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\begin{titlepage}

\noindent
%%%Date:     03/31/2004 \\
%%%Version:  1.0        \\
%%%Editors:  Gerhard Brandt, Christian Veelken, Stefania Xella (junior editor: CD)\\
%%%Referees: Hinrich Meyer, David South \\
%%%%Comments by

%%%\vspace{2cm}

\vspace{1cm}
\begin{center}
{\large \bf H1prelim-04-042 }
\end{center}
\vspace{1cm}

\begin{center}
\begin{Large}

{\bf Measurement of the Inclusive DIS Cross Section at Low {\boldmath $Q^2$}
and High {\boldmath $x$} using Events with Initial State Radiation}

\vspace{2cm}

H1 Collaboration

\end{Large}
\end{center}

\vspace{2cm}


\begin{abstract}
The inclusive DIS cross section is measured at low $Q^2$ and relatively large
$x$ using events with initial state photon radiation from the 
incoming electron. In this analysis the radiated photon is not explicitly
detected. Instead its energy is inferred from a longitudinal momentum 
imbalance, such that the energy of the interacting electron and the event
kinematics can be reconstructed. The neutral current cross section
is thus measured
for $0.35 \leq Q^2 \leq 0.85 \ {\rm GeV^2}$
and $10^{-4} \ \lapprox \ x \ \lapprox \ 5 \cdot 10^{-3}$.
\end{abstract}

\vspace{1.5cm}

\begin{center}
Prepared for DIS 2004, Strbske Pleso, Slovakia
\end{center}

\end{titlepage}

%\newpage

\section*{Brief Analysis Details}

These results represent an extension to our previous measurements \cite{sv00}
of inclusive DIS cross sections at $Q^2 \ \lapprox \ 1 \ {\rm GeV^2}$,
obtained using a dedicated sample corresponding to around 
$600 \ {\rm nb^{-1}}$ for which the $ep$ interaction region was shifted
by $70 \ {\rm cm}$ in the outgoing proton direction. The shifted
vertex extends the detector
acceptance to smaller electron scattering angles and hence 
to lower $Q^2$ values. In the new analysis, an extension to larger $x$ values
at low $Q^2$ is achieved by making use of events with initial state photon 
radiation (ISR) from the incoming
electron. The photon radiation results in a reduced effective incoming
electron energy, such that the $ep$ centre of mass energy is reduced and
larger values of $x$ are accessed at fixed $Q^2$ than is the case for
non-radiative events. 

In contrast to earlier ISR analyses \cite{ISRold}, this analysis does not
require the observation of the radiated photon. Instead, its presence is
inferred from energy and longitudinal momentum conservation. 
Assuming that the photon is radiated collinear with the electron beam, 
the energy
$E_\gamma$ of the radiated photon is then given by 
$2 E_\gamma = 2 E_e^0 - (E-p_z)_{e^\prime} - (E-p_z)_h$, where 
$E_e^0 = 27.6 \ {\rm GeV}$ is the electron beam energy, 
$(E-p_z)_{e^\prime}$ is the measured difference between the energy and
the longitudinal momentum of the scattered electron and
$(E-p_z)_h$ is the same quantity for the full hadronic final state. The
reduced incoming electron beam energy $E_e$ is then given by 
$E_e = E_e^0 - E_\gamma$.
The reconstruction of $y$ and $Q^2$ proceeds using the 
`$\Sigma$ method', which relies on $\Sigma = (E - p_z)_h$. The reconstruction
of $x$ is then performed in a manner that is independent
of the electron beam energy $E_e^0$. The kinematics are resonstructed using
\begin{eqnarray*}
  y_\Sigma = \frac{\Sigma}{\Sigma + E_{e^\prime} (1 - \cos \theta_e)}
  \hspace*{1.5cm}
  Q^2_\Sigma = \frac{E_{e^\prime}^2 \sin^2 \theta_e}{1 - y_\Sigma}
  \hspace*{1.5cm}
  x_R = \frac{Q^2_\Sigma}{2 \Sigma E_p}
\end{eqnarray*}
where $\theta_e$ is the electron scattering angle. 
The remaining details of the analysis procedure closely
follow those reported in \cite{sv00}.

Control distributions corresponding to the measured ISR-dominated 
phase space are shown in figure~\ref{one}. 
There is good agreement between the observed uncorrected data distributions
and the expectation based on a DJANGO simulation of inclusive DIS together
with a PHOJET simulation of the photoproduction background. 

Figure~\ref{two} shows
the resulting measurements, expressed in the form of the reduced
cross section, 
\begin{eqnarray*}
  \sigma_r & = & \frac{Q^4 x}{2 \pi \alpha^2 Y_+} \ \
                 \frac{{\rm d} \sigma}{{\rm d} x {\rm d} Q^2} \\
           & = & F_2(x, Q^2) - \frac{y^2}{Y_+} \cdot F_L(x, Q^2) \ ,
\end{eqnarray*}
where $Y_\pm = 1 \pm (1 - y)^2$.
The data points have total uncertainties of around $10 \%$
and cover the region
$0.35 \leq Q^2 \leq 0.85 \ {\rm GeV^2}$
and $10^-4 \ \lapprox \ x \ \lapprox \ 5 \cdot 10^{-3}$. They are
compared with the extrapolated
predictions of a fit for $F_2$ based on a self-similar
structure to the proton (FRACTAL FIT $F_2$) \cite{tomas},
to which an $F_L$ term has also been added, based on a
dipole model \cite{kgbw}.They are also compared with the results from a 
parameterisation (ALLM97 $F_2$) \cite{allm} of inclusive
and exclusive DIS and photoproduction data. All predictions
are in good agreement with the data. 

The extension in
kinematic phase space achieved using the new method is 
illustrated in figure~\ref{three}, where the present data are
compared with the results from the non-radiative shifted
vertex analysis \cite{sv00}. Figure~\ref{four} shows the
overall status of DIS measurements in the low $Q^2$ region,
including in addition data from the ZEUS beampipe 
tracker \cite{bpt}, from a further H1 measurement at low $Q^2$ and
large $x$
using QED-Compton events \cite{qedc} and from NMC \cite{nmc}.
The new data are compatible with the previous measurements.

The new data allow improved extractions of the parameter
$\lambda$, which describes the growth of $F_2$ at low
$x$ according to $F_2 = c(Q^2) \cdot x^{- \lambda (Q^2)}$. 
Figure~\ref{five} shows the results for $\lambda$ obtained
by fitting the current data
at fixed $Q^2$ values, together with the previous
shifted vertex measurements \cite{sv00}. Also shown are
H1 results from larger $Q^2$ values \cite{f29697} and
ZEUS results \cite{bpt}. The new measurements
confirm the change in behaviour of $\lambda$ from a logarithmic
dependence on $Q^2$ at large $Q^2$ to a weaker dependence
compatible with reaching a constant consistent with the soft
pomeron intercept as $Q^2 \rightarrow 0$. The change takes
place on distance scales of the order of $0.3 \ {\rm fm}$
and can be interpreted as being related to a transition 
from partonic to hadronic degrees of freedom. 

\begin{thebibliography}{9}

\bibitem{sv00} H1 Collaboration, contributed paper 082 to EPS03, Aachen.

\bibitem{ISRold} H1 Collaboration, contributed paper 976 to ICHEP02, Amsterdam.

\bibitem{tomas} T. La\v{s}tovi\v{c}ka,
Eur.~Phys.~J. C {\bf 24} (2002) 529 [hep-ph/0203260].

\bibitem{kgbw} K. Golec-Biernat and M. W\"usthoff, Phys.~Rev. D {\bf 59}
(1999) 014017, [hep-ph/9807513].

\bibitem{allm} H. Abramowicz and A. Levy,
DESY-97-251, [hep-ph/9712415].

\bibitem{bpt} ZEUS Collaboration,
Phys.~Lett. B {\bf 487} (2000) 53.

\bibitem{qedc} H1 Collaboration, contributed paper 084 to EPS03, Aachen.

\bibitem{nmc} NMC Collaboration, Nucl.~Phys. {\bf  B483} (1997) 3.

\bibitem{f29697} H1 Collaboration, 
Eur.~Phys.~J. C {\bf 21} (2001) 33 [hep-ex/0012153]; \\
H1 Collaboration,
Phys.~Lett. B {\bf 520} (2001) 183 [hep-ex/0108035]. 

\end{thebibliography}

\newpage

\begin{figure}[hhh]
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\put(0,-20){\epsfig{file=H1prelim-04-042.fig1.eps, width=\textwidth}}
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\caption{Control distributions for the ISR-dominated event selection.
The uncorrected data distributions are compared with the sum of 
the DIS expectation (DJANGO Monte Carlo model) and the expected photoproduction
background (PHOJET Monte Carlo model). The comparisons are shown for the 
effective incoming 
electron energy $E_e$, the electron scattering angle $\theta_e$, 
the sum of the electron and
hadron $E - p_z$ and the reconstructed $y$, $Q^2$ and $x$ as used in the
measurement.}
\label{one}
\end{figure}

\newpage

\begin{figure}[hhh]
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\put(0,-30){\epsfig{file=H1prelim-04-042.fig2.eps, width=\textwidth}}
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\caption{Measured reduced cross section from the shifted vertex ISR analysis,
compared with the extrapolated predictions of a `fractal' fit based on
self-similar proton structure, with the sum of the fractal fit result for
$F_2$ and a $F_L$ contribution from a dipole model and with the ALLM97
parameterisation.}
\label{two}
\end{figure}

\newpage

\begin{figure}[hhh]
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\caption{Measured reduced cross section from both ISR and non-radiative
measurements using shifted vertex data.}
\label{three}
\end{figure}

\newpage

\begin{figure}[hhh]
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\put(0,-30){\epsfig{file=H1prelim-04-042.fig4.eps, width=\textwidth}}
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\caption{Compilation of reduced cross section measurements 
with $Q^2 < 1 \ {\rm GeV^2}$ from H1, ZEUS and NMC.}
\label{four}
\end{figure}

\newpage

\begin{figure}[hhh]
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\put(0,-30){\epsfig{file=H1prelim-04-042.fig5.eps, width=\textwidth}}
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\end{center}
\caption{Compilation of selected HERA results on the parameter $\lambda$, 
obtained from fits of the form $F_2 = c(Q^2) \cdot x^{- \lambda (Q^2)}$ to
low $x$ data.}
\label{five}
\end{figure}

\end{document}




