure constant taken to be $\alpha  
\equiv \alpha(Q^2=0)$ and the helicity dependencies of the electroweak 
interactions are contained in the functions \ $Y_{\pm} \equiv 1 \pm 
(1-y)^2$. The dominant contribution to the cross-section comes from  
the structure function \Ftwo. The \FL\ contribution is largest at high  
$y$ and is expected to diminish with increasing $Q^2$, whereas the  
structure function $x$\Fz\ contributes in the high  $Q^2$ regime of   
$Z^0$ exchange. 

It is convenient make use of the NC ``reduced 
cross-section'' in which the $Q^2$  
dependence due to the photon propagator is removed
\begin{equation}
\label{Rnc}
\tilde{\sigma}_{NC}(x,Q^2) \equiv  \frac{1}{Y_+} \ 
\frac{ Q^4 \ x  }{2 \pi \alpha^2}
\          \frac{{\rm d}^2 \sigma_{NC}}{{\rm d}x{\rm d}Q^2}\;\;\;.
\end{equation}
Note that \FL\ and $x$\Fz\ can be neglected over most of the kinematic range
of this measurement such that the reduced cross-section is given
essentially by
\Ftwo. Only at high $y$ and high $Q^2$ the contributions from \FL\ and
$x$\Fz\ become important. In these regions the reduced cross-section differs
for different centre-of-mass energies while in most of the kinematic
range it is independent of the beam energies. 

The leading order double differential CC cross-section 
for $e^+p \rightarrow \nu X$ can be written as 
\begin{equation}
\frac{{\rm d}^2\sigma_{CC}}{{\rm d}x\;{\rm d}\QQ} =
 \frac{G_F^2}{2\pi x } \left(\frac{M_W^2}{M_W^2+Q^2} \right)^2 
x \left [ (\bar{u}+\bar{c})+(1-y)^2(d+s) \right ]\;\;\;, 
\label{Scc}
\end{equation}
where $G_F$ is the Fermi coupling constant, and $\bar{u}$, $\bar{c}$,
$d$, $s$ are the quark distributions. 
%zhang The description of $e^+p
%zhang \rightarrow \bar{\nu} X$ is obtained by changing all quarks with
%zhang anti-quarks (and vice-versa) in eq.~\ref{Scc}. 
The CC reduced cross-section is defined as
\begin{equation}
\label{Rcc}
\tilde{\sigma}_{CC}(x,Q^2) \equiv  
\frac{2 \pi  x}{ G_F^2}
\left( \frac {M_W^2+Q^2} {M_W^2} \right)^2
          \frac{{\rm d}^2 \sigma_{CC}}{{\rm d}x{\rm d}Q^2}\;\;\;.
\end{equation}

\section{Experimental Technique}

%\subsection{Detector and Simulation}
\subsection{Detector and Kinematic Reconstruction}
The H1 detector is described in detail elsewhere~\cite{h1detector}.
The co-ordinate system of H1 defines the positive $z$ axis to be in
the direction of the incident proton beam. The polar angle $\theta$ is
then defined with respect to the positive $z$ axis. The forward
direction is the region of increasing $z$. 

In order to determine acceptance corrections and background
contributions for the DIS cross-section measurements, the detector
response to events produced by various Monte Carlo generation programs
is simulated in detail, and is described in ref.~\cite{h1hiq2}.
The present analysis closely follows that of ref.~\cite{h1hiq2}. 
The NC event kinematics are reconstructed
using the energy and polar angle of the scattered electron,
$E^{\prime}_e$ and $\theta_e$ respectively.  The total $E-p_z$ of the
event is then obtained from the relation $E{\rm-}p_z = \Sigma
+E^{\prime}_e(1-\cos{\theta_e})$. Here $\Sigma=\sum_i{(E_i-p_{z,i})}$,
where the summation is performed over all hadronic final state
particles.  These quantities are used to determine the kinematic
variables $x$, \qsq, and $y$ in the $e\Sigma$ method~\cite{esigma}:
\begin{equation}
  y_{e\Sigma} = 2 E_e \frac{\Sigma}{(E{\rm-}p_z)^2} 
  \hspace*{1.5cm}
  Q^2_{e\Sigma} = \frac{P_{T,e}^2}{ 1-y_e} 
  \hspace*{1.5cm}
  x_{e\Sigma} = \frac{P_{T,e}^2}{s \ y_{\Sigma} (1-y_{\Sigma})}\;\;\;,
  \label{kinematics1}
\end{equation}
where $E_e$ is the incident electron beam energy, and
\begin{equation}
  y_{\Sigma} = \frac{\Sigma} {E{\rm-}p_z}
  \hspace*{1cm}
  y_e =1- \frac {E_e^{'} (1-\cos{\theta_e})} {2 \ E_e}
  \hspace*{1cm}
  P_{T,e} = E^{\prime}_e \sin{\theta_e}\;\;\;.
\end{equation}

The resolution of the reconstruction method is controlled by requiring
the purity and stability of any ($x$, \qsq) bin to be larger than $30\%$.
The stability (purity) is defined as the fraction of events which
originate from a bin and which are reconstructed in it, divided by the
number of generated (reconstructed) events in that bin.  
%In addition
%the acceptance is required to be more than $20\%$ in any bin, where
%the acceptance is the ratio of events reconstructed in a bin to the
%number of events generated in that bin.

The CC event kinematics can only be determined with the hadron method
($h$ method)~\cite{jbmethod}. 
The $h$ method kinematic variables are reconstructed using the
relations
\begin{equation}
   y_{h} = \frac{\Sigma}{ 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 $P_{T,h}=\sqrt{(\sum_i{p_{x,i}})^2+(\sum_i{p_{y,i}})^2}$ and is
summed over all particles of the hadronic final state. This method is
influenced by particle losses in the beam pipe and fluctuations of the
detector response to hadronic final state particles, and therefore has
moderate precision.

%\subsection{Detector Calibration}
%The electromagnetic calibration of the detector performed on the 1997
%high statistics data in~\cite{h1hiq2} is applied to the current data
%set. The same calibration procedure is then repeated for the
%individual calorimeter modules where there are sufficient statistics.
%The new calibration constants are found to be within $1\%$ of those
%determined in 1997. The systematic uncertainty of the absolute
%electromagnetic energy scale varies from 1\% in the backward region to
%3\% in the forward region of the calorimeter.

%The hadronic response of the detector is calibrated in a two step
%procedure after first applying the calibration of~\cite{h1hiq2}. In
%the first step the simulation is used to determine a $z$ dependant
%energy correction to high $E_t$ jets. The corrections show a marked
%$z$ dependence following the 

% Then jets with $P_T\geq 5$ GeV are used to determine
%$z$ dependant energy correction factors with the calibrated electron
%energy as the reference scale. Finally the hadronic $P_T$.....

\subsection{Measurement Procedure}

%\subsection{Selection of NC events}
High \qsq NC events are selected by requiring that the event has a
compact electromagnetic cluster, taken to be the scattered electron,
in addition to a vertex position within $\pm 35$ cm of its nominal
position. The cluster is validated by requiring that an extrapolated
track have a distance of closest approach to the cluster of less than
$12$ cm. This loose cluster-track matching requirement is 
only applied for $\theta_e\geq 40^{\circ}$, where
$\theta_e$ is the polar angle of the scattered electron. In this
analysis the polar angle is determined using the position of the
electromagnetic cluster and assigned a systematic uncertainty of $3$
mrad.  The energy of the cluster, $E_e^{\prime}$, is required to be
larger than $11$ GeV where the trigger efficiency is greater than
$99.5\%$. The total
$E-P_z$ summed over all particles is required to be larger than $35$
GeV to reduce the photo-production background, and the influence of
QED radiative corrections to the measured cross-sections.  Fiducial
cuts are also made to remove local regions where the electromagnetic
shower of the scattered electron is not fully contained in the
calorimeter, and where the trigger is not fully efficient. Since the
signal to background ratio is reduced in the region of high $y$, a
further kinematic cut is made requiring $y_e \leq 0.9$. The remaining
photo-production contribution to the NC cross-sections is never more
than 5\% at the highest $y$ and negligible elsewhere. The double
differential NC reduced cross-section data have a statistical
precision of $\approx$ 2\% at low \qsq compared to a total systematic
uncertainty of $\approx$ 4\%. At the highest $x$ the statistical error
increases to about 20\% and the 
systematic errors to about 10\%. The total
uncertainty is dominated by the statistical error for $Q^2>1\,000$
GeV$^2$. The final sample of selected data consists of about $130\,000$
events. The comparison of the data and the simulation is shown in
fig.\ref{nc_cont} for the scattered electron energy spectrum, and the
polar angle $\theta_e$.  Both distributions are well described by the
simulation.

%\subsection{Selection of CC events}
The selection of CC events is based on the expectation that such
events have a large missing transverse momentum, $P_{T,h}$, assumed to
be carried by an unseen neutrino. Therefore a requirement that
$P_{T,h}\geq 12$~GeV is made. In addition the event must have a
reconstructed vertex within $\pm 35$ cm of its nominal position. The
non-$ep$ and $ep$ background is rejected using the same method as
detailed in~\cite{h1hiq2}. The remaining $ep$ background is dominantly
due to photo-production events and is negligible for most of the
measured kinematic domain, though it may reach up to 3\% at
$Q^2=500\,{\rm GeV}^2$.  The contribution is subtracted statistically
from the CC data sample with a systematic uncertainty of 30\% of the
subtracted events. In order to restrict the measurement to a region
where the kinematic reconstruction is optimal the events are required
to have $y_h<0.85$. The CC trigger efficiency is determined using NC
events in which all information associated to the scattered electron
is suppressed. This method gives a precise measure of
the efficiency which is found to be $78\%$ at $Q^2=500\,{\rm GeV}^2$
and reaches 99\% at $Q^2=5000\,{\rm GeV}^2$.  The measurement is
restricted to the region where the trigger efficiency is acceptable by
demanding $y_h>0.03$. After all selection criteria are
applied, the final CC data sample contains about 1000 events. The data 
and simulation are compared in fig.\ref{cc_cont} for the $P_{T,h}$ and
$y_h$ spectra. In both cases the simulation gives a good description
of the data.

The electromagnetic and hadronic response of the detector is
calibrated using NC events similar to the analysis described 
in~\cite{h1hiq2}. The procedure is found to give good agreement between
data and simulation. The systematic uncertainty of the absolute electromagnetic energy
scale varies from 1\% in the backward region to 3\% in the forward
region of the calorimeter. For the hadronic energy scale a
conservative uncertainty of 3\% is assigned. 

The selected events are corrected for detector acceptance, and
migrations using the simulation and converted to bin centred
cross-sections using the prediction from the NLO QCD
fit~\cite{h1hiq2}. The cross-sections are corrected for the effects of 
QED radiation.

%\subsection{Systematic Uncertainties}
%The following systematic uncertainties were considered:
%\item An error of $1-3$ \% on the electromagnetic energy scale;
%\item an error of $3$ \% on the hadronic energy scale;
%\item an error of $25$ \% on the subtracted noise contribution;
%\item an error of $3$ mrad on the electron scattering angle; 
%\item an error of $30$ \% on the normalisation of the photoproduction
%  background; 
%\item an error of $0.5$ ($2-7$) \% on the trigger efficiency in the NC
%  (CC) analysis;
%\item an error of $1$ \% on the track-link efficiency in the NC analysis;
%\item an error of $2-5$ \% on the vertex efficiency only in the CC
%  analysis; 
%\item an error on the $V_

\subsection{Combination with previous measurements}
The new data are combined with the previously published 94-97 $e^+p$
data in order to improve the statistical precision which is the dominant
error source for $Q^2>1\,000$ GeV$^2$ in the NC cross-section and at all $Q^2$
in the CC cross-section.

For this combination the 94-97 data are
scaled to the new centre-of-mass energy using the prediction from the
NLO QCD fit \cite{h1hiq2}. 
The combined measurement of any measured cross-section
$\sigma_i$ is then given by 
$$\sigma_{i}=\frac{\sigma^{meas}_{i,820} \cdot {\cal L}^{820}+
\sigma^{meas}_{i,920} \cdot {\cal  L}^{920}}
{{\cal L}^{820}\cdot(\sigma^{th}_{i,820}/\sigma^{th}_{i,920})+{\cal L}^{920}}$$

where $\sigma^{meas}_{i,E_p}$ and $\sigma^{th}_{i,E_p}$
are the measured and theoretical cross-sections at a proton energy $E_p$
respectively. 
The statistical error is determined correspondingly 
and the systematic error is assumed to be $100 \%$ correlated between
the two data sets and conservatively taken from the 99-00 data
set. These combined data correspond to a luminosity of $81.5$
pb$^{-1}$. 

For the NC reduced cross-sections the correction factor for the beam energy
is relatively small. For $Q^2<5000$ GeV$^2$ it is only required
for the lowest $x$ bins and is always smaller than $2$ \%. The largest
correction of about $10$ \% is required at the highest $Q^2$ and low
$x$. For the CC reduced cross-section it varies between $5$ \% at low
$Q^2$ and $20$ \% at high $Q^2$.
For the cross-sections $\rd \sigma /\rd Q^2$ the correction factor is
about $5\%$ at low $Q^2$ and $50 \%$ at the highest $Q^2$.

\section{Results}

\subsection{Cross-section measurement}

The reduced $e^+p$ NC cross-section is shown in fig. \ref{nc_stamp}
where the results from the new measurement at $\sqrt{s}=320$ GeV
 are compared to the ones obtained at $\sqrt{s}=300$ GeV.
Both sets of measurements are seen to provide comparable precision and
are found to be fully compatible.
Both data sets also
agree well with the prediction of the NLO QCD fit which is also
indicated. This  NLO QCD fit was
performed on low $Q^2$ fixed target data from NMC \cite{nmc} and BCDMS
\cite{bcdms} and the previous H1 high $Q^2$ $e^+p$ data from 1994-1997.
It is shown for the two different centre-of-mass
energies of the two data sets. 

%The reduced NC cross-sections measured at $\sqrt{s}=300$ GeV and
%$\sqrt{s}=320$ GeV are shown in
%fig.\ref{fig:nc_hix4}a,b as a function
%of $Q^2$ for the two highest $x$ values. The two data sets are
%found to be in agreement with each other and with the expectation from
%the NLO QCD fit. 
%In fig.\ref{fig:nc_hix4}c,d the combined result of all 1994 to 2000 $e^+p$ data
%is shown. The H1 data are also
%compared to the precise data from fixed-target experiments BCDMS, NMC and SLAC
%\cite{slac}.
%The strong fall of the cross-section with
%$Q^2$ due to the scaling violations is observed over more than four
%orders in magnitude.  
%At $Q^2=20\,000$ GeV$^2$ and $x=0.4$ the new data are below the
%expectation from the NLO QCD fit while the 94-97 measurement exceeded
%the expectation. The combined result from all $e^+p$ data shows no
%significant deviation from the expectation except for a slight deficit
%at $Q^2=12\,000$ GeV$^2$ and a slight excess above expectation at
%$Q^2=30\,000$ GeV$^2$.

%The $Q^2$ dependence of the reduced NC cross-section is also shown in
%fig. \ref{fig:nc_hix} for $x \geq 0.08$ for the 94-00 data. Also shown are
%the measurements at lower $Q^2$ by the fixed-target experiments
%BCDMS and NMC and from H1 at lower $Q^2$ \cite{h1lowq2}. 
%It is seen that the QCD Fit provides a good description
%of the $Q^2$ dependence for all data sets in the valence quark
%region. At $x=0.4$ overlap between the H1 data and the fixed-target data
%is achieved. At the highest $Q^2$ a decrease of the cross-section is
%expected due to the negative $\gamma Z$ interference in $e^+p$
%scattering. This decrease is clearly seen in the data at $x=0.18$ and
%$x=0.25$. 

The reduced NC cross-sections measured at $\sqrt{s}=300$ GeV and
$\sqrt{s}=320$ GeV are shown in
fig.\ref{fig:nc_hixc} as a function
of $Q^2$ for the high $x$ region. The two data sets are
found to be in agreement with each other and with the expectation from
the NLO QCD fit. Shown are also the recent H1 measurement at lower
$Q^2$ \cite{h1lowq2} and the fixed-target data from BCDMS and NMC.
%The strong fall of the cross-section with
%$Q^2$ due to the scaling violations is observed over more than four
%orders in magnitude.
The strong scaling violation is observed over more than four orders of
magnitude in $Q^2$.
At the highest $Q^2$ a decrease of the cross-section is
expected due to the negative $\gamma Z$ interference in $e^+p$
scattering. This decrease is clearly seen in the data at $x=0.18$ and
$x=0.25$. 
At $Q^2=20\,000$ GeV$^2$ and $x=0.4$ the new data undershoot the
expectation from the NLO QCD fit while the measurement in 1994-1997 exceeded
the expectation. In fig. \ref{fig:nc_hix} the combined results from the
data from 1994 to 2000 is shown. 
While some structure is noticed the combined result from all $e^+p$ data shows no
significant deviation from the expectation.
%zhang except for a slight deficit
%zhang at $Q^2=12\,000$ GeV$^2$ and a slight excess above expectation at
%zhang $Q^2=30\,000$ GeV$^2$. 


Shown in fig. \ref{cc_stamp} is the reduced CC cross-section for the new
data and the data in 1994-1997. It is seen that those data are
also consistent within the statistical errors. The
kinematic range for the cross-section measurement could be slightly
extended at high and low $x$ mainly due to an improved trigger 
efficiency and hadronic
calibration. The combined result is shown in fig. \ref{cc_stampcomb} 
and is found to be in good agreement with
the theoretical prediction from the NLO QCD fit. The 
contribution to the CC reduced cross-section from the $d$-quark
density is also shown. This illustrates that the CC cross-section at high $x$ is
mainly sensitive to the $d$ quark (see eq.~3). The precision of the CC
cross-section at $x=0.4$ from all data 1994-2000 is about $20$ \%. 

The single differential NC cross-section ${\rm d}\sigma/\rm{ d}Q^2$ for
$e^+p$ data is shown in fig.\ref{dsdq2nc}(a) for $y\leq 0.9$.
\footnote{These measured NC cross-sections are corrected for the small
  effect of the cut $E_e^{\prime}>11$ GeV. Similarly the CC
  cross-sections are corrected for the cuts $0.03<y<0.85$} The new data
are compared to the H1 $e^+p$ measurements based on data in 1994-1997
and the NLO QCD fit.  The new preliminary cross-sections are higher than the 
measurement from 1994-1997 due to the increase in centre-of-mass energy. 

Figures \ref{dsdq2nc} (b) show the ratios of the
measurements to their corresponding Standard Model expectation. 
The global 1.5 \% luminosity uncertainty of the new data is not included
in the error 
bars.  The Standard Model uncertainty represents the uncertainty of
the expectation due to assumptions made in the NLO QCD fit, as
well as the uncertainties of the experimental data entering the fit,
and is detailed in~\cite{h1hiq2}. Here it is seen that the new data
agree well with the published data. 
%Only at $Q^2=20\,000$ GeV$^2$ where
%the 94-97 data slightly exceed the expectation a deficit is seen in the
%new data. 
Shown in \ref{dsdq2nc} (c) is the ratio of the combined 
$e^+p$ cross-section from 1994 to 2000 
to the Standard Model and the data exhibit a similar feature as seen in 
fig. \ref{fig:nc_hix}.
%with a slight deficit at
%$Q^2=12\,000$ GeV$^2$ and a slight excess at $Q^2=30\,000$ GeV$^2$. 

The $Q^2$ dependence of the CC cross-section is shown in fig.\ref{dsdq2cc}(a) and
compared to the previous measurements.  Again the effect of the
increased centre-of-mass energy is seen resulting in a higher
cross-section for the new data set. The ratio of data to expectation 
is shown in fig.\ref{dsdq2cc}(b) together with the Standard Model
uncertainty. The two data sets agree well with each other and with the
expectation from the Standard Model. The ratio of the combined 94-00
measurement is also shown in fig. \ref{dsdq2cc}(c).

The $Q^2$ dependence of the NC and CC cross-sections are compared in
fig. \ref{fig:dsdq2nccc} for the combined 94-00 data. 
At low $Q^2$ the NC cross-section is about 1000 times larger than the
CC cross-section since the CC cross-section is suppressed due to the
propagator term in eq. \ref{Scc}. At the highest values of $Q^2$ they
are of similar size as expected from the Standard Model.

%The integrated $x$ dependence of the NC and CC cross-sections are shown in
%fig.\ref{nc_dsdx}. The data are
%shown for $Q^2>1\,000$ GeV$^2$ and $y<0.9$ in fig.\ref{nc_dsdx}a,b and are in
%agreement with the expectation from the Standard Model and with the
%94-97 data. The combined cross-sections from 94-97 data and 99/00 data
%are shown in fig.\ref{nc_dsdx}c,d. 

\subsection{Valence quark distributions at high $Q^2$ and high $x$}

The new combined $e^+p$ double differential NC and CC cross-sections
together with the $e^-p$ NC and CC cross-sections measured previously
based on the data taken in years from 1998 to 1999~\cite{h1e-9899} 
are used in a NLO QCD fit to determine the dominant valence quark 
distributions $xu_v$ and $xu_d$ at high $Q^2$ and high $x$. 
The fit is performed using the NLO DGLAP evolution equations~\cite{dglap} 
in the $\overline{\rm MS}$ factorization scheme and treating the heavy flavours
as massless quarks. In addition to the two valence quarks, gluon,
{\it up}-type and {\it down}-type sea quarks are parameterised at $Q^2_0=15\,{\rm GeV}^2$
in an MRS like 
form $A_qx^{B_q}(1+x)^{C_q}(1+a_qx^{b_q})$~\cite{mrst} with $b_q=1/2$ for the
valence quarks and $b_q=1$ for the rest of quark components.
The usual sum rules are imposed.
In order to have a reliable constraint on the gluon and sea quarks, 
the new H1 low $Q^2$ data~\cite{h1lowq2} are also included. The minimum
$Q^2$-cut on the data is $Q^2_{\rm min}=20$ ${\rm GeV}^2$. 

The resulting valence quark densities of this fit are shown 
in fig. \ref{fig:xuxd} labelled ``NLO QCD Fit: H1 only''
with the estimated uncertainty. The result is
compared to other parameterisations MRST~\cite{mrst},
CTEQ5~\cite{cteq5}, and the previous H1 fit~\cite{h1hiq2} which all used 
fixed target data of BCDMS~\cite{bcdms} and NMC~\cite{nmc}.
The uncertainty on the parton densities was estimated from the experimental 
errors on the 
data following the prescription given in~\cite{zomer}. The relative 
precision on the $u$ valence varies between 6\% for $x=0.25$ and 10\% for 
$x=0.65$. The $d$ valence is essentially constrained by the 
$e^+p$ CC data only and has a precision of about 20\%.
The fit agrees with the other parameterisations within the errors at
all values of $x$ shown for both $xu_v$ and $xd_v$ except for $xu_v$ at
$x=0.65$ where it is $\sim 17\%$ lower than the
other parameterisations with little dependence in the range of $Q^2$ shown.
The difference remains within about two standard
deviations. The uncertainty on the valence quark densities comes solely
from the high $Q^2$ data as no difference was found in the central value 
or the uncertainty when raising the $Q^2_{min}$ cut to $200$ GeV$^2$ 

Also shown in the figure are the valence quark densities determined with 
the local extraction method which was introduced in the previous 
publication~\cite{h1hiq2} and is defined again here:
\begin{equation}
xq_v(x,Q^2)=\sigma_{\rm meas}(x,Q^2)\left(\frac{xq_v(x,Q^2)}{\sigma(x,Q^2)}\right)_{\rm para}\,,
\end{equation}
where $\sigma_{\rm meas}(x,Q^2)$ is the measured NC or CC double differential
cross-sections, and the second factor on the right-hand-side of the equation
is the theoretical
expectation from the previous H1 fit~\cite{h1hiq2}. Only those points
where the $xq_v$ contribution is greater than 70\% of the total cross section
are selected. The extracted parton densities are thus rather independent of 
the theoretical input as the uncertainty on the dominant valence quark 
contribution and that of the corresponding cross-section largely cancel 
in the ratio. 
The extracted valence quark densities combining $\sigma^{e^\pm p}_{\rm NC}$
and $\sigma^{e^-p}_{\rm CC}$ represent an improved statistical
precision of typically 50\% and up to 100\% at high $Q^2$ compared to
using the 1994 to 1997 $e^+p$ data only. 
The local measurements are in good agreement with the global fit.

\section{Summary}
The NC and CC cross-sections have been measured for $e^+p$ scattering
at a centre-of-mass energy of $\sqrt{s} \approx 320$ GeV.  Standard
Model expectations based on the NLO QCD fit to NMC, BCDMS, and
H1 94-97 $e^+p$ data~\cite{h1hiq2} are able to provide a good description of
all the measured cross-sections. 

Comparisons of these cross-sections with the H1 measurements of
NC and CC cross-sections in $e^+p$ scattering from 94-97 data which were
taken at a centre-of-mass energy of $\sqrt{s} \approx 300$ GeV are made.
The influence of the different centre-of-mass energy is seen in the $\rd
\sigma / \rd Q^2$ cross-section which is about $5$ \% higher at low
$Q^2$ and $50$ \% at the highest $Q^2$. This difference is in agreement
with the Standard Model expectation. 

The double differential NC reduced cross-sections are measured in the
\qsq range $200 \leq Q^2 \leq 30\,000$ GeV$^2$, and $0.0032 \leq x
\leq 0.65$. The new data agree well with the measurements from
94-97. 

The double differential CC reduced cross-sections are measured in the 
\qsq range $300 \leq Q^2 \leq 15\,000$ GeV$^2$, and $0.008 \leq x
\leq 0.4$. The new data agree well with the theoretical
prediction and with the 94-97 measurements. 
Since the dominating error is statistical for the CC
cross-section the precision is improved from about 30 \% to 20 \% for
each data point when combining the 99/00 data with those from 94-97. 

A new NLO QCD fit was performed using all available cross-sections measured
by H1. It is seen for the first time that the valence quark distributions
$xu_v$ and $xd_v$ can be separately constrained from the HERA high $Q^2$ data
alone with an experimental precision of about 10\% and 20\% respectively for 
$xu_v$ and $xd_v$ at $x=0.65$ and $x=0.4$. The $u$ valence quark density is 
found to be about $17$ \% lower than the other parameterisations using 
the fixed target data.
The parton densities determined with the local extraction method are in good
agreement with the global QCD fit. 

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

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H1 Collab., C. Adloff et al., Eur. Phys. J. {\bf C13} (2000) 609-639 ,   08/99 
\bibitem{zeushiq2} 
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\bibitem{h1exc}   
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\bibitem{zeusexc}
  ZEUS Collab., J. Breitweg et al., Z. Phys. {\bf C74} (1997) 207.
\bibitem{h1detector}
H1 Collab., I.~Abt et al., \Journal{\NIMA}{386}{1997}{310 and 348}.
\bibitem{esigma} 
  U. Bassler and G. Bernardi, Nucl. Instr. Meth. {\bf A361} (1995) 197; \\
  U. Bassler and G. Bernardi,  Nucl. Instr. Meth. {\bf A426} (1999) 583.

\bibitem{jbmethod}
A.~Blondel and F.~Jacquet, Proceedings of the Study of an $ep$ Facility for
Europe, ed. U.~Amaldi, DESY 79/48 (1979) 391.

\bibitem{bcdms} BCDMS Collab., A.C. Benvenuti et al., 
Phys. Lett. {\bf B223} (1989) 485.
\bibitem{nmc} NMC Collab., M. Arneodo et al.,
Phys. Lett. {\bf B364} (1995) 107.
\bibitem{slac} E. D. Bloom et al., Phys. Rev. Lett. {\bf 23} (1969) 930;\\
M. Breitenbach et al., Phys. Rev. Lett. {\bf 23} (1969) 935.
\bibitem{h1lowq2} H1 Collab., Conf. Paper 944, 30th Intern. Conf. on
High-Energy Physics, Osaka, Japan (2000), July 2000

\bibitem{h1e-9899} H1 Collab., Conf.\ Paper 971, 30th Intern.\ Conf.\ on
High-Energy Physics, Osaka, Japan (2000), July 2000 

\bibitem{dglap}L.~N.~Lipatov, {\em Sov.\ J.\ Nucl.\ Phys.}\ {\bf 20} (1975)
 95; V.~N.~ Gribov and L.~N.~Lipatov, {\em Sov.\ J.\ Nucl.\ Phys.}\ {\bf 15}
 (1972) 438; G.~Altarelli and G.~Parisi, {\em Nucl.\ Phys.}\ {\bf B126}
 (1977) 298; Yu.~L.~Dokshitzer {\em Sov.\ Phys.\ JETP} {\bf 46} (1977) 641.
\bibitem{zomer} C. Pascaud and F. Zomer, LAL preprint, LAL/95-05 (1995)
\bibitem{mrst}A.~D.~Martin {\it et al}., {\em Eur.\ Phys.\ J.}\ {\bf C4} 
 (1998) 463; hep-ph/9803455.

\bibitem{cteq5}See e.g. CTEQ Collab., H.~L.~Lai {\it et al}., 
{\em Phys.\ Rev.}\ {\bf D}55 (1997) 1280; hep-ph/9701256, 
hep-ph/9903282.

\end{thebibliography}
\newpage
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htb]   
\begin{center} 
\begin{picture}(140,122.5)(0,0)
\setlength{\unitlength}{1 mm}
\put( 0, -10){\epsfig{file=H1prelim-00-152.fig1.eps,width=14cm}}
\put(25,97){\bf (a)}
\put(25,35){\bf (b)}
\put(83,35){\bf (c)}
\end{picture}
\end{center}    
\caption{Distributions of (a) $\theta_e$ and $E_e^{\prime}$ for (b)
  $Q^2>200$ GeV$^2$ and (c) $Q^2>5000$ GeV$^2$
  (solid points) and simulation (solid line). The lower histograms
  show the photo-production contribution.}
\label{nc_cont}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htb]   
\begin{center} 
\begin{picture}(140,55)(0,0)
\setlength{\unitlength}{1 mm}
\put(10,-10){\epsfig{file=H1prelim-00-152.fig2.eps,bbllx=40,bblly=260,bburx=520,bbury=520,width=12cm}}
\put(55,25){\bf (a)}
\put(113,25){\bf (b)}
\end{picture}
\end{center}    
\caption{Distributions of (a) $P_{T,h}$ and (b) $y_h$ for CC data 
  (solid points) and simulation (solid line). The lower histograms
  show the photo-production contribution.}
\label{cc_cont}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[hhh]
\center
%\epsfig{file=fig/f2.eps,width=15cm}
\epsfig{file=H1prelim-00-152.fig3.eps,bbllx=48,bblly=30,bburx=550,bbury=780,width=14cm}
\caption{The NC $e^+p$ reduced cross-section
  $\tilde{\sigma}_{NC}$ is compared to the NLO QCD fit. Shown are
  the 99-00 and the 94-97 measurements and the NLO QCD Fit predictions
  for the different centre-of-mass energies. The
  inner error bars represent the statistical error, and the outer error
  bars show the total error.}

\label{nc_stamp} 
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\begin{figure}[hhh]
%\setlength{\unitlength}{1 mm}
%\begin{center}
%\begin{picture}(160,160)(0,0)
%\epsfig{file=H1prelim-00-152.fig4.eps,width=15cm}
%\put(-130,110){\bf (a)}
%\put(-55,110){\bf (b)}
%\put(-130,30){\bf (c)}
%\put(-55,30){\bf (d)}
%\end{picture}
%\end{center}
%\caption{The NC reduced cross-section $\tilde{\sigma}_{NC}$ is
%  shown at $x=0.4$ and $x=0.65$ compared to the NLO QCD fit. Fig. (a) and (b)
%  show $\tilde{\sigma}_{NC}$ both the new 99-00 data and the
%  94-97 data. Fig. c) and d) show the result from all $e^+p$ data
%  (94-00). The inner error bars represent the statistical error, and the
%  outer error bars show the total error.}
%\label{fig:nc_hix4} 
%\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[hhh]
\setlength{\unitlength}{1 mm}
\begin{center}
\begin{picture}(160,160)(0,0)
\put(-3,-12){
\epsfig{file=H1prelim-00-152.fig4.ps,bbllx=40,bblly=70,bburx=530,bbury=730,,width=15cm}}
\end{picture}
\end{center}
\caption{The NC reduced cross-sections $\tilde{\sigma}_{NC}$ from the
  combined 94-97 and 99-00 data are shown at
  high $x$ compared to the NLO QCD fit. Also shown are data from
  the fixed-target experiments BCDMS and NMC. The solid (dashed) curve 
  represents
  the Standard Model expectation based on the NLO QCD fit for
  $\sqrt{s}=320$ GeV ($\sqrt{s}=300$ GeV). The
  inner error bars represent the statistical error, 
and the outer error bars show the total error.}
\label{fig:nc_hixc} 
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[hhh]
\epsfig{file=H1prelim-00-152.fig5.ps,bbllx=40,bblly=70,bburx=530,bbury=730,width=15cm}
\caption{The NC reduced cross-section $\tilde{\sigma}_{NC}$ from the
  combined 94-00 data is shown at
  high $x$ compared to the NLO QCD fit. Also shown are data from
  the fixed-target experiments BCDMS and NMC. The solid curves represent
  the Standard Model expectation based on the NLO QCD fit. The
  inner error bars represent the statistical error, 
and the outer error bars show the total error.}
\label{fig:nc_hix} 
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[hhh]
\center \epsfig{file=H1prelim-00-152.fig6.ps,bbllx=40,bblly=140,bburx=560,bbury=660,width=15cm}
\caption{The CC reduced cross-section $\tilde{\sigma}_{CC}(x,Q^2)$
  is shown for $e^+p$ scattering for the new data from 1999-2000
  at $\sqrt{s} \approx 320$ GeV (solid
  squares) and the data from 1994-1997 at $\sqrt{s} \approx 300$ GeV
  (open squares). The data are compared to the NLO QCD fit with the full and
  dashed curves showing respectively for $\sqrt{s} \approx 320$ GeV and
  $\sqrt{s} \approx 300$ GeV. The
  inner error bars represent the statistical error, and the outer
  error bars show the total error. }  \label{cc_stamp}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[hhh]
\center \epsfig{file=H1prelim-00-152.fig7.ps,bbllx=40,bblly=140,bburx=560,bbury=660,width=15cm}
\caption{The CC reduced cross-section $\tilde{\sigma}_{CC}(x,Q^2)$
  for $e^+p$ scattering is shown for the combined data from 94-00 at
  $\sqrt{s} \approx 320$ GeV. The data are compared to the NLO QCD fit. The
  inner error bars represent the statistical error, and the outer
  error bars show the total error. }  \label{cc_stampcomb}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[h*]
\setlength{\unitlength}{1 mm}
\begin{center}
\begin{picture}(160,185)(0,0)

\put(15,-10){\epsfig{file=H1prelim-00-152.fig8.ps,bbllx=94,bblly=73,bburx=500,bbury=720,height=19cm}}
\put(34,128){\bf (a)}
\put(34,66){\bf (b)}
\put(34,20){\bf (c)}
\end{picture}
\end{center}
\caption{The $Q^2$ dependence of NC cross-sections $d\sigma/dQ^2$ is
  shown for the new preliminary $e^+p$ (solid points) and published
  94-97 $e^+p$ (open points) measurements. The data are compared to the
  Standard Model expectation determined from the NLO QCD fit. The dashed 
  line corresponds to a centre-of-mass energy of $\sqrt{s}=300$ GeV the
  full for $\sqrt{s}=320$ GeV.
  The ratio of the
  94-97 and 99-00 data to their respective Standard Model expectation is shown 
  in figure (b). In fig. (c) the ratio of the combined 94-00 NC
  cross-section to the Standard Model is shown. The Standard Model
  uncertainty is shown as the shaded band. The 1.5\% luminosity uncertainty
  is not included in the error bars.} 
\label{dsdq2nc}

\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[h*]
\setlength{\unitlength}{1 mm}
\begin{center}
\begin{picture}(160,185)(0,0)

\put(15,-10){\epsfig{file=H1prelim-00-152.fig9.ps,bbllx=94,bblly=73,bburx=500,bbury=720,height=19cm}}
\put(34,128){\bf (a)}
\put(34,70){\bf (b)}
\put(34,26){\bf (c)}
\end{picture}
\end{center}
\caption{The $Q^2$ dependence of CC cross-section $d\sigma/dQ^2$ is
  shown for the new preliminary $e^+p$ (solid points) and published
  94-97 $e^+p$ (open points) measurements. The data are compared to the
  Standard Model expectation determined from the NLO QCD fit. The dashed 
  line corresponds to a centre-of-mass energy of $\sqrt{s}=300$ GeV the
  full for $\sqrt{s}=320$ GeV. The ratio of the
  94-97 and 99-00 data to their respective Standard Model expectation is shown 
  in figures (b). In fig. (c) the ratio of the combined 94-00 CC
  cross-section to the Standard Model is shown. The Standard Model
  uncertainty is shown as the shaded band. The 1.5\% luminosity uncertainty
  is not included in the error bars.} 
\label{dsdq2cc}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[h*]
\setlength{\unitlength}{1 mm}
\begin{center}
\begin{picture}(160,160)(0,0)


\put(0,0){\epsfig{file=H1prelim-00-152.fig10.ps,bbllx=40,bblly=150,bburx=550,bbury=660,height=16cm}}
\end{picture}
\end{center}
\caption{The $Q^2$ dependence of the NC (circles) and CC (squares) 
  cross-sections $d\sigma/dQ^2$ is shown for the combined 94-00 
  $e^+p$ measurements. The data are compared to the
  Standard Model expectations determined from the NLO QCD fit
  including the 94-97 H1 $e^+p$ data. The 1.5\% luminosity uncertainty
  is not included in the error bars.} 
\label{fig:dsdq2nccc}
\end{figure}
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\begin{figure}[htbp]
\begin{center}
\begin{picture}(50,160)
\put(-65,-50){\epsfig{file=H1prelim-00-152.fig11.ps,bbllx=0pt,bblly=0pt,
bburx=594pt,bbury=842pt,width=190mm}}
\end{picture}
\end{center}
\caption{The valence quarks distributions $xu_v$ and $xd_v$ determined 
both with the NLO QCD fit (shaded error bands) using all cross-section
measurements from H1 only and with the local 
extraction method (data points with the inner and full error bars showing 
respectively the statistical and total errors) in comparison with other 
parameterizations which used fixed target data at low $Q^2$.}
\label{fig:xuxd}
\end{figure}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\begin{figure}[hhh]
%\setlength{\unitlength}{1 mm}
%\begin{center} 
%\begin{picture}(160,120)(0,0)
%\put( 10, 0){\epsfig{file=fig/dsigdxnc.hqn.both.eps,width=15cm}}
%\put( 35,85){\bf (a)}
%\put( 85,85){\bf (b)}
%\put( 35,50){\bf (c)}
%\put( 85,50){\bf (d)}
%\end{picture}
%\end{center}
%\caption{The NC cross-sections $d\sigma/dx$ for the preliminary $e^-p$ data are shown in (a) for $Q^2>1\,000$ GeV$^2$ and in (c) for $Q^2>10\,000$ GeV$^2$. The H1 $e^+p$ cross-sections are shown in (b) and (d) for $Q^2>1\,000$ GeV$^2$ and $10\,000$ GeV$^2$ respectively. The solid curves show the Standard Model expectation based on the NLO QCD fit. The dashed curves show the contribution of photon exchange only. All cross-sections are shown for $y<0.9$.}
%\label{nc_dsdx} 
%\end{figure}
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%\begin{figure}[hhh]
%  \center \epsfig{file=fig/dsigdxcc.hqn.both.eps,width=15cm}
%\caption{The CC cross-section $d\sigma/dx$ for $Q^2>1\,000$ GeV$^2$ and $y<0.9$ is shown for the preliminary H1 $e^-p$ data (solid points) and the H1 $e^+p$ data (open points). The solid curves show the Standard Model expectation based on the NLO QCD fit. The dashed curve shows the influence of the increased centre-of-mass energy.}
%\label{cc_dsdx} 
%\end{figure}
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\end{document}

