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% Some useful tex commands
%
\newcommand{\GeV}{\rm GeV}
\newcommand{\TeV}{\rm TeV}
\newcommand{\cm}{\rm cm}
\newcommand{\hdick}{\noalign{\hrule height1.4pt}}
\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}\,$}
\begin{document}

\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},
                July~12,~2001,~Budapest} \\
 {\bf EPS 2001:} 
                 & Abstract:        & {\bf 799}    &\\
                 & Parallel Session & {\bf 1}   &\\[.7em]
\multicolumn{4}{l}{{\bf
               XX International Symposium on Lepton and Photon Interactions}, 
               July~23,~2001,~Rome} \\ 
{\bf LP 2001:}  
                 & Abstract:        & {\bf 492} &\\
                 & Plenary Session  & {\bf S7, S8}   &\\ \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 A New Measurement of the \\
       Deep Inelastic Scattering Cross Section and of {\boldmath $F_L$} \\
       at Low {\boldmath $Q^2$} and Bjorken {\boldmath $x$} at HERA \\}
  \vspace*{1cm}

  {\Large H1 Collaboration \\
% DRAFT  by D.Eckstein, M.Klein and T.La\v{s}tovi\v{c}ka 
} 
\end{center}
%%%%%
\begin{abstract}

\noindent

Preliminary, new results are presented on the deep inelastic
scattering cross section in the range of momentum transfers $Q^2 =
1.5-12$~GeV$^2$. The data were taken in 1999 by the H1 Collaboration
at HERA, with positrons of 27.6 GeV energy and protons of \mbox{920~GeV}
energy, in a dedicated low $Q^2$ running period with an integrated
luminosity of about $3$~pb$^{-1}$. The cross section is measured to a few
per cent accuracy with upgraded silicon tracking. It complements
and extends a recent measurement of the proton structure functions \F
and \FL by H1 to even lower Bjorken $x$.
\end{abstract}
%%%%%

\end{titlepage}
%
\pagestyle{plain}

\section{Introduction}
%
The accurate measurement of the inclusive neutral current deep inelastic
scattering (DIS) cross section $\sigma (ep \rightarrow eX)$ has been
one of the prime tasks at HERA.  The H1 Collaboration has recently
published a comprehensive
analysis~\cite{thepaper} of data taken in the years 1996 and 1997 with
beam energies $E_e = 27.6$~GeV and $E_p = 820$~GeV.  The proton
structure function \F was measured using the Born approximation of
the reduced scattering cross section
\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 $Q^2$ is the four-momentum transfer squared carried by the
  virtual photon, $y$ is the inelasticity and $x=Q^2/sy$ is the
  Bjorken variable. The beam energies determine the energy squared $s$
  in the centre of mass system, $s=4E_eE_p$, and $Y_+$ is defined as
  $1+ (1-y)^2$. The longitudinal structure function \FL was accessed
  at large inelasticities $y$ corresponding to the low $x$ region.
  
  The 1997 data for $Q^2$ below 15\gv\, were obtained in a dedicated
  running period with a luminosity of 1.8\pb. In this range \Fc was
  measured to about 2-6\% precision and \FLc was determined
  with an absolute accuracy of about 0.15.  In 1999 the H1
  Collaboration has taken data at HERA with an increased proton beam
  energy $E_p$ of 920 GeV in a further short running period with
  special triggers of 2.8\pb luminosity.  The purpose of this run
  was to complement the recent low $Q^2$ cross-section
  measurement and to obtain new data on the longitudinal structure
  function. The results are reported in this paper.
   The increased proton beam energy extends the phase space
  towards lower $x$ at a given $Q^2$.  An upgraded backward silicon
  tracker allows the range in $y$ to be extended from 0.75 up to 0.89.
  The kinematic plane and its extension with the new 1999 data is
  illustrated in Figure~\ref{kinfull}.
  
  This paper is organised as follows. Section 2 briefly describes the
  experimental methods, i.e. the kinematic reconstruction with the H1
  detector, the event selection and simulation, calibration and
  background handling. The cross section measurement and the
  extractions of the structure functions are discussed in Section~3.
  A short 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}
Q^2_e= \frac{E^{'2}_e \sin^2{\theta_e}}{ 1-y_{e}}
 \hspace*{2cm}
y_e=1-\frac{E_e'}{E_e}~\sin^2(\theta_e/2)
\label{qy}
\end{equation}
which define the electron method of reconstruction.  The scattered
positron energy $E_e'$ is measured in the backward electromagnetic
lead-fibre calorimeter SPACAL \cite{Spacal}.
%which has an integrated timing function to veto proton beam induced
%background interactions. 
The polar angle $\theta_e$ is measured in the backward silicon tracker
(BST).  It is defined with respect to the proton beam direction,
defining the $z$ axis.  The BST has an extended configuration of 8
concentric detector planes placed perpendicularly to the beam axis,
each consisting of 16 wafers measuring the radial coordinate of tracks
with an intrinsic resolution of better than 20~$\mu$m ($r$ modules)\footnote{
In a pilot installation, made for one of the 16 $\phi$ sectors, the BST
in 1999 was equipped with so-called $\phi$ detectors. These are wedge
shaped, single sided Silicon detectors with strips parallel to one
wafer edge at fixed $\phi$. They are mounted back-to-back to the $r$
detectors. Their efficiency is 98\% based on a signal-to-noise ratio
of 26.}.
A scattered positron candidate is defined as a vertex pointing track
associated with the cluster in SPACAL of maximum energy having less
than two Moli\`{e}re radii lateral extension.

%\footnote{Tracks in the BST are reconstructed using two
%  independent algorithms. Use of the SPACAL cluster position allows
%  the minimum number of hits defining a track to be reduced from 3, in
%  the stand-alone track reconstruction, to 2.  This enhances the polar
%  angle acceptance and the track reconstruction efficiency.}. 
% Besides measuring $\theta_e$, the
%BST is essential in rejecting neutral particle background to the cross
%section measurement at low energies and in the determination of the
%event vertex at large $x$ where the hadronic final state escapes
%detection in the forward direction.
 
Because of the degradation of the resolution of $y_e \propto 1/y$ the
kinematics at low $ y < 0.1$ are reconstructed using also information
from the hadronic final state reconstructed in the Liquid Argon
calorimeter (LAr) and the SPACAL, and from the central drift chambers,
the jet chamber (CJC) and the $z$ chambers~\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.
If a calorimeter cluster can be masked by a track in the central
chambers, the momentum from the tracker is used instead of the LAr
energy.  In the analysis $Q^2$ and $y$ are reconstructed using the
$\Sigma$ method which combines $E_e�$, $\theta_e$, and $y_h$ according
to
%
\begin{equation}
   Q^2_{\Sigma} = \frac{E^{'2}_e \sin^2{\theta_e}}{ 1-y_{\Sigma}}
   \hspace*{2cm}
   y_{\Sigma} = \frac{y_h}{ 1+y_h-y_e} =
   \frac{\sum_h}{\sum_h+E_e'(1-cos \theta_e)}.
   \label{ys}
\end{equation}
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 cross section is extracted using both the electron method and the
sigma method. This allows important cross checks to be performed on
the accuracy of the calorimeter calibrations and the final cross
section to be obtained with optimum kinematic reconstruction.

The luminosity is determined from the cross section of the elastic
bremsstrahlung process, measured with a precision of 1.2\% . The
luminosity measurement is by about 4\% corrected for the occurence of
proton beam satellites which do not enter the selected data sample.
%
\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 5~GeV.  This trigger is
used in the main data analysis for the cross-section measurement for
$y < 0.67$.  In addition a high $y$ trigger, accepting SPACAL energies
down to 2~GeV, is realised by requiring a coincident vertex trigger
signature in the proportional chamber system.  These data are subject
to a special, high $y$ data analysis which is used for $0.89 > y >
0.67$.

Low energy deposits can also be caused by particles 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 in the electron tagger calorimeters
upstream the positron beam.

The efficiency of all trigger elements exceeds 97\% 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 ($E_e� >
15$~GeV), the efficiency of all 128 BST $r$ modules is determined to
be 97\% on average.

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 with an electromagnetic energy deposition in the
SPACAL (cluster) defined by a small lateral extension.  Any energy
behind the electromagnetic cluster measured in the hadronic SPACAL may
not exceed a small fraction of $E'$.  Radiative effects and background
contributions are suppressed requiring energy-momentum conservation
using the total $E-p_{z}$ reconstructed in the detector. All criteria
are essential in distinguishing the genuine scattered positron from
neutral or charged hadrons originating from photoproduction
%d%neutral electromagnetic or charged hadronic background contributions
which  otherwise by far exceeds the DIS signal at low energies.  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     &  $|z| < 30$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. Note
that in the high $y$ data analysis, which extends down to 3~GeV, a
second cluster in the SPACAL of energy larger than 2~GeV is required
to reduce low energy background effects.}}
\end{table}  

A high statistics simulation of deep inelastic and photoproduction
events is performed using the programs, GEANT~\cite{geant},
DJANGO~\cite{django} and PHOJET~\cite{fojet}, and methods as described
in \cite{thepaper}.  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.
%
\subsection{Alignment and Calibration}
%
The measurement of $\theta_e$ requires the BST to be accurately
aligned. After the internal adjustment of the detector planes, the BST
is aligned using the $z$ position of the interaction vertex $z_v$.
This is determined by the central tracker which defines the H1
coordinate system and measures the inclination of the beam with
respect to the detector axis.  A measurement accuracy of $\theta_e$ of
0.2~mrad is obtained by comparing the angle measured in the BST with
the one resulting from $z_v$ and the hit position in the backward
drift chamber (BDC).  The alignment of the $\phi$ detectors is done
using the vertex position and approximating tracks in the strip
coordinates by a quadratic form. From high energy tracks, a resolution
of better than 20$\mu$m is measured and the modules are found to be
aligned to within 5$\mu$m accuracy.  The SPACAL position is adjusted
using QED Compton events which have the signature of back-to-back
positron and photon clusters.

The energy scale of the electromagnetic SPACAL cells in the region of
large $E' > 17$~GeV is determined from the measurement of the angles
$\theta_e$ and $\theta_h$  to within a remaining uncertainty of
0.3\%.  This scale is verified in the low energy range to
better than 2\% from a comparison of $E'$ with the corresponding
momentum $p$, measured with the BST, and the transverse vertex
position, see Section~\ref{sighiy}.  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
uncertainty is obtained from an extension of the cross section
measurement, using the electron method to very low $y \geq 0.005$ and
the sigma method to large $y \leq 0.6$, respectively. The resulting
cross sections agree to within the statistical accuracy.
%
\subsection{Estimation of Photoproduction Background  \label{sighiy}}
%
The present analysis includes data down to $E' = 3$~GeV which is the
smallest scattered positron energy reached so far in the low $Q^2$
inclusive cross section measurements of H1~\cite{thepaper}. In this range
the photoproduction background is large. For most of the DIS events
a second particle, besides the positron, is scattered into the backward region.
Thus for the data at $y > 0.67$ two clusters in the SPACAL are required
for  a DIS candidate event. This requirement
reduces the photoproduction background by a factor of about 5 while
retaining 90\% of the genuine DIS events as estimated in the simulation.

The remaining photoproduction background is subtracted using a high
statistics PHOJET simulation which is normalised using the
photoproduction events registered in the electron tagger.  This
normalisation is verified by a complementary analysis to within 25\%
utilising the track momentum measurement with the BST.  This enables,
on a statistical basis, the photoproduction background to be removed
from the DIS positron signal, see Section~\ref{comp}.

Figure~\ref{eovp} shows the distribution of the ratio of the energy
$E$ measured in the SPACAL to the momentum $p$ measured with the BST
$r-\phi$ detectors in two intervals of $E$.  For low energies a small
enhancement is observed at about $E/p \simeq -1$. This represents the
negatively charged background\footnote{From the tagged events a charge
  asymmetry of $6 \pm 3$\% is determined, in agreement with
  \cite{thepaper}, which is corrected for in the dedicated $r-\phi$
  BST analysis.} to the truely DIS signal which dominates the peak at
$E/p \simeq +1$.  At larger energies, the background is seen to be
reduced to a much smaller level.  The peak position for positive
charges represents a verification of the SPACAL low energy scale
at the per cent level of accuracy.
%
%-------------------------------------------------------------------
%\section{The Cross Section and  {\boldmath $ F_2(x,Q^2)$}}    
\section{The Cross Section and  the Proton Structure Functions}
%------------------------------------------------------------------- 
%
%
\subsection{Data and Simulation Comparisons \label{comp}}
%
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 related to the main data
analysis are for $E'>7$~GeV shown in
Figure~\ref{maincont}. The experimental distributions for the basic
kinematic variables, the scattered positron energy $E'$ and angle
$\theta_e$ and the inelasticity $y_h$ are seen to be well described by
the DIS simulation.  The event selection criteria, discussed in
Section~\ref{evsel}, reduce the photoproduction background in
this analysis and energy range to a very small level.
 
Control distributions for the high $y$ region are displayed in
Figures~\ref{xqcont} and \ref{s9cont}.  The $Q^2_e$ and $y_e$
distributions in Figure~\ref{xqcont} are seen to be well described by
the simulation of DIS and photoproduction events.  The normalisation
of the simulated photoproduction background is based on the tagged
event sample and, as explained in Section~\ref{sighiy}, it is verified
with a special data analysis utilising the BST momentum measurement.
Figure~\ref{s9cont} shows the scattered energy and angle distributions
in this dedicated analysis. The background shown is determined from
data with a track of negative charge.  The histogram represents the
sum of this experimentally measured background and of the simulation
of the genuine DIS events.  The understanding of the data down to
3~GeV scattered positron energy allows the measurement of cross
sections at high $y$ which are essential for the \FLc determination.
%Based on the understanding of the data down to
%3~GeV scattered positron energy, the cross section is measured here in
%an extended range of high inelasticities. This provides a better
%sensitivity to the longitudinal structure function at low $Q^2$ than
%hitherto since the \FLc contribution enters the cross section $\propto y^2$.
%
\subsection{Systematic Uncertainties}
%
The uncertainties of this cross section measurement are divided into
four different kinds:
\begin{itemize}
\item{The data have a normalisation uncertainty of 1.3\% resulting
    from the uncertainty of the luminosity measurement (1.2\%) and of
    the trigger efficiency determination (0.5\%). This uncertainty is not
    included in any error bar subsequently shown.}
\item{The statistical uncertainty of the data is about 2\%.}
\item{An about 2\% uncorrelated cross-section uncertainty is due to
    the Monte Carlo event statistics. Moreover, uncorrelated errors
    with weak kinematic dependencies result from the BST track
    reconstruction (1-2\%), from the uncertainty of the radiative
    corrections (0.5\%) and from the positron identification
    uncertainty (1\%).}
\item{Correlated cross-section uncertainties result from the $E'$ and
    $E_h$ measurements (0.5-2\%), from the $\theta_e$ reconstruction (0.5\%),
the calorimeter noise  (2\% at low $y$) and from the photoproduction background
 (5\% at high $y$).}
\end{itemize}
The total cross-section uncertainty is about 3\% in the bulk data
region increasing to about 7\% at the edges of the $y$ range covered.
This is comparable to the low $Q^2$ data recently published by the H1
Collaboration~\cite{thepaper}.
%
\subsection{Determination of the Cross-Section and Extraction of {\boldmath $ F_2(x,Q^2)$}}
%
The kinematic region accessed in this measurement is divided into
eight $Q^2$ intervals for a range $1 < Q^2 < 14$~\gv, as used
previously.  Since an essential goal of this analysis has been the
extraction of \FLc, the $x$ range is subdivided using the $y=Q^2/sx$
variable. At high $y$, bin edges ($y=0.89,~0.79,~0.67,~0.53$) are
chosen which are adapted to the $y$ bins used for the 820~GeV data
analysis~\footnote{The previous analysis extended to a maximum $y$ of
  0.75 which corresponds to $y=0.67$ for $E_p=920$~GeV.}. Below this
range four $y$ intervals per decade are used until at $y \leq 0.016$
the bin size is doubled. The binning is well adapted to the
resolution in the measurement of the kinematic variables.  Bins are
accepted if the purity and stability are bigger than 30\% with typical
values being 70\%. 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~\cite{doris,tomas}
(Equation~\ref{sig}) is shown in Figure~\ref{sigr}. The cross section
rises towards low $x$ until it is tamed and $\sigma_r$ even turns over
at $x$ values corresponding to $x \simeq Q^2/0.6s$. This behaviour,
for $Q^2 \geq 2.5$~\gv, is well described by the NLO QCD fit to the
820~GeV data which is discussed in detail in~\cite{thepaper}.  Note
that this fit used H1 data with a minimum $Q^2$ of $3.5$~\gv. The
extrapolation to lower $Q^2 < Q^2_{min}$ is again found to be lower
than the measured data, in particular at high $y$.

Using the NLO QCD calculation of \FLc, the proton structure function
\F is extracted from the data. The analysis has been limited to
maximum $y$ values of 0.6 in order to reduce the effect of the calculated
\FLc on \Fc to the few per cent level. It is seen in Figure~\ref{f2new}
that the new data agree well with the recently published H1 data and
also with the data from the NMC Collaboration~\cite{nmc} obtained in
deep inelastic, fixed-target muon-proton scattering. The rise of \Fc
towards low $x$ is observed to be continuous beyond the previously
accessible kinematic range extending the observation recently
made~\cite{therise}. At larger $x$ the data extend into the
kinematic region of the fixed target experiments, and good agreement
is found.
%-------------------------------------------------------------------
\subsection{The Longitudinal Structure Function {\boldmath $ F_L(x,Q^2)$}}                                       
%------------------------------------------------------------------- 
The measured cross section is sensitive to the longitudinal structure
function \FL at low $x$. An extension towards lower $x$ than accessed
in~\cite{thepaper} is achieved with the increase of the proton beam
energy, from 820~GeV to 920~GeV, and of the maximum $y$, from 0.75 to
0.89.

A suitable method, introduced in~\cite{thepaper}, to extract \FLc at
low $Q^2$ is based on the partial derivative of the reduced cross
section, taken at fixed $Q^2$, i.e.
%
\begin{equation}
  \left(\frac {\partial \sigma_r }{ \partial \ln y}\right)_{Q^2}=
   \left(\frac {\partial F_2 }{ \partial \ln y}\right)_{Q^2}
   - F_L \cdot 2y^2 \cdot \frac{2-y}{Y_+^2}
   -\frac {\partial F_L }{ \partial \ln y} \cdot \frac{y^2}{Y_+}.
       \label{dsig}
\end{equation}
%
Contrary to the cross section itself, the \FLc contribution to this
derivative is of size similar to the \Fc contribution.  Taking into
account the systematic error correlations, the derivative is
determined for a rebinned $Q^2$ division of the data. The derivative
is shown in Figure~\ref{deriva} and, for illustration, compared with
the NLO QCD fit result using different assumptions on \FLc.


For $y \leq 0.2$, straight line fits are performed in $\ln y$ to the
derivative \pdsi.  These are extrapolated to determine the
contribution of \pdff at high $y$ and to subtract it from the cross
section derivative. The uncertainty on this extrapolation is included
in the systematic errors of \FLc, taking into account the correlations
of errors at low $y$ with those at high $y$. The contribution of the
\FLc derivative is calculated to be negligible using parton
distribution parameterisations and also the H1 QCD fit. The estimated
size is added to the systematic uncertainty of the \FLc extraction.

The new data points for \FL are shown in Figure~\ref{flext}.  They
extend into a lower range of $x$ and are consistent with the previous
H1 result. The curves are a NLO QCD calculation of \FLc based on a fit
to the previous \Fc data for $y<0.35$, i.e. in a region where \Fc is
practically independent of \FLc. An overview of the full H1 data,
obtained for \FL from $Q^2 = 2.2$~\gv\, to $700$~\gv\,~\cite{hiqfl},
is given in Figure~\ref{flall}. The apparent rise of \FL towards low
$x$ is related to a large gluon momentum distribution.  At the
presently reached accuracy, all data are well described by the NLO QCD
calculation in which the gluon distribution is determined from the
scaling violations of \F.
%-------------------------------------------------------------------
\section{Summary}                                       
%------------------------------------------------------------------- 
A new measurement of the deep-inelastic positron-proton scattering
cross section is presented for squared four-momentum transfers $1.5
\leq~Q^2~\leq 12{~ \rm GeV^2}$ and Bjorken-$x$ values $2 \cdot
10^{-5}~\leq x~\leq 0.07$. These data are complementary to low $Q^2$
data recently published as they are taken at a proton beam energy
increased to 920~GeV and measured with an upgraded backward silicon
tracker. The new ability  to measure low particle momenta with the BST 
allows the analysis to be reliably performed down to 3~GeV of scattered
positron energy.  The kinematic range is thus extended towards lower
$x$ and larger $y \leq 0.89 $, respectively.

The accuracy of these cross section data is about 3\% in most of the
kinematic range. The cross section is well described by a NLO QCD
analysis performed on previous H1 cross-section data.  It exhibits a
turn over at low $x$, for fixed large $y \simeq 0.6$, which is thus attributable
to the influence of the longitudinal structure function.

The new \F data confirm and complement the H1 data recently published.
The rise of \Fc towards low $x$ is observed to continue beyond the
previously accessible kinematic range.  At larger $x$ the data extend
into the kinematic region of the fixed target muon-proton scattering
experiments, and good agreement is found.

The partial derivative of the reduced cross section, \pdsi, is measured
and used to obtain new data on the longitudinal structure function
\FL. The data extend to lower $x$ and are, in the region of overlap, 
consistent with previous determinations of \FLc. 


\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{thepaper}
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        [hep-ex/0012153].
%
\bibitem{Spacal}
R.~Appuhn {\it et al.}, Nucl.~Instr.~and Meth. {\bf A386} (1996) 397.
% 
\bibitem{h1detec} 
I.~Abt {\it et al.} [H1 Collaboration], Nucl.~Instr.~and Meth. {\bf A386} (1997) 310 and 
{\bf A386} (1997) 348. 
%
\bibitem{geant}
R. Brun {\it et al.}, GEANT3 User's Guide, CERN-DD/EE 84-1, Geneva (1987).
%
\bibitem{django}
G.~A.~Schuler and H.~Spiesberger, Proc. Workshop
on HERA Physics, Vol~3, eds. W.~Buchm\"uller and G.~Ingelman,
Hamburg, DESY (1992), p. 1419; \\
        A.~Kwiatkowski, H.~Spiesberger and H.-J.~M\"ohring,
        Comp.~Phys.~Comm. {\bf 69}~(1992)~155; \\
 L.~L\"onnblad, Comp.~Phys.~Comm. {\bf 71} (1992) 15.
%
\bibitem{fojet}
R. Engel and J. Ranft, Phys. Rev. {\bf D54} (1996) 4244.  
%
\bibitem{vova}
V.V. Arkadov, PhD Thesis, Berlin, Humboldt-University, 2000, DESY-Thesis-2000-046. 
%
%\bibitem{compton}
% A.~Courau and P.~Kessler, Phys.~Rev. {\bf D46} (1992) 117. 
%
 \bibitem{doris}
D. Eckstein, PhD Thesis, Berlin, Humboldt-University, in
preparation. 
%
 \bibitem{tomas}
T. La\v{s}tovi\v{c}ka, PhD Thesis, Berlin, Humboldt-University, in
preparation. 
%
\bibitem{nmc}
 M.~Arneodo {\it et al.} [NMC Collaboration], Nucl.~Phys. {\bf  B483} (1997) 3. 
%     
\bibitem{therise}
         C.~Adloff {\it et al.} [H1 Collaboration], {\it A Measurement of the Rise of 
         \F towards Low $x$}, paper 141, submitted to the EPS Conference, Budapest, 2001.
%to be published.
%     
\bibitem{hiqfl}
         C.~Adloff {\it et al.} [H1 Collaboration], {\it Measurement of Neutral and Charged Current
       Cross Sections and of $F_L$ at High $Q^2$}, paper 803, submitted to the
       EPS Conference, Budapest, 2001.
\end{thebibliography}


%\clearpage
\vspace{3cm}


\clearpage
% \input{figures}

%
% Kinematic Plane full   FIG1
% 
\begin{figure}[p] 
  \begin{center}
%    \epsfig{file=ps/kine_full.epsi,width=16cm}
 \epsfig{file=H1prelim-01-041.fig1.eps,width=16cm}
  \end{center}
  \caption{Kinematic region covered by this measurement at 920~GeV proton beam 
   energy, by the recently published H1 data at 820~GeV and by the muon-proton
   scattering experiments NMC and BCDMS. The lines of constant $y$ correspond 
   to this analysis, i.e. $E_e = 27.6$~GeV and $E_p = 920$~GeV.} 
  \label{kinfull}
\end{figure} 
%
% E/p                    FIG2
%
\begin{figure}[p]
 \begin{picture}(200,80)
 \put(0,0){
%  \epsfig{file=ps/phi3-6gev.epsi,width=7cm}}
 \epsfig{file=H1prelim-01-041.fig2a.eps,width=7cm}}
 \put(75,0){
%  \epsfig{file=ps/phi6-10gev.epsi,width=7cm}}
 \epsfig{file=H1prelim-01-041.fig2b.eps,width=7cm}}
 \end{picture}
  \caption{Ratio of the energy measured in the SPACAL calorimeter and
    the momentum measured with the BST $r$- and $\phi$-detectors for
    two energy ranges. The enhancement at about $-1$ is due to
    negatively charged tracks mainly due from photoproduction events.
    The peak at $+1$ is due to scattered positrons with a small
    admixture of background. Events are selected according to the
    requirements quoted in Table~\ref{tabcut}.}  \protect\label{eovp}
\end{figure}
%
% Control Distributions, main S0/S3   FIG3
%
\begin{figure}[b] 
  \begin{center}
%    \epsfig{file=ps/s03_control.eps,width=17cm}
 \epsfig{file=H1prelim-01-041.fig3.eps,width=17cm}
  \end{center}
  \caption{Event distributions of the energy and the polar angle of the scattered
    positron candidates, and of $y_h$ in the main data analysis. The histograms
    represent the simulation of DIS and the small photoproduction
    background (shaded).}
  \label{maincont}
\end{figure} 
%
% Control Distributions S9      FIG 4
%
\begin{figure}[t] 
  \begin{center}
%    \epsfig{file=ps/s9_control.eps,width=17cm}
\epsfig{file=H1prelim-01-041.fig4.eps,width=17cm}
  \end{center}
  \caption{Even distributions of $Q^2$ and $y$ of the scattered positron candidates,
    illustrating the cross section measurement at high $y$.  Solid
    points: H1 data; shaded histograms: simulation of photoproduction
    events; open histograms: added distributions of simulated DIS and
    photoproduction events. }
  \label{xqcont}
\end{figure} 
%
% Control Distributions S9 phi and E/p for BST phi   FIG 5
%
\begin{figure}[b] 
  \begin{center}
%    \epsfig{file=ps/s9_phi_etheta.epsi,width=16cm}
\epsfig{file=H1prelim-01-041.fig5.eps,width=16cm}
  \end{center}
  \caption{Distributions of the energy and polar angle $\theta_e$ of the 
    scattered positron in a high $y$ data analysis employing the
    charge measurement with the BST $r$ and $\phi$ detectors in 1/16
    of $2 \pi$. Solid points: data with positive charge assignment;
    open histogram: sum of data with negative charge assignment and
    DIS event simulation, normalised to the data luminosity. The
    distributions are shown before subtracting the measured background
    (shaded histogram) given by data with negative charge assignment.}
  \label{s9cont}
\end{figure} 
%
% reduced x-section 99     FIG 6
%
\begin{figure}[p] 
  \begin{center}
%    \epsfig{file=ps/sigr.eps,width=16cm}
\epsfig{file=H1prelim-01-041.fig6.eps,width=16cm} \end{center}
  \caption{Measurement of the reduced DIS cross section (closed
  points) from the 920 GeV proton energy data taken in 1999. The
  curves represent a NLO QCD fit to the H1 1996/97 data which was
  limited to $Q^2 \ge 3.5$ GeV$^2$.  The dashed curves show the
  extrapolation of this fit below $Q^2_{min}$. For each $Q^2$ bin two
  curves are drawn which represent the reduced cross section
  $\sigma_r$ (lower curve, turning at low $x$) and the structure
  function $F_2$, which rises towards low $x$ (upper curve). For
  larger $x$, corresponding to lower $y$, $\sigma_r \simeq F_2$.} \label{sigr}
\end{figure} 
%
% F2 '97+'99+NMC           FIG 7
%
\begin{figure}[p] 
  \begin{center}
%    \epsfig{file=ps/f2.eps,width=16cm}
\epsfig{file=H1prelim-01-041.fig7.eps,width=16cm}
  \end{center}
  \caption{Measurement of the structure function $F_2(x,Q^2)$ by the H1 and NMC
    experiments. The curves represent a NLO QCD fit to the H1 96/97
    data which was limited to $Q^2 \ge 3.5$ GeV$^2$.  The dashed
    curves show the extrapolation of this fit below $Q^2_{min}$. }
  \label{f2new}
\end{figure} 
%
% Kinematic Plane high y 
%
%\begin{figure}[p] 
%  \begin{center}
%    \epsfig{file=ps/kinehy.epsi,width=16cm}
%  \end{center}
%%  \caption{The high $y$ region of the kinematic plane
%covered by the previous 1996/7 H1 data (shaded) and by the
%new data (crossed). The previous data are limited to a maximum $y$ of
%0.75 while the new data extend to 0.89.}
%  \label{kinhiy}
%\end{figure} 
%
% derivative dsigma/dlny   FIG 8  (old 8 left out)
%
\begin{figure}[p] 
  \begin{center}
%    \epsfig{file=ps/deriva.epsi,width=16cm}
\epsfig{file=H1prelim-01-041.fig8.eps,width=16cm}
  \end{center}
  \caption{Measurement of the derivative \pdsi.
           The curves represent the QCD fit result to the H1 96/97 data for $y<0.35$ 
           and $Q^2 \ge 3.5$ GeV$^2$ calculated with different assumptions on  
           $F_L$. The inner error bars represent the statistical errors and the total
           error bars the statistical and systematical errors, added in quadrature.
}
  \label{deriva}
\end{figure} 
%
% Fl low Q2 low x - extension plot   FIG 9
%
\begin{figure}[p] 
  \begin{center}
%    \epsfig{file=ps/flext.epsi,width=16cm}
\epsfig{file=H1prelim-01-041.fig9.eps,width=16cm}
  \end{center}
  \caption{The longitudinal structure function $F_L(x,Q^2)$ 
    determined with the derivative method from the new cross-section
    data (triangles) compared with the previous result (points).The
    inner error bars represent the statistical errors and the total
    error bars the statistical and systematical errors, added in
    quadrature. The curves represent the QCD fit result to the H1
    1996/97 data for $y<0.35$ .}
  \label{flext}
\end{figure} 
%
% Fl low Q2 and high Q2   FIG 10
%
\begin{figure}[p] 
  \begin{center}
%    \epsfig{file=ps/flall99.epsi,width=16cm}
\epsfig{file=H1prelim-01-041.fig10.eps,width=16cm}
  \end{center}
  \caption{The longitudinal structure function $F_L(x,Q^2)$ as obtained by H1 and
    by charged lepton-nucleon fixed target experiments. The inner
    error bars represent the statistical errors and the total error
    bars the statistical and systematical errors, added in quadrature.
    The error bands are due to the experimental (inner) and model
    (outer) uncertainty of the calculation of $F_L$ using the NLO QCD
    fit to the H1 96/97 data for $y < 0.35$ and $Q^2 \ge 3.5$
    GeV$^2$.}
  \label{flall}
\end{figure} 
%
%
\end{document}
