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%
\newcommand{\GeV}{\rm GeV}
\newcommand{\TeV}{\rm TeV}
\newcommand{\cm}{\rm cm}
\newcommand{\F}{$ F_{2}(x,Q^2)\,$}
\newcommand{\FL}{$ F_{L}(x,Q^2)\,$}
\newcommand{\Fc}{$ F_{2}\,$}
\newcommand{\gv}{~GeV$^2$}
\newcommand{\FLc}{$ F_{L}\,$}
\newcommand{\pb}{~pb$^{-1}\,$}
\newcommand{\xg}{$xg(x,Q_o^2)\,$}
\newcommand{\pdsi}{$(\partial \sigma_r / \partial \ln y)_{Q^2}\,$}
\newcommand{\pdff}{$(\partial F_2/ \partial \ln y)_{Q^2}\,$}
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\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
                & & & \\
\multicolumn{4}{l}{{\bf
                International Europhysics Conference 
                on High Energy Physics, EPS03},
                July~17-23,~2003,~Aachen} \\
                (Abstract {\bf 082} & Parallel Session & {\bf 4}) & \\
                & & & \\
\multicolumn{4}{l}{{\bf
                XXI International Symposium on  
                Lepton and Photon Interactions, LP03},
                August~11-16,~2003,~Fermilab} \\ 
                & & & \\
                \hline
 & \multicolumn{3}{r}{\footnotesize {\it
    www-h1.desy.de/h1/www/publications/conf/conf\_list.html}} \\[.2em]
\end{tabular}
\end{small}
\end{center}
\vspace*{2cm}



\begin{center}
  \Large
  {\bf
 Measurement of the Inclusive Deep Inelastic Scattering Cross Section
 at {\boldmath $Q^2 \sim 1$}~GeV$^2$ with the H1 Experiment
\\}
  \vspace*{1cm}

  {\Large H1 Collaboration \\
}
\end{center}


%%%%%
\begin{abstract}
\vspace{2cm} \noindent New data are presented of the inclusive
$ep$ scattering cross section in the kinematic region of very low
Bjorken $x$ and four-momentum transfer squared $Q^2 \sim 1$~GeV$^2$,
in the transition region from the non-perturbative to the deep-inelastic 
domain. The data were taken at HERA in the summer 2000,
with a proton beam energy of 920 GeV and an electron beam energy of 27.5 GeV.
In a dedicated HERA run, the interaction vertex was shifted by +70~cm, 
thereby accessing a region of lower $Q^2$ than at nominal vertex position. 
With a fourfold increase in statistics and new instrumentation the
accuracy of the measurement is improved as compared to previous
shifted vertex data. The cross-section measurement is used to
obtain new, preliminary data on the proton structure function \F,
and its rise towards low $x$ is studied.
\end{abstract}
%%%%%

\end{titlepage}
%
\pagestyle{plain}

\section{Introduction}
%
The region of momentum transfer squared $Q^2$ around 1~GeV$^2$
deserves particular attention because it corresponds to the transition
between the non-perturbative and the perturbative domains in deep-inelastic scattering (DIS).  Thus at HERA a special positron-proton scattering run was
performed in which the interaction vertex was shifted by about 70~cm
in the proton beam direction which allows larger positron scattering
angles\footnote{Note that the polar angles $\theta$ are defined with respect 
to the proton beam direction.} $\theta_e = \angle(\vec{e}\,',\vec{p})$ 
and thus lower values of $Q^2$ to be accessed.

The data presented here were taken in August 2000.  With a luminosity
of 0.6\pb the statistics is larger by about a factor of four as
compared to the initial shifted vertex run in 1995 which lead to
first data on the proton structure function \F in this kinematic
region, by H1~\cite{h1svx} and ZEUS~\cite{zeussvx}. 
Based on the larger statistics and
using the new Backward Silicon Tracker (BST), the accuracy of the previous 
first shifted vertex data of H1 is superseded by this analysis.

Besides extending the kinematic range to lower $Q^2$ the new shifted
vertex data also overlaps, for larger $Q^2$, with nominal vertex data
presented recently~\cite{h1bol}. These new low $Q^2$ data sets use an 
extended silicon tracker and
were obtained with a proton beam energy, $E_p$, enlarged from 820 GeV to
920 GeV.
They thus complement
the published H1 measurement~\cite{thepaper} of the inclusive neutral
current deep-inelastic scattering (DIS) cross section, $\sigma (ep
\rightarrow eX)$.   The kinematic plane and its extension with the new data
towards low $Q^2$ is illustrated in Figure~\ref{kinfull}.

The inclusive measurements determine the cross section which at low $Q^2$ 
in the one-photon exchange approximation can be written in reduced form as
%
\begin{equation}
   \frac{Q^4 x}{2\pi \alpha^2 Y_+}  \cdot \frac{d^2\sigma}{dxdQ^2}  =
 \sigma_r =        F_2(x,Q^2) - \frac{y^2}{Y_+} \cdot F_L(x,Q^2).
       \label{sig}
  \end{equation}
%
Here $y$ is the inelasticity which is related to $x$ and $Q^2$ as
$y=Q^2/sx$. The beam energies determine the centre of mass energy 
squared, $s=4E_eE_p$, and $Y_+$ is defined as
$1+(1-y)^2$.  In the region of inelasticity  below $y = 0.6$ the
contribution of the longitudinal structure function \FL is small
due to the kinematic factor $y^2/Y_+$ and since $F_L \le F_2$. 
Thus the measurement of $\sigma_r$ at lower $y$ directly determines 
\Fc with a small correction for $F_L$.

Section 2 of this paper describes the experimental methods, i.e.
the kinematic reconstruction with the H1 detector, the event
selection, simulation and calibration.  The cross-section
measurement and the extraction of the structure function \F are
discussed in Section~3 which is complemented by a study of the rise of
\F towards low $x$. A brief summary is given in Section~4.
%
%-------------------------------------------------------------
\section{Experimental Methods}
%-------------------------------------------------------------
%
\subsection{Kinematic Reconstruction with the H1 Detector}
%
The event kinematics are reconstructed using the energy $E_e'$ and the
polar angle $\theta_e$ of the scattered positron according to the
relations
\begin{equation}
y_e=1-\frac{E_e'}{E_e}~\sin^2(\theta_e/2);
 \hspace*{2cm}
Q^2_e= \frac{E^{'2}_e \sin^2{\theta_e}}{1-y_{e}}.
\label{qy}
\end{equation}
which define the electron reconstruction method. The scattered positron 
energy $E_e'$ is measured in the backward electromagnetic lead 
scintillating fibre calorimeter SPACAL \cite{Spacal}. The polar angle 
$\theta_e$ is measured in the BST \cite{vova, doris}. 
%It is defined with respect to the proton 
%beam direction, defining the $z$ axis. 
%%The BST has a configuration of 8 
%%detector planes placed perpendicularly to the beam axis,
%%each consisting of 16 concentric wafers measuring the radial hit coordinates.
%A scattered positron candidate is defined as a vertex pointing track
%associated to the highest energetic cluster in SPACAL, where the cluster 
%is required to extend by less than two Moli\`{e}re radii in the transverse 
%plane.

Since  the resolution of $y_e$ degrades as $1/y$, the
kinematics at low $ y$ are obtained using information
from the hadronic final state which is reconstructed in the Liquid
Argon calorimeter (LAr) and the SPACAL~\cite{h1detec}. This determines
the inelasticity variable $y$ to be
\begin{equation}
       y_h=\frac{\sum_{i}(E_i-p_{z,i})}{2E_e} = \frac{\sum_h}{2E_e},
       \label{yh}
\end{equation}
where $E_i$ and $p_{z,i}$ are the energy and longitudinal momentum
component of a final state particle $i$, the masses being
neglected. In the analysis $Q^2$ and $y$ are
also determined using the $\Sigma$ method which combines $E_e'$,
$\theta_e$, and $y_h$ according to
%
\begin{equation}
   y_{\Sigma} = \frac{y_h}{ 1+y_h-y_e} =
   \frac{\sum_h}{\sum_h+E_e'(1-cos \theta_e)};
   \hspace*{2cm}
   Q^2_{\Sigma} = \frac{E^{'2}_e \sin^2{\theta_e}}{ 1-y_{\Sigma}}.
   \label{ys}
\end{equation}
%
The kinematics are reconstructed using both the electron method and
the sigma method which allows the final cross section to be obtained
with optimum accuracy. For the cross section determination the
electron method is used at $y>0.05$. At $y<0.05$, where the
resolution of $y_e$ degrades, the kinematics are reconstructed with
the $\Sigma$ method.

The hadronic scattering angle is defined as
%
\begin{equation}
    \tan \frac{\theta_{h}}{2} = \frac{\sum_h}{P_{t,h}},
                       \label{thetah}
\end{equation}
%
where $P_{t,h}$ is the total transverse momentum of the hadronic final
state particles. The two angles $\theta_{e}$ and $\theta_{h}$
are used to calibrate the positron energy measurement of the SPACAL
calorimeter.

%
\subsection{Triggers and Event Selection \label{evsel}}
%
The data are triggered using the local energy sums in the SPACAL calorimeter 
with an energy threshold set to 6~GeV. Low energy deposits can also be caused 
by hadrons and photons from events at very low $Q^2\ \ll\ 1$\gv\, 
which mimic a positron signal in the SPACAL. Part of these photoproduction 
background events is recognised by tagging a scattered positron at very 
small angles in the electron tagger calorimeter upstream the positron beam.

The efficiency of all trigger elements exceeds 98\% and is
controlled by independent tracking triggers to an accuracy of
0.5\%.  From a monitor event sample, defined by a vertex
accurately reconstructed in the central tracker and by a high
energy SPACAL cluster, the BST efficiency is determined and the 
Monte-Carlo simulation correspondingly adjusted.
The hit efficiency of the BST is 97\% on average,
excluding a few malfunctioning sensor modules.

DIS events are required to have a vertex reconstructed from a track
measured in the BST and its intersection with the beam axis. The track
has to be associated to the highest energetic cluster in the SPACAL, where 
the cluster is required to extend by less than two Moli\`{e}re radii in 
the transverse plane. Any energy behind the
electromagnetic cluster measured in the hadronic SPACAL may not exceed
a small fraction of $E'$. QED radiative effects and background
contributions are suppressed requiring energy-momentum conservation
using the total $E-p_{z}$ reconstructed in the detector.
The criteria of the DIS event selection are summarised in
Table~\ref{tabcut}.
%
\begin{table}[tb] \centering
\begin{tabular}{|l|c|}
\hline
$z$ vertex position     &  $|z-70| < 45$cm           \\
SPACAL cluster radius   &  $< 4$cm                   \\
SPACAL-BST  matching     &  $\delta r < 2$cm         \\
electromagnetic SPACAL energy      & $ >$ 7~GeV      \\
hadronic SPACAL energy      &  $<$ 15\% of $E_{e}'$  \\
total $E-p_{z}$             &  $> 35$ GeV            \\
\hline
\end{tabular}
\caption{\label{tabcut} {\it Basic criteria to select DIS events.}}
\end{table}

A high statistics simulation of DIS
%and photoproduction
events is performed using the program
%, GEANT~\cite{geant},
DJANGO~\cite{django} with a parameterisation of the parton
distributions (MRST 3,75)~\cite{MRST} extended to very low $Q^2$.
For the extraction of the cross section and comparisons of
experimental with simulated spectra, a recent fit to previous low
$Q^2$ data \cite{thepaper, bpt} was used for reweighting which is
based on the fractal proton structure concept.  This
fit~\cite{tomas} describes the data in the non-perturbative region
and the data in the deep-inelastic domain very well. 
Photoproduction events are
simulated with the program PHOJET~\cite{fojet}. The simulated
events are subject to the same reconstruction and analysis chain
as the real data. In the comparisons of experimental distributions
with the Monte-Carlo spectra, these are normalised to the measured
luminosity.

The luminosity as determined from the cross section of the elastic
bremsstrahlung process is measured with a precision of 1.8\% .  
%The luminosity measurement is corrected by a few per cent for the
%occurrence of proton beam satellites which do not enter the selected
%data sample. This leads to an additional uncertainty of 1\% yielding a
%total luminosity measurement error in this analysis of 1.8\%.
%
\subsection{Alignment and Calibration}
%
The measurement of the polar angle $\theta_e$ requires the Backward
Silicon Tracker to be accurately aligned. After the internal
adjustment of the detector planes, the BST is aligned by comparing the 
interaction vertex ($z_v$) reconstructed from the electron in the BST with 
that reconstructed from hadrons in the central tracker ($z$).
A measurement accuracy of $\theta_e$ of 0.3~mrad is obtained as deduced 
from comparison of the angle measured in the BST with the one resulting from
$z_v$ and the hit position in the Backward Drift Chamber (BDC) in front of 
the SPACAL.  The SPACAL and the BDC positions are adjusted using QED Compton 
events which have the signature of back-to-back positron and photon clusters
in the plane transverse to the beam axis.

The energy scale of the electromagnetic SPACAL cells is determined
using the double angle method~\cite{sasha} in
the region of large $E' > 20$~GeV to within a remaining
uncertainty of 0.3\%. This scale was verified in the low energy
range, at about 7~GeV, to better than 2\% from a comparison of
$E'$ with the corresponding momentum $p$, measured with the BST,
and the transverse vertex position~\cite{h1bol}.  The hadronic
energy scales in the LAr calorimeter and in the SPACAL are
determined to an accuracy of 2\% and 5\%, respectively, using a
global minimisation technique~\cite{vova} for the influence of the
calorimeter constants on the transverse momentum balance for the
DIS events.  A direct verification of the electromagnetic and the
hadronic energy scale uncertainties is obtained from an extension of
the cross-section measurement, using the electron method down to very
low $y \geq 0.005$ and the sigma method up to large $y \leq 0.7$,
respectively. The resulting cross sections agree to within the
statistical accuracy.
%
%-------------------------------------------------------------------
%\section{Results}
%\section{The Cross Section and  {\boldmath $ F_2(x,Q^2)$}}
%-------------------------------------------------------------------
%
%
\subsection{Systematic Uncertainties}
%
A precise measurement of the DIS cross section requires the data to be
corrected for acceptance, inefficiency, resolution and radiative
effects. It is thus important to compare experimental and simulated
distributions.  Such control distributions are shown in
Figure~\ref{maincont}. The experimental distributions for geometric quantities,
($z_v,~\theta_e$), energy ($E_e'$) and basic kinematic variables
($x_e,~Q^2_e,~y_{\Sigma}$), are seen to be well described by the DIS
simulation. The track requirement with the BST and the momentum
conservation requirement ($E-p_z$ cut) reduce the photoproduction
background in this analysis to a very small level. Note that the
normalisation of the photoproduction simulation was adjusted by about
20\% based on the electron tagger information. The full size of this 
renormalisation factor is chosen as the uncertainty of the photoproduction 
simulation luminosity.
%

The uncertainties of this cross-section measurement are divided into
four different kinds:
\begin{itemize}
\item{The data have a normalisation uncertainty of 1.8\% resulting
    from the uncertainty of the luminosity measurement. This
    uncertainty is not included in any error bar subsequently shown.}
\item{The statistical uncertainty of the data is about 1-5\%.}
\item{An about 2\% uncorrelated cross section uncertainty is due to
    the simulated event statistics. Moreover, uncorrelated errors
    with weak kinematic dependencies result from the BST track
    reconstruction (1-2\%), from the uncertainty of the radiative
    corrections (1\%) and from the determination of the SPACAL trigger
    efficiency (0.5\%).}
\item{Correlated cross section uncertainties are due to the $E'$ and
    $E_h$ measurements (0.5-2\%), the $\theta_e$ reconstruction (1\%),
    the calorimeter noise (about 2-5\% at low $y$) and due to the
    photoproduction background (2\% at large $y$).}
\end{itemize}
%
The total cross section uncertainty is about 4\% in the bulk data
region. This is an approximately twofold increase in measurement
accuracy as compared to the previous H1 shifted vertex
data~\cite{h1svx}. Moreover, since the vertex is not anymore
reconstructed from hadrons but from the positron track in the BST, the
new data extend by one order of magnitude deeper into the low $y$
region than the 1995 data. Thus they close the kinematic gap to the
fixed target $\mu p$ data from NMC.
%
\section{Results}
%
\subsection{Cross Section and the Proton Structure Function {\boldmath $ F_2$}}
%
The kinematic region accessed in this measurement is divided into nine
$Q^2$ intervals in the range $0.3 < Q^2 < 4.2$~\gv. The data are also
divided in bins of $y$.  The binning is adapted to the resolution in
the measurement of the kinematic variables.  Bins are accepted if the
purity and stability are bigger than 30\%. Here the purity (stability)
is defined as the number of simulated events which originate from a
bin and which are reconstructed in it, divided by the number of
reconstructed (generated) events in that bin.

The measured reduced cross-section, shown in Figure~\ref{signew},
represents the most accurate low $x$ inclusive DIS data in the
transition region, $Q^2 \sim 1$~GeV$^2$, obtained so far\footnote{The
larger $x$ H1 data at $Q^2 \leq 1$~GeV$^2$ are measured using the lower
edge of the SPACAL calorimeter and of the Silicon tracker (BST) which
causes larger statistical and systematic uncertainties.}. It is seen
that the shifted vertex data agree well with the recently presented H1
1999 nominal vertex data in the region of overlap, extending the
measurement to lower $Q^2$. The new data are found to be consistent
also with data at larger Bjorken $x$, from the ZEUS measurement with
the Beam Pipe Tracker (BPT)~\cite{bpt}, placed downstream the positron
beam direction, and from the NMC Collaboration~\cite{nmc}.

The present cross-section data cover a region of inelasticity up to
$y=0.75$.  At large $y$ effects of the longitudinal structure function
may be observed leading to a taming of the cross section rise towards
low $x$. Such a behaviour is indeed observed in the data, see
Figure~\ref{signew}.  The solid curves in Figure~\ref{signew}
represent a calculation of the reduced cross section using the fractal
model~\cite{tomas} for \Fc and a dipole model calculation of
\FLc~\cite{kgb}. In this dipole model \FL, for $x=10^{-4}$, rises from
about 0.05 up to 0.2 in the range $Q^2 = 0.35 ... 3.5$~GeV$^2$ covered
by the data.  Using this prediction for \FLc, new data are obtained on
the proton structure function \F in the range $0.003 < y < 0.6$, which
are shown in Figure~\ref{f2new}. The data are in very good agreement
both with the recently published H1 data and also with the preliminary
data from a dedicated run at the end of 1999~\cite{h1bol} which used
the same BST-SPACAL detector configuration and analysis methods.

In Figure~\ref{f2new} the new \Fc data are compared with
phenomenological predictions obtained from fits to previous data.
The best description is given by the fractal model
parameterisation~\cite{tomas} (solid curves) the few parameters of
which were determined with the ZEUS BPT data~\cite{bpt} and the
published low $Q^2$ H1 data~\cite{thepaper}. The ALLM97~\cite{allm97}
parameterisation (dashed-dotted curves) similarly used previous
data which leads to an acceptable description of the present \Fc
data with a slightly stronger rise towards $x$ for $Q^2 \geq
1$\gv ~than is observed in the H1 data. Also shown is the \Fc
representation from the H1 NLO QCD fit~\cite{thepaper} (dashed
curves). The fit included only data with $Q^2 \geq 3.5$~\gv. Its
backward extrapolation is here seen to undershoot the measured
behaviour for lower $Q^2$. At $Q^2 \lesssim 1$\gv
~the strong coupling constant $\alpha_s(Q^2)$ is too large which
renders a NLO QCD comparison with data meaningless.

Another representation of this data (see Figure~\ref{f2W}) shows the
virtual photon-proton cross section, $\sigma_{\gamma^*p} \propto
F_2/Q^2$, as a function of $Q^2$ at fixed $W^2 \simeq sy$, where $W$ is
the invariant mass of the $\gamma^*p$ system. The new data fill the
gap between previous data obtained at lower and higher $Q^2$ and
reach similar accuracy. As for the previous figure the three
different parametrisations of \Fc ~are presented. At $Q^2
\simeq 1$\gv ~the ALLM97 parameterisation is too large at high $W$
and the QCD fit fails. The fractal model fit, for $Q^2 \rightarrow 0$, is
too steep to describe the total photoproduction cross-section data
(not shown here), which, however, can be cured by considering mass
effects in the fractal ansatz~\cite{tomascrac}.
%
\subsection{Rise of {\boldmath $ F_2(x,Q^2)$} Towards Low  {\boldmath $x$}}
%
Recently the H1 Collaboration has presented~\cite{h1rise} a measurement
of the derivative
%
\begin{equation}
    \left( \frac{\partial \ln F_2(x,Q^2)}{\partial \ln x}\right)_{Q^2}  \equiv
    - \lambda(x,Q^2)
\end{equation}
%
which quantifies the behaviour of the rise of \F towards low $x$ at
fixed $Q^2$. With the present data this measurement can be extended to
lower $Q^2$, as is demonstrated in Figure~\ref{lamx}. In the region of
overlap the new measurement confirms the previous data. The trend of
the derivative to be independent of $x$ at fixed $Q^2$ is seen to hold
down to about 1~\gv, the accuracy and kinematic range of the data
below this value, however, prevent definite conclusions.

The independence of the derivative \llam of $x$ implies that the $x$
dependence of \Fc at low $x$ is consistent with a power law, $F_2
\propto x^{-\lambda}$, for fixed $Q^2$, and that the rise of
\Fc, i.e. $(\partial F_2 / \partial x)_{Q^2}$, is proportional to
$F_2/x$.  As for the previously published H1 data, the exponent
$\lambda (Q^2)$ was determined from fits of the form
$F_2(x,Q^2)=c(Q^2) \cdot x^{-\lambda (Q^2)}$.  The result is shown in
Figure~\ref{lamh1}. Within the accuracy reached, the trend of a linear
decrease of $\lambda (Q^2)$ is found to continue down to $Q^2 \sim 1$~GeV$^2$ 
with a slight tendency, at very low $Q^2$, to lie above.

In order to increase the $x$ range of this investigation the new data
are combined with published H1 data~\cite{thepaper}, with NMC
data~\cite{nmc} and with ZEUS data~\cite{bpt} at very low $Q^2$
(see Figure~\ref{lamall}).  The decrease of $\lambda (Q^2)$ towards
low $Q^2$ is now seen to deviate significantly from an extrapolation of the linear 
behaviour determined from the data in the deep inelastic scattering
region~\cite{h1rise}. Correlated with this behaviour, the function
$c(Q^2)$ is observed to decrease with decreasing $Q^2$, for $Q^2 <
3.5$~\gv.
%
%-------------------------------------------------------------------
\section{Summary}
%-------------------------------------------------------------------
%
A new measurement of the deep-inelastic positron-proton scattering
cross section is presented for squared four-momentum transfers
$0.35 \leq~Q^2~\leq 3.5{~ \rm GeV^2}$ and for Bjorken-$x$ values 
$ 7\cdot 10^{-6}~\leq x~\leq 2 \cdot 10^{-3}$. The data were taken in
August 2000 with the interaction-vertex shifted by 70 cm in
proton-beam direction thereby allowing the acceptance to be extended
to lower $Q^2$ than previously accessible. The scattered positron
angle and the interaction vertex are reconstructed using the extended
Backward Silicon Tracker of the H1 experiment.
% The positron energy is triggered and measured precisely in the backward SPACAL calorimeter. 
The hadronic final state is reconstructed using 
%the central tracking chambers and 
the LAr and SPACAL calorimeters.  Thus the measurement
range in inelasticity $y$ is much extended and the measurement
uncertainty halved as compared to previous H1 shifted vertex data.

This measurement provides the first precise low $x$ data on the inclusive DIS
cross-section in the transition region from the non-perturbative to
the deep-inelastic domain. A taming of the cross section rise towards
low $x$ is observed which occurs at large inelasticities $y \simeq
0.5$ and thus is attributed to a non-vanishing longitudinal structure
function \FLc at low $Q^2$.  In the kinematic region of this
measurement \F still rises towards low $x$ at fixed $Q^2$ like
$F_2(x,Q^2) = c(Q^2) \cdot x^{-\lambda(Q^2)}$.  The functions $c(Q^2)$
and $\lambda(Q^2)$, however, are observed to deviate from expectations
based on the linear dependence of $c$ and $\lambda$ on $\ln Q^2$ as
determined in the deep inelastic scattering region.

%Deviations from the linear dependence of
%the power $\lambda$ of $F_2 \propto x^{-\lambda}$ on $\ln Q^2$ are
%observed, however, which hint on a change of strong interaction
%dynamics at low $x$ in the region of $Q^2 \simeq 1$~GeV$^2$.
%
\vspace{0.5cm}
%
{\bf Acknowledgements}
%=====================
\normalsize
\noindent We are very grateful to the HERA machine group whose
outstanding efforts made this experiment possible. We acknowledge the
support of the DESY technical staff. We appreciate the substantial
effort of the engineers and technicians who constructed and maintain
the detector. We thank the funding agencies for financial support of
this experiment.  We wish to thank the DESY directorate for the
support and hospitality extended to the non-DESY members of the
collaboration.
%
%   References
%
\begin{thebibliography}{99}
%
\bibitem{h1svx}
H1 Collaboration, C.~Adloff {\it et al.}, Nucl.~Phys. {\bf B497} (1997) 3.
%
\bibitem{zeussvx}
ZEUS Collaboration, J.~Breitweg {\it et al.}, Eur.~Phys.~J. C {\bf 7} (1999) 609-630, [hep-ex/9809005].
%
\bibitem{h1bol}
D. Eckstein [H1 Collaboration], in``DIS 2001 - 9th Int. Workshop
on Deep Inelastic Scattering'',  G. Bruni, G. Iacobucci and
R. Nania (eds.), World Scientific (2002); \\
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%
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%
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%%CITATION = HEP-EX 0108035;%%
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%

\end{thebibliography}

%\clearpage
%\vspace{3cm}
\clearpage
%\input{cracamst02figs}
%\end{document}
%
% Kinematic Plane full   FIG1
%
\begin{figure}[p]
  \begin{center}
%    \epsfig{file=ps/kine_full.epsi,width=16cm}
 \epsfig{file=H1prelim-02-041.fig1.eps,width=16cm} \end{center}
 \caption{Kinematic region covered by the preliminary H1 measurements
 at 920~GeV proton beam energy~\cite{h1bol} (H1 svtx00 prel. and H1 99 prel.),
 by the recently published
 H1 data at 820~GeV~\cite{thepaper}, by the ZEUS Backward Pipe
 Detector (BPT)~\cite{bpt} and by the muon-proton scattering
 experiments NMC~\cite{nmc} and BCDMS~\cite{bcdms}. The lines of
 constant $y$ correspond to this analysis, i.e. $E_e = 27.5$~GeV and
 $E_p = 920$~GeV.}  \label{kinfull}
\end{figure}
%
% Control Distributions   FIG2
%
\begin{figure}[b]
  \begin{center} \epsfig{file=H1prelim-02-041.fig2.eps,width=17cm}
  \end{center} \caption{Event distributions of: $z$ vertex position
  and polar angle reconstructed with the BST; energy of the scattered
  positron candidate measured in the SPACAL backward calorimeter;
  Bjorken-$x$ and $Q^2$ from the positron kinematics and inelasticity
  from the $\Sigma$ method, see text. Histograms: DIS and
  photoproduction background (green shaded) simulation normalised to
  the measured luminosity.  } \label{maincont}
\end{figure}
%
% xsection           Fig.3
%
\begin{figure}[p]
  \begin{center}
\epsfig{file=H1prelim-02-041.fig3.eps,width=16cm}
  \end{center}
  \caption{Measurements of the inclusive DIS cross section -
    H1 shifted vertex data 2000, this analysis (green squares), and
    H199 nominal vertex data (red points), compared to larger $x$
    data from ZEUS (BPT97 blue triangles) and from  NMC (purple stars).
    The curves are a phenomenological parameterisation of the cross section
    calculating \Fc within the fractal proton structure concept
    and using a dipole model prediction for \FLc (solid)
    and $F_L=0$ (dashed).
     }
  \label{signew}
\end{figure}
%
% F2           Fig.4
%
\begin{figure}[p]
  \begin{center}
\epsfig{file=H1prelim-02-041.fig4.eps,width=16cm}
  \end{center}
  \caption{Measurements of the structure function $F_2(x,Q^2)$  -
    H1 shifted vertex data 2000, this analysis (green squares),
    H1 99 and 97 nominal vertex data (red points and triangles), 
    compared to larger $x$
    data from ZEUS (BPT97 blue triangles) and from  NMC (purple stars).
    Solid curves: phenomenological parameterisation
    of \F based on the fractal proton structure concept;
    Dashed curves: NLO QCD fit to the H1 96/97
    data which was performed to data for $Q^2 \ge 3.5$ GeV$^2$, i.e. it is
    extrapolated here into the lower $Q^2$ region.
    Dashed-dotted curves: ALLM97.
     }
  \label{f2new}
\end{figure}
%
% F2W           Fig.5
%
\begin{figure}[p]
  \begin{center}
\epsfig{file=H1prelim-02-041.fig5.eps,width=15cm}
  \end{center} \caption{Measurements of the structure function \Fc
  represented as $F_2/Q^2$ which is proportional to the total cross section 
  for virtual photon-proton scattering. Green squares: H1 2000
  shifted vertex data, this analysis.  The solid curves represent the fractal
  \Fc fit which was fixed using the two data sets shown at
  lower $Q^2$ (ZEUS 97 BPT, blue triangles) and higher $Q^2$ (H1
  96/97, red points). Dashed-dotted curves: the ALLM97 parameterisation;
  Dashed curves: H1 NLO QCD fit, with  $Q^2_{min} = 3.5$ GeV$^2$, extrapolated
  down to 1~GeV$^2$.}
  \label{f2W}
\end{figure}
%
% derivative vs. x in q2 bins  Fig.6
%
\begin{figure}[ht]
\epsfig{file=H1prelim-02-041.fig6.eps,width=15.cm}
  \caption{ Measurement of the derivative function \llam with the
  present shifted vertex data (blue squares) and the nominal vertex
  data~\cite{h1rise} (red points): the inner error bars represent the
  statistical uncertainty; the full error bars include the systematic
  uncertainty added in quadrature; the solid curves represent the
  fractal fit to the ZEUS BPT and published H1 data~\cite{thepaper};
  the dashed curves represent the extrapolation of the H1 NLO QCD
  fit~\cite{thepaper} below the minimum $Q^2$ of 3.5~GeV$^2$.}
  \protect\label{lamx}
\end{figure}
%
% lambda H1 alone  Fig 7a,b
%
\begin{figure}[ht]
 \epsfig{file=H1prelim-02-041.fig7a.eps,width=13.7cm}
 \epsfig{file=H1prelim-02-041.fig7b.eps,width=13.7cm} \caption{ Determination
 of the coefficients $c(Q^2)$ (upper plot) and of the exponents \lam
 (lower plot) from fits of the form $F_2(x,Q^2) = c(Q^2)
 x^{-\lambda(Q^2) }$: blue points - previous H1 structure function
 data~\cite{thepaper} for $x \leq 0.01$; red squares - present data.
 The inner error bars illustrate the statistical uncertainties, the
 full error bars represent the statistical and systematic
 uncertainties added in quadrature. The straight lines represent the
 mean coefficient $c$ (upper plot) and a fit of the form $ a \ln
 [Q^2/\Lambda^2]$ (lower plot), respectively, using data for $Q^2 \geq
 3.5$ GeV$^2$.}  \protect\label{lamh1}
\end{figure}
%
% lambda all
%
\begin{figure}[ht]
 \epsfig{file=H1prelim-02-041.fig8a.eps,width=13.7cm}
 \epsfig{file=H1prelim-02-041.fig8b.eps,width=13.7cm} \caption{ Determination
 of the coefficients $c(Q^2)$ (upper plot) and of the exponents \lam
 (lower plot) from fits of the form $F_2(x,Q^2) = c(Q^2)
 x^{-\lambda(Q^2) }$ for $x \leq 0.01$: blue stars - previous H1 $F_2$
 data~\cite{thepaper}; green points - present data combined with the
 H1 data~\cite{thepaper}; red squares - present data combined with NMC
 data; red triangles - present data combined with low $Q^2$ ZEUS BPT
 data~\cite{bpt}. The inner error bars illustrate the statistical
 uncertainties, the full error bars represent the statistical and
 systematic uncertainties added in quadrature. The straight lines
 represent the mean coefficient $c$ (upper plot) and a fit of the form
 $ a \ln [Q^2/\Lambda^2]$ (lower plot), respectively, using data for
 $Q^2 \geq 3.5$ GeV$^2$.}  \protect\label{lamall}
\end{figure}
%

\end{document}
