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\begin{document}

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\noindent
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 {\bf H1prelim-08-041} Submitted to & & &
 \epsfig{file=/h1/iww/ipublications/H1PublicationTemplates/H1logo_bw_small.epsi
 ,width=1.5cm} \\[.2em] \hline
 \multicolumn{4}{l}{{\bf
                XVI International Workshop on Deep-Inelastic Scattering, DIS2008},
                 April 7-11,~2008,~London} \\
%                  Abstract:        & {\bf }    & & \\
                  Parallel Session & {\bf Structure Functions}   & & \\ \hline
   \multicolumn{4}{l}{\footnotesize {\it Electronic Access:https://www-h1.desy.de/publications/H1preliminary.short\_list.html
     %www-h1.desy.de/h1/www/publications/conf/conf\_list.html
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\begin{center}
  \Large
  {\bf 
   A Measurement of the Longitudinal Proton Structure Function $F_{L}(x,Q^{2})$ at low $x$ and medium $Q^{2}$ in the H1 Experiment at 
HERA}

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

\begin{abstract}

\noindent
A measurement of the longitudinal proton structure function $F_{L}(x,Q^{2})$ derived from inclusive deep inelastic 
$ep$ scattering cross section measurements with the H1 detector at HERA is presented. The data were taken in the year 2007 
at a positron beam energy of $E_{e}=27.5$~GeV and proton beam energies $E_{p}$ of 920~GeV, 575~GeV and 460~GeV. 
The cross section measurement is performed in a range of medium four-momentum transfer 
squared $12 \leq Q^2 \leq 90~$GeV$^2$ and correspondingly low Bjorken-$x$ between $0.00024\leq x \leq 0.00362$. 
The measured longitudinal structure function is found to be consistent with the NLO QCD calculations based on H1PDF fit and MSTW.

\noindent
\end{abstract}


\end{titlepage}

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%\section{Cross Section Measurement}

%The cross section of the inclusive DIS NC ($ep\rightarrow eX$), depends on three independent variables: $x$, $Q^{2}$ and $s$, the centre of mass energy squared. The double differential DIS cross section can be written as:
%\begin{eqnarray*}
%\label{sigmared}
%\frac{d^{2}\sigma}{dxdQ^{2}}=\frac{2\pi\alpha^{2}}{xQ^{4}}(Y_{+}F_{2}(x,Q^{2})-y^{2}F_{L}(x,Q^{2}))
%\end{eqnarray*}
%The longitudinal proton structure function  $F_{L}$ get sizable values only at high values of $y$ and can be measured directly at different values of $y$ for the same values of $x$ and $Q^{2}$. This has been achieved via reducing the centre of mass energy at HERA by performing dedicated runs at lower proton beam energies. Therefore, in year 2007 HERA had run at three different proton beam energies: the nominal energy run at 920~GeV, medium energy run at 575~GeV and low energy run at 460~GeV with corresponding luminosities of 21.9~$pb^{-1}$, 6.2~$pb^{-1}$ and 12.4~$pb^{-1}$, respectivelly.



%\newpage
%\begin{thebibliography}{99}

%\bibitem {klein}
%\cite{Klein:vs}
%M.~Klein and T.~Riemann,
%``Electroweak Interactions Probing The Nucleon Structure,''
%Z.\ Phys.\ C {\bf 24} (1984) 151.
%%CITATION = ZEPYA,C24,151;%%

%\bibitem{h1hiq2}
%C.~Adloff {\it et al.}  [H1 Collaboration],
%``Measurement and QCD Analysis of Neutral and Charged Current Cross Sections 
% at HERA''
%Eur.\ Phys.\ J.\ C {\bf 30} (2003) 1-32
%[hep-ex/0304003].
%%CITATION = HEP-EX 0304003;%%
%\vspace{-2mm}

%\bibitem{h1det}
% H1 Collaboration, I.~Abt {\it et al.}, Nucl.\ Instr.\ Meth.\ A386 (1997)
% 310 and 348.  -> No, 310 & 397
%I.~Abt {\it et al.}  [H1 Collaboration],
%``The H1 detector at HERA,''
%Nucl.\ Instrum.\ Meth.\ A {\bf 386} (1997) 310 and 348; \\
%%CITATION = NUIMA,A386,310;%%
%
%R.~D.~Appuhn {\it et al.}  [H1 SPACAL Group Collaboration],
%``The H1 lead/scintillating-fibre calorimeter,''
%Nucl.\ Instrum.\ Meth.\ A {\bf 386} (1997) 397.
%%CITATION = NUIMA,A386,397;%%

%\bibitem{spin}
% A.A.~Sokolov and I.M.~Ternov, Sov.\ Phys.\ Dokl.\ {\bf 8} No. 12 (1964) 1203.;
 
%\bibitem{tpol}
% D.B.~Barber {\it et al.}, Nucl.\ Instrum.\ Meth.\ A {\bf 329} (1993) 79.;
 
%\bibitem{lpol}
% M.~Beckmann {\it et al.}, Nucl.\ Instrum.\ Meth.\ A {\bf 479} (2002) 334.;

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

\newpage
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htb]
\begin{center}
\begin{picture}(90,60)(0,0)
\setlength{\unitlength}{1 mm}
\put(-5,  -10){\epsfig{file=H1prelim-08-041.fig1.eps,width=9cm}}
\end{picture}
\end{center}
\caption{Comparison of the correct charge sign data (points) with a sum of background determined from the wrong charge sign data (green histogram) and DIS MC (open histogram) for the low proton beam energy (460~GeV). The distributions from the left to the right and from the top to the bottom are the scattered electron energy $E_{e}^{'}$, the scattered electron polar angle $\Theta_{e}$, the z-position of the event vertex $Z_{vtx}$ and the sum $E-p_{z}$ of all final state particles. The vertical lines in $Z_{vtx}$ and $E-p_{z}$ distributions indicate cut values.}
\label{cp460} 
\end{figure}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htb]
\begin{center}
\begin{picture}(90,80)(0,0)
\setlength{\unitlength}{1 mm}
\put(-5,  -10){\epsfig{file=H1prelim-08-041.fig2.eps,width=9cm}}
\end{picture}
\end{center}
\caption{Comparison of signal distributions (background subtracted with corresponding asymmetry factor) for the low proton beam energy (460~GeV). The distributions from the left to the right and from the top to the bottom are the scattered electron energy $E_{e}^{'}$, the scattered electron polar angle $\Theta_{e}$, the z-position of the event vertex $Z_{vtx}$ and the sum $E-p_{z}$ of all final state particles. The vertical lines in $Z_{vtx}$ and $E-p_{z}$ distributions indicate cut values.}
\label{cp460nobg}
\end{figure}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htb]
\begin{center}
\begin{picture}(90,60)(0,0)
\setlength{\unitlength}{1 mm}
\put(-5,  -10){\epsfig{file=H1prelim-08-041.fig3.eps,width=9cm}}
\end{picture}
\end{center}
\caption{Comparison of the correct charge sign data (points) with a sum of background determined from the wrong charge sign data (green histogram) and DIS MC (open histogram) for the medium proton beam energy (575~GeV). The distributions from the left to the right and from the top to the bottom are the scattered electron energy $E_{e}^{'}$, the scattered electron polar angle $\Theta_{e}$, the z-position of the event vertex $Z_{vtx}$ and the sum $E-p_{z}$ of all final state particles. The vertical lines in $Z_{vtx}$ and $E-p_{z}$ distributions indicate cut values.}
\label{cp575}
\end{figure}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htb]
\begin{center}
\begin{picture}(90,80)(0,0)
\setlength{\unitlength}{1 mm}
\put(-5,  -10){\epsfig{file=H1prelim-08-041.fig4.eps,width=9cm}}
\end{picture}
\end{center}
\caption{Comparison of signal distributions (background subtracted with corresponding asymmetry factor) for the medium proton beam energy (575~GeV). The distributions from the left to the right and from the top to the bottom are the scattered electron energy $E_{e}^{'}$, the scattered electron polar angle $\Theta_{e}$, the z-position of the event vertex $Z_{vtx}$ and the sum $E-pz$ of all final state particles. The vertical lines in $Z_{vtx}$ and $E-p_{z}$ distributions indicate cut values.}
\label{cp575nobg}
\end{figure}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htb]
\begin{center}
\begin{picture}(90,60)(0,0)
\setlength{\unitlength}{1 mm}
\put(-15,  -5){\epsfig{file=H1prelim-08-041.fig5.eps,width=12cm}}
\end{picture}
\end{center}
\caption{Comparison of the correct charge sign data (points) with a sum of background determined from the wrong charge sign data (green histogram) and DIS MC (open histogram) for the low proton beam energy (460~GeV). The distributions from the left to the right are the inelasticity $y$, the four-momentum transfer squared $Q^{2}$ and Bjorken $x$.}
\label{cp460kin}
\end{figure}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htb]
\begin{center}
\begin{picture}(90,80)(0,0)
\setlength{\unitlength}{1 mm}
\put(-15,  -5){\epsfig{file=H1prelim-08-041.fig6.eps,width=12cm}}
\end{picture}
\end{center}
\caption{Comparison of signal distributions (background subtracted with corresponding asymmetry factor) for the low proton beam energy (460~GeV). The distributions from the left to the right are the inelasticity $y$, the four-momentum transfer squared $Q^{2}$ and Bjorken $x$.}
\label{cp460kinnobg}
\end{figure}

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

\begin{figure}[htb]
\begin{center}
\begin{picture}(90,60)(0,0)
\setlength{\unitlength}{1 mm}
\put(-15,  -5){\epsfig{file=H1prelim-08-041.fig7.eps,width=12cm}}
\end{picture}
\end{center}
\caption{Comparison of the correct charge sign data (points) with a sum of background determined from the wrong charge sign data and DIS MC (open histogram) for the medium proton beam energy (575~GeV). The distributions from the left to the right are the inelasticity $y$, the four-momentum transfer squared $Q^{2}$ and the Bjorken $x$.}
\label{cp575kin}
\end{figure}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htb]
\begin{center}
\begin{picture}(90,80)(0,0)
\setlength{\unitlength}{1 mm}
\put(-15,  -5){\epsfig{file=H1prelim-08-041.fig8.eps,width=12cm}}
\end{picture}
\end{center}
\caption{Comparison of signal distributions (background subtracted with corresponding asymmetry factor) for the the medium proton beam energy (575~GeV). The distributions from the left to the right are the inelasticity $y$, the four-momentum transfer squared $Q^{2}$ and the Bjorken $x$.}
\label{cp575kinnobg}
\label{pol}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htb]
\begin{center}
\begin{picture}(90,70)(0,0)
\setlength{\unitlength}{1 mm}
\put(-5,  -10){\epsfig{file=H1prelim-08-041.fig16.eps,width=9cm}}
\end{picture}
\end{center}
\caption{Comparison of the correct charge sign data (points) with a sum of background determined from the wrong charge sign data (green histogram) and DIS MC (open histogram) for the low proton beam energy (460~GeV). The distributions are distance between the extrapolated CJC track and cluster in SpaCal $D_{CJC-SpaCal}$ and fraction of the energy in the hadronic SpaCal behind the electromagnetic cluster $E_{h}/E_{e}$, respectively. The vertical lines in $D_{CJC-SpaCal}$ and $E_{h}/E_{e}$ distributions indicate cut values.}
\label{cp460cjceh} 
\end{figure}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htb]
\begin{center}
\begin{picture}(90,80)(0,0)
\setlength{\unitlength}{1 mm}
\put(-5,  -10){\epsfig{file=H1prelim-08-041.fig17.eps,width=9cm}}
\end{picture}
\end{center}
\caption{Comparison of the correct charge sign data (points) with a sum of background determined from the wrong charge sign data (green histogram) and DIS MC (open histogram) for the medium proton beam energy (575~GeV). The distributions are distance between the extrapolated CJC track and cluster in SpaCal $D_{CJC-SpaCal}$ and fraction of the energy in the hadronic SpaCal behind the electromagnetic cluster $E_{h}/E_{e}$, respectively. The vertical lines in $D_{CJC-SpaCal}$ and $E_{h}/E_{e}$ distributions indicate cut values.}
\label{cp575cjceh}
\end{figure}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htb]
\begin{center}
\begin{picture}(90,60)(0,0)
\setlength{\unitlength}{1 mm}
\put(-25,  -10){\epsfig{file=H1prelim-08-041.fig9.eps,width=13cm}}
\end{picture}
\end{center}
\caption{Comparison of the data (points) with a sum of background (green histogram) and DIS MC (open histogram) for the complete analysis range in $y$ corresponding to the low proton beam energy (460~GeV). The distributions from the left to the right and from the top to the bottom are the scattered electron energy $E_{e}^{'}$, scattered electron polar angle $\Theta_{e}$, the z-position of the event vertex $Z_{vtx}$ and the sum $E-p_{z}$ of all final state particles, the logarithmic weighted cluster radius $R_{SpaCal}$ and momentum balance $P_{t}^{h}/P_{t}^{e}$.}
\label{cp460all}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{figure}[htb]
\begin{center}
\begin{picture}(90,80)(0,0)
\setlength{\unitlength}{1 mm}
\put(-25,  -10){\epsfig{file=H1prelim-08-041.fig10.eps,width=13cm}}
\end{picture}
\end{center}
\caption{Comparison of data (points) with a sum of background determined from photoproduction MC (green histogram) and DIS MC (open histogram) for the complete analysis range in $y$ corresponding to the medium proton beam enery (575~GeV). The distributions from the left to the right and from the top to the bottom are the scattered electron energy $E_{e}^{'}$, the scattered electron polar angle $\Theta_{e}$, the z-position of the event vertex $Z_{vtx}$ and the sum $E-p_{z}$ of all final state particles, the logarithmic weighted cluster radius $R_{SpaCal}$ and the momentum balance $P_{t}^{h}/P_{t}^{e}$.}
\label{cp575all}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htb]
\begin{center}
\begin{picture}(90,60)(0,0)
\setlength{\unitlength}{1 mm}
\put(-25,  -15){\epsfig{file=H1prelim-08-041.fig11.eps,width=13cm}}
\end{picture}
\end{center}
\caption{Comparison of the data (points) with a sum of background determined from photoproduction MC (green histogram) and DIS MC (open histogram) for the complete analysis range in $y$ corresponding to the nominal proton beam energy (920~GeV). The distributions from the left to the right and from the top to the bottom are of the scattered electron energy $E_{e}^{'}$, scattered electron polar angle $\Theta_{e}$, the z-position of the event vertex $Z_{vtx}$ and the sum $E-p_{z}$ of all final state particles, logarithmic weighted cluster radius $R_{SpaCal}$ and the momentum balance $P_{t}^{h}/P_{t}^{e}$.}
\label{cp920all}
\end{figure}

\newpage
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htb]
\begin{center}
\begin{picture}(90,85)(0,0)
\setlength{\unitlength}{1 mm}
\put(-10,  -12){\epsfig{file=H1prelim-08-041.fig12.eps,width=10.5cm}}
\end{picture}
\end{center}
\caption{Reduced cross section measured at medium $Q^{2}$ as a function of $x$ using data taken at different proton beam energies of 920~GeV (full boxes), 575~GeV (stars) and 460~GeV (full points). The error bars represent the statistical and systematic errors, added in quadrature. Theoretical predictions of reduced cross section are shown as the solid lines for 920~GeV (blue), 575~GeV (black) and 460~GeV (red) line. The dashed line represents the QCD expectation of $F_{2}$ derived from H1PDF fit.}
\label{sigmared}
\end{figure}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htb]
\begin{center}
\begin{picture}(90,60)(0,0)
\setlength{\unitlength}{1 mm}
\put(-15,  -10){\epsfig{file=H1prelim-08-041.fig13.eps,width=11cm}}
\end{picture}
\end{center}
\caption{The reduced cross section $\sigma_{r}(x,Q^{2},y)$ measured at $Q^{2}=25~GeV^{2}$ and fixed values of $x$ as a function of $f(y)=\frac{y^{2}}{1+(1-y)^{2}}$. The full boxes represent the nominal energy data (920~GeV), stars the medium energy data (575~GeV) and full circles the low energy data (460~GeV). The inner error bars are the statistical errors and the full error bars represent the statistical and systematic errors, added in quadrature. The lines show the linear fits used to determine $F_{L}$.}
\label{rosenbluth}
\end{figure}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htb]
\begin{center}
\begin{picture}(90,85)(0,0)
\setlength{\unitlength}{1 mm}
\put(-25,  -10){\epsfig{file=H1prelim-08-041.fig14.eps,width=13cm}}
\end{picture}
\end{center}
\caption{The longitudinal structure function $F_{L}$ measured as a function of $x$ at fixed values of $Q^{2}$ obtained by H1 using data taken at different proton beam energies of 460~GeV, 575~GeV and 920~GeV. The inner error bars are the statistical errors and the full error bars represent the statistical and systematic errors, added in quadrature. The solid red line represents a QCD prediction based on H1 PDF 2000 fit, the dashed red line $F^{H1PDF 2000}_{2}/3$ and the dashed blue line a QCD prediction based on MSTW PDF.}
\label{fl}
\end{figure}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[htb]
\begin{center}
\begin{picture}(90,60)(0,0)
\setlength{\unitlength}{1 mm}
\put(-20,  -10){\epsfig{file=H1prelim-08-041.fig15.eps,width=10cm}}
\end{picture}
\end{center}
\caption{The longitudinal structure function $F_{L}(x,Q^{2})$ averaged for a given $Q^{2}$ as measured by H1 using data taken at different proton beam energies of 460~GeV, 575~GeV and 920~GeV. The $x$ values of the measurements contributing to the $Q^{2}$-value are indicated in grey. The inner error bars are the statistical errors and the full error bars represent the statistical and systematic errors, added in quadrature. The solid red line represents QCD prediction based on H1 PDF 2000 fit and the dashed blue line QCD prediction based on MSTW.}
\label{flvsq2}
\end{figure}

%------------------------------------------------
\begin{table}
\fontsize{12}{12pt}\selectfont
 \begin{center}
 \begin{tabular}{|l|l|}
 \hline\hline
  {\bf Systematic source} & {\bf Effect on the cross section } \\ \hline\hline
  Kinematic reconstruction & $\sim 3\%$ \\ \hline
  Electron identification and event selection & $\sim 2\%$ \\ \hline
  Background subtraction & max $4\%$\\ \hline
  Radiative corrections & $\sim 1\%$ \\ \hline\hline
\end{tabular}
 \end{center}
\caption{Sources of systematic uncertainties and their impact on the cross section measurement.}
\label{tab:syserr}
\end{table}
%------------------------------------------------


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