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\begin{titlepage}

\noindent
\hfill \bf{H1prelim-13-141} \rm and \bf{ZEUS-prel-13-003}\rm \\
\today       \\
%Version:     0.6         \\
%Editors:     \myref{mailto:voica@mail.desy.de}{V.~Radescu},\myref{mailto:a.cooper-sarkar1@physics.ox.ac.uk}{A.~Cooper-Sarkar},  \myref{mailto:hannes.jung@desy.de}{H.~Jung}, \myref{mailto:katarzyna.wichmann@desy.de}{K.~Wichmann}       \\
%Referees:         \\
%Comments by  Deadline       

\vspace{2cm}

\begin{center}
\begin{Large}

{\bf HERAPDF1.5LO PDF Set with Experimental Uncertainties}

\vspace{2cm}

H1 and ZEUS Collaborations

\end{Large}
\end{center}

\vspace{2cm}

\begin{abstract}
This note presents the HERAPDF1.5 PDF set evolved to leading order (LO) $\alpha_s$ using DGLAP evolution equations. This LO PDF is particularly useful for Monte Carlo event generators, based on LO matrix elements plus parton showers.
% and the simulation of higher order corrections via parton showers. Of special interest is this PDF set for the simulation of the parton shower and underlying event properties in calculations which match a NLO hard process calculation with parton showers and hadronsiation as done in  POWHEG or MC@NLO.

\end{abstract}

\vspace{1.5cm}

%\begin{center}
%To be submitted to the LHAPD online repository
%\end{center}

\end{titlepage}

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\newpage

\section{Introduction}
\noindent
%HERAPDF PDF presents a valuable alternative to other PDF sets
%available for standard Monte Carlo generators such as PYTHIA or HERWIG, 
%which will require LO PDFs rather than the NLO ones.

Parton densities evolved to leading order (LO) in $\alpha_s$ are essential for the proper simulation
of parton showers (PS) and underlying event properties in LO+PS Monte Carlo (MC) event generators. 
%In the PS approach the parton densities
%are used to simulate higher order parton emissions (usually in the leading $\log$ approximation) from
%the hard scattering process to a low scale, typically of ${\cal O}(1\mbox{ GeV})$. A physical behavior of the parton densities at such low scales is essential, in particular the parton densities must be positive to represent a probability distribution to be used in a Monte Carlo event simulation.
% A set of LO pdfs together with a corresponding PDF set evolved to NLO are of special interest to NLO + PS calculations like  MC@NLO~\cite{Frixione:2002ik} and POWHEG \cite{Nason:2004rx,Frixione:2007vw}.


In the light of the imminent restart of the LHC with upgraded proton energy beams, 
new tunes for the underlying events and minimum bias are needed using 
various MC generators. Since the higher energies at the LHC 
will cover measurements to lower values of the Bjorken-$x$ variable,  the HERAPDF PDF sets with its special emphasis on the 
small-$x$ structure functions and its validity at small scales is important for equipping the MC generators with accurate PDFs that enable precise predictions of the underlying event properties and also for minimum bias events and the simulation of pile-up events.

In this note we present the HERAPDF1.5 LO set based on the same settings 
as used for the HERAPDF1.5 NLO PDF set\cite{HERAPDF1.5NLO}, with the exception
of the use of the LO DGLAP splitting kernel and, correspondingly, of a 
different value for the strong coupling constant.

 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\begin{equation}
%x_\pom = \frac{\qsq+M_X^2-t}{\qsq+W^2+M_p^2} \; .
%\label{eq:xpom}
%\end{equation}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%Equation (\ref{eq:xpom}) gives ...

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\begin{figure}[hhh]
%  \begin{center}
%    \includegraphics[width=\textwidth]{d98-029f6}
%    \caption{ The average squared transverse momentum 
%$\langle p_t^{*2} \
%rangle$ of hadrons is shown as 
%a function of Feynman $x_F$,}
%    \label{fig:diff} 
%  \end{center}
%\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\section{Technical Description of the HERAPDF1.5 LO PDF set}
The framework used in this QCD analysis is based on the HERAFitter project \cite{HERAFitter}, with evolution code as implemented in the QCDNUM package \cite{QCDNUM}. The results were cross checked by an independent framework referred to as the ZEUS Fitter \cite{ZEUSfitter}.
The QCD fit settings are adopted from  the previous HERAPDF fits to preliminary combined H1 and ZEUS  HERA I+II data of inclusive
 deep-inelastic scattering used to extract HERAPDF1.5 NLO \cite{HERAPDF1.5NLO} and NNLO PDF \cite{HERAPDF1.5NNLO} sets. 
The experimental uncertainties of data are treated in the same way as in the HERAPDF1.5 NLO and NNLO fits.
%with $130$ sources of systematic uncertainties 
%treated uncorrelated bin to bin, as well as  correlated among four data sets of neutral current (NC) and charged current (CC) of  $e^+p$ and  $e^-p$ 
%scattering and with three sources of systematic uncertainties arising from the data combination procedure treated as correlated bin to bin and as well as 
%among data sets (referred to as $proced1$, $proced2$, $proced3$ in the results table).


 The PDFs parametrised at the starting scale of the evolution\footnote{chosen 
to be below the charm mass threshold as required by the QCDNUM package} of 
$Q^2_0=1.9$~\gevsq are the valence distributions
  $xu_v$ and $xd_v$, the gluon distribution $xg$, and the $x\bar{U}$ and $x\bar{D}$ distributions, where 
  $x\bar{U} = x\bar{u}$ , $x\bar{D} = x\bar{d}+x\bar{s}$.
The following functional form is used to parametrise them and is identical to the HERAPDF1.5 NLO set:
\begin{eqnarray}
  x u_v(x) &=&  A_{u_v} x^{B_{u_v}} (1-x)^{C_{u_v}} ( 1 + E_{u_v} x^2) \\
  x d_v(x) &=&  A_{d_v} x^{B_{d_v}} (1-x)^{C_{d_v}}  \\
  x \bar{U} (x) &=& A_{\bar{U}} x^{B_{\bar{U}}} (1-x)^{C_{\bar{U}}}  \\  
  x \bar{D} (x) &=& A_{\bar{D}} x^{B_{\bar{D}}} (1-x)^{C_{\bar{D}}}  \\
  x g(x)   &=& A_g x^{B_g} (1-x)^{C_g} \,.
  \label{eq:param}
\end{eqnarray}
where the normalization parameters ($A_{u_v}; A_{d_v}; A_g$) are constrained by 
quark counting and momentum sum rules. The $B$ exponents for the quark sea and 
valence distributions, respectively, are set equal, 
$B_{\bar{U}} = B_{\bar{D}}$ and $B_{u_v} = B_{d_v}$.
%, such that there is a single $B$ parameter for
% the quark sea distributions, as well as a single parameter $B$ for the valence quark distributions. 
The strange quark distribution at the starting scale is assumed to be a constant fraction of $\bar{D}$,
 $x\bar{s} = f_s x\bar{D}$, chosen to be $f_s = 0.31$ such that $\bar{s} \approx \bar{d}/2$. In addition, to ensure that 
 $x\bar{u} = x \bar{d}$ as $x \to 0$, $A_{\bar{U}}=A_{\bar{D}}(1-f_s)$.
This yields the same 13 free parameters as in the NLO fit.

The PDFs are evolved using the DGLAP evolution equations at LO with the squared
renormalisation and factorisation scales set to the squared momentum transfer 
of the NC or CC interaction, $Q^2$.
The value for $\alpha_s(M_Z)$ has been chosen to be $0.13$, which yields the 
best level of agreement between data and the fit\footnote{
This value agrees with the value used by the CTEQ LO set \cite{CTEQ} of  
$\alpha_s(M_Z)=0.12978$, which is different from the value chosen by the 
MSTW LO set \cite{MSTW} of  $\alpha_s(M_Z)=0.136$.}.


As for previous HERAPDF PDF sets, the analysis is performed accounting for the 
charm and beauty quark masses in the Thorne-Roberts (TR) Variable Flavour 
Number Scheme \cite{RT}.
%a check against the ACOT scheme is also performed as usual.

 
 The experimental uncertainties on the PDFs are determined using the $\Delta\chi^2 = 1$ criterion leading to uncertainties with a confidence level of $68\%$. The 
$\chi^2$ is defined as in \cite{ref:sasha}:
 \begin{equation}
\chi^2=\sum_i\frac{\left[ \mu_i - m_i\left(1-\sum_j\gamma_j^i b_j\right) \right]^2}{\delta_{i,{\rm unc}}^2 m_i^2+\delta_{i,{\rm stat}}^2\mu_i m_i\left(1-\sum_
j\gamma_j^i b_j\right)} +\sum_j b_j^2 
%+ \sum_i \ln \frac{\delta_{i,{\rm unc}}^2 m_i^2+\delta_{i,{\rm stat}}^2\mu_i m_i}{\delta_{i,{\rm unc}}^2 \mu_i^2+\delta_
%{i,{\rm stat}}^2\mu_i^2},
\label{eq:chi2}
\end{equation}
where $m_i$ is the theoretical prediction and $\mu_i$ is the measured cross 
section at point $i$, $(Q^2,x,s)$ with the relative statistical and 
uncorrelated systematic uncertainty $\delta_{i,{\rm stat}}$, 
$\delta_{i,{\rm unc}}$, respectively. 
%
The values $\gamma_j^i$ denote the relative correlated systematic uncertainties
and $b_j$ their shifts with a penalty term $\sum_j\!b^2_j$ added. 

% In
%order to protect from a bias introduced by statistical fluctuations,
%the expected rather than the observed number of events are used, with
%the corresponding errors scaled accordingly.  
%This scaling of errors
%introduces a $\ln$ term, coming from the likelihood transition to
%$\chi^2$. Neglecting the $\ln$ term gives very similar results and
%does not alter any of the conclusions.


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{QCD Fit Results and Comparisons}

The LO QCD fit to the preliminary combined H1 and ZEUS HERA I+II 
data\cite{HERAPDF1.5NLO} yields a reasonable total 
$\chi^2$ of $762$ for $664$ degrees of freedom, slightly 
worse than the NLO $\chi^2$ of $736$.  
% indicating a fair fit quality.
%are summarized in table \ref{tab:results}.
The choice of $\alpha_s(M_Z)=0.13$ was motivated through a scan procedure, 
where the data were refit with other choices of the strong coupling and the 
best value in terms of quality of fit was chosen.
%
%The dependence on the choice of $\alpha_s(M_Z)$ value is given in table \ref{tab:alphas}. The PDF parameters from the fit are listed in table \ref{tab:param}.
The resulting PDF distribution plots for the starting scale as well as for 
momentum transfers of 10, 100 and 10000 GeV$^2$ can be found in Figs.
 \ref{fig:summary1.9}-\ref{fig:summary10000}.
They are presented together with uncertainty bands reflecting the experimental 
uncertainties transferred from the data to the PDFs. In line with the 
restricted purpose of the LO sets, no further model or theoretical 
uncertainties were evaluated.

% %%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{table}[!htb]
% \begin{center}
% \caption{\label{tab:results} $\chi^2$ values for the HERAPDF1.5 LO fit results to the preliminary HERA-I+II data.}
% \begin{tabular}{l|c|c}
% \hline
% \hline
% Data Set & partial $\chi^2$ & Nr. points \\
% \hline
% NC cross section HERA-I+II H1-ZEUS combined e-p. & 237.57 &  182 \\
% NC cross section HERA-I+II H1-ZEUS combined e+p. & 430.74 &  412 \\
% CC cross section HERA-I+II H1-ZEUS combined e-p. & 42.44  &  41  \\
% CC cross section HERA-I+II H1-ZEUS combined e+p. & 50.38   &  39  \\ 
% \hline
% Correlated & 1.18 & 3 (sources) \\
% Total & 762.30 & 664 (dof) \\
% \hline
% \hline
%   Sys. Source & Sys. Shift (in $\sigma$) & Uncert. of Shift \\
% \hline
%      proced1                &                     -0.0125    &   0.2252\\ 
%      proced2                &                     -0.9479   &   0.2633\\ 
%      proced3               &                      -0.5260   &   0.2852\\ 
% \hline
% \hline
% \end{tabular}
% \end{center}
% \end{table}
% %%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{table}[!htb]
% \begin{center}
% \caption{\label{tab:alphas} $\chi^2$ values for the LO fit to the HERA-I+II data using various values for strong couplings.}
% \begin{tabular}{l|c}
% \hline
% \hline
% $\alpha_s(M_Z)$ & Total $\chi^2$ \\
% \hline
% 0.1176  & 791.86 \\
% 0.1200  & 780.93\\
% 0.1250  & 766.77 \\
% %0.12978 & 762.30 \\
% 0.1300  & 762.29 \\
% 0.1350  & 766.22 \\
% 0.1390  & 775.62 \\
% \hline
% \hline
% \end{tabular}
% \end{center}
% \end{table}
% %%%%%%%%%%%%%%%%%%%%%%%%%

% \begin{table}[!htb]
% \begin{center}
% \caption{\label{tab:param} PDF parameters from LO fit at the starting scale.}
% \begin{tabular}{l|c|c}
% \hline
% \hline
%      PDF Param & Central Value &  Uncertainty \\
% \hline
%      $B_g$  &-0.17 &   0.01 \\
%       $C_g$    &5.85   & 0.34 \\
%      $B_{u_v}$    &0.60   & 0.02 \\
%      $C_{u_v}$    &4.22    &0.09 \\
%       $E_{u_v}$   &10.38    &1.20 \\
%       $C_{d_v}$    &3.69    &0.19 \\
%       $C_{\bar{U}}$   & 2.80  &  0.40 \\
%       $A_{\bar{D}}$  &  0.147   & 0.005 \\
%       $B_{\bar{D}}$  & -0.198   & 0.005 \\
%       $C_{\bar{D}}$ &   4.38    &0.84\\
% \hline
% \hline
% \end{tabular}
% \end{center}
% \end{table}
% %%%%%%%%%%%%%%%%%%%%%%%%%

Figures  \ref{fig:ncepa}-\ref{fig:ccep} show LO cross section predictions 
obtained from the fitted PDFs, overlayed on the data used in the fits, for 
the neutral current and charged current $e^+p$ and $e^-p$ differential 
measurements. Good agreement is achieved.
%\ref{fig:ncepb},\ref{fig:ncem}, \ref{fig:ccep},





%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[]
  \begin{center}
    \includegraphics[width=\textwidth]{figures/herapdf15lo_q2_1pt9.eps}
%    \includegraphics[width=\textwidth]{figures/herapdf15lo_q2_2.pdf}
    \caption{Summary of LO PDFs at $Q^2=1.9$ \gevsq. }
    \label{fig:summary1.9} 
  \end{center}
\end{figure}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[]
  \begin{center}
    \includegraphics[width=\textwidth]{figures/herapdf15lo_q2_10.eps}
    \caption{Summary of LO PDFs at $Q^2=10.0$ \gevsq. }
    \label{fig:summary10} 
  \end{center}
\end{figure}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[]
  \begin{center}
    \includegraphics[width=\textwidth]{figures/herapdf15lo_q2_100.eps}
    \caption{Summary of LO PDFs at $Q^2=100$ \gevsq. }
    \label{fig:summary100} 
  \end{center}
\end{figure}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[]
  \begin{center}
    \includegraphics[width=\textwidth]{figures/herapdf15lo_q2_10000.eps}
    \caption{Summary of LO PDFs at $Q^2=10000$ \gevsq.}
    \label{fig:summary10000} 
  \end{center}
\end{figure}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[]
  \begin{center}
    \includegraphics[width=\textwidth]{figures/ncepb_corrected_x1_new.eps}
    \caption{Neutral current $e^+p$ differential cross section measurements 
(data points, part I, for lower $Q^2$ bins) compared to predictions based on 
the HERAPDF1.5 LO PDF set with experimental uncertainties included in the 
predictions (contious bands). The dashed line indicates predictions for regions
not included in the fit.}
    \label{fig:ncepa} 
  \end{center}
\end{figure}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[]
  \begin{center}
    \includegraphics[width=\textwidth]{figures/ncepc_new.eps}
    \caption{Neutral current $e^+p$ differential cross section measurements 
(data points, part II, for higher $Q^2$ bins) compared to predictions based on 
the HERAPDF1.5 LO PDF set with experimental uncertainties included in the 
predictions (continous bands).}
    \label{fig:ncepb} 
  \end{center}
\end{figure}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[]
  \begin{center}
    \includegraphics[width=\textwidth]{figures/ncem_new.eps}
    \caption{Neutral current $e^-p$ differential cross section measurements 
(data points) compared to predictions based on the HERAPDF1.5 LO PDF set with 
experimental uncertainties included in the predictions (continous bands).}
    \label{fig:ncem} 
  \end{center}
\end{figure}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[]
  \begin{center}
    \includegraphics[width=\textwidth]{figures/ccem_new.eps}
    \caption{Charged current $e^-p$ differential cross section measurements 
(data points) compared to predictions based on the HERAPDF1.5 LO PDF set with 
experimental uncertainties included in the predictions (continous bands).}
    \label{fig:ccem} 
  \end{center}
\end{figure}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[]
  \begin{center}
    \includegraphics[width=\textwidth]{figures/ccep_new.eps}
    \caption{Charged current $e^+p$ differential cross section measurements 
(data points) compared to predictions based on the HERAPDF1.5 LO PDF set with 
experimental uncertainties included in the predictions (continous bands).}
    \label{fig:ccep} 
  \end{center}
\end{figure}



The LO PDF set has been formatted to match
the LHAPDF style, similarly to what was done for the HERAPDF1.5 NLO set,
compatible with the LHAPDFv5 grid style.
The LHAPDF grid contains $21$ members with member $0$ representing the central fit, 
while members $1-20$ correspond to the experimental uncertainties on the PDFs.
The $20$ error PDFs should be treated two by two as the up and    
down excursions for each of the $10$ eigenvectors defined by the number of free PDF parameters in the fit, such that the symmetric error is calculated as the quadratic sum of the difference between the up and down eigenvectors divided by two. 
If asymmetric errors are desired equation $43$ of \cite{CHS} may be used.


\section{Summary}

We have extracted a HERAPDF1.5 LO PDF set based on the preliminary HERA I+II 
H1 and ZEUS combined NC and CC measurements, providing 
experimental uncertainties. The fit describes the data reasonably well.
The set has been formatted to match the LHAPDF style, similarly to what was 
done for the HERAPDF1.5 NLO set, compatible with the LHAPDFv5 grid style.



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



\section*{Acknowledgements}

We are grateful to the HERA machine group whose outstanding
efforts have made this experiment possible. 
We thank the engineers and technicians for their work in constructing and
maintaining the H1 detector, our funding agencies for 
financial support, the
DESY technical staff for continual assistance
and the DESY directorate for support and for the
hospitality which they extend to the non DESY 
members of the collaboration.
We would like to give credit to all partners contributing to the EGI 
computing infrastructure for their support for the H1 and ZEUS  Collaborations.



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

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%S.~Frixione and B.~R. Webber.
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%\newblock {\em JHEP}, 0206:029, 2002.

%\bibitem{Nason:2004rx}
%P.~Nason.
%\newblock {A New method for combining NLO QCD with shower Monte Carlo
%  algorithms}.
%\newblock {\em JHEP}, 0411:040, 2004.

%\bibitem{Frixione:2007vw}
%S.~Frixione, P.~Nason, and C.~Oleari.
%\newblock {Matching NLO QCD computations with Parton Shower simulations: the
%  POWHEG method}.
%\newblock {\em JHEP}, 0711:070, 2007.

\bibitem{HERAPDF1.5NLO}
  A.~M.~Cooper-Sarkar [ZEUS and H1 Collaborations],
  %``PDF Fits at HERA,''
  %PoS EPS {\bf -HEP2011}, 320 (2011)
  arXiv:1112.2107 [hep-ph]. \\
   V.~Radescu {\it et al.}  [H1 and ZEUS Collaborations],
  %``Combination and QCD Analysis of the HERA Inclusive Cross Sections,''
  arXiv:1308.0374 [hep-ex].

\bibitem{HERAFitter} 
 % "Combined Measurement and QCD Analysis of the Inclusive e+- p Scattering Cross Sections at HERA."
F.D. Aaron et al. [H1 and ZEUS Collaborations],   
%DESY-09-158, Oct 2009. 61pp. 
%Published in
JHEP 1001:109 (2010); 
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%"A Precision Measurement of the Inclusive ep Scattering Cross Section at HERA."
%By H1 Collaboration (F.D. Aaron et al.). DESY-09-005, 2009. 35pp. 
Eur.\ Phys.\ J. {\bf C 64} (2009) 561; 
%e-Print: 
[arXiv:0904.3513 [hep-ex]]. 

\bibitem{QCDNUM} 
M. Botje, arXiv:1005.1481 [hep-ph].

\bibitem{ZEUSfitter}
%\bibitem{Chekanov:2005nn} 
  S.~Chekanov {\it et al.}  [ZEUS Collaboration],
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  Eur.\ Phys.\ J.\ {\bf C 42} (2005) 1;
  [hep-ph/0503274].
  %%CITATION = HEP-PH/0503274;%%
  %177 citations counted in INSPIRE as of 29 Aug 2013

\bibitem{HERAPDF1.5NNLO}
  V.~Radescu [H1 and ZEUS Collaborations],
  %``Hera Precision Measurements and Impact for LHC Predictions,''
  arXiv:1107.4193 [hep-ex].

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\bibitem{MSTW}                                                          
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%  "Parton distributions for the LHC"
 Eur. Phys. J. {C 63} (2009) 189;                             
 [arXiv:0901.0002 [hep-ph]].    

%"A Precision Measurement of the Inclusive ep Scattering Cross Section at HERA."
%By H1 Collaboration (F.D. Aaron et al.). DESY-09-005, 2009. 35pp. 
%Published in Eur.Phys.J.C64:561-587,2009. 
%e-Print: 
%arXiv:0904.3513 [hep-ex] 

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%\bibitem{ACOT}   
%M.A.G. Aivazis, John C. Collins, Fredrick I. Olness, Wu-Ki Tung
%arXiv:hep-ph/9312319v2
          
\bibitem{ref:sasha}
%\bibitem{Collaboration:2010ry} 
  F.~D.~Aaron {\it et al.}  [ H1 Collaboration],
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  %%CITATION = ARXIV:1012.4355;%%
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[hep-ph/0611148].                                                  
\end{thebibliography}





\newpage

% \section{Auxiliary plots - NOT FOR APPROVAL}

% In Fig.~\ref{fig:glu} one can see that the gluon density at small scales has a different shape compared to other PDFs. This is of special interest for small $x$ processes and the simulation of parton shower as well as the underlying event.


% \begin{figure}[]
%   \begin{center}
%     \includegraphics[width=0.5\textwidth]{figures/glu19.pdf}\includegraphics[width=0.5\textwidth]{figures/glu6464.pdf}
%     \caption{Gluon PDF at $Q^2=1.9$ \gevsq (left) and at  $Q^2=M_W^2$ \gevsq (right) }
%     \label{fig:glu} 
%   \end{center}
% \end{figure}


% \begin{figure}[]
%   \begin{center}
%     \includegraphics[width=0.5\textwidth]{figures/uval19.pdf}\includegraphics[width=0.5\textwidth]{figures/uval6464.pdf}
%     \caption{Valence of $xu$ PDF at $Q^2=1.9$ \gevsq (left) and at  $Q^2=M_W^2$ \gevsq (right) }
%     \label{fig:uval} 
%   \end{center}
% \end{figure}

% \begin{figure}[]
%   \begin{center}
%     \includegraphics[width=0.5\textwidth]{figures/dval19.pdf}\includegraphics[width=0.5\textwidth]{figures/dval6464.pdf}
%     \caption{Valence of $xd$ PDF at $Q^2=1.9$ \gevsq (left) and at  $Q^2=M_W^2$ \gevsq (right) }
%     \label{fig:dval} 
%   \end{center}
% \end{figure}

% \begin{figure}[]
%   \begin{center}
%     \includegraphics[width=0.5\textwidth]{figures/Ubar19.pdf}\includegraphics[width=0.5\textwidth]{figures/Ubar6464.pdf}
%     \caption{Sea of $U$ PDF at $Q^2=1.9$ \gevsq (left) and at  $Q^2=M_W^2$ \gevsq (right) }
%     \label{fig:Ubar} 
%   \end{center}
% \end{figure}

% \begin{figure}[]
%   \begin{center}
%     \includegraphics[width=0.5\textwidth]{figures/Dbar19.pdf}\includegraphics[width=0.5\textwidth]{figures/Dbar6464.pdf}
%     \caption{Sea of $D$ PDF at $Q^2=1.9$ \gevsq (left) and at  $Q^2=M_W^2$ \gevsq (right) }
%     \label{fig:Dbar} 
%   \end{center}
% \end{figure}


% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{figure}[]
%   \begin{center}
%     \includegraphics[width=0.5\textwidth]{figures/ratglu19.pdf}\includegraphics[width=0.5\textwidth]{figures/ratglu6464.pdf}
%     \caption{Ratio plot for Gluon at $Q^2=1.9$ \gevsq (left) and at  $Q^2=M_W^2$ \gevsq (right) }
%     \label{fig:ratglu} 
%   \end{center}
% \end{figure}

% \begin{figure}[]
%   \begin{center}
%     \includegraphics[width=0.5\textwidth]{figures/ratuval19.pdf}\includegraphics[width=0.5\textwidth]{figures/ratuval6464.pdf}
%     \caption{Ratio plot for Valence of $xu$ PDF at $Q^2=1.9$ \gevsq (left) and at  $Q^2=M_W^2$ \gevsq (right) }
%     \label{fig:ratuval} 
%   \end{center}
% \end{figure}

% \begin{figure}[]
%   \begin{center}
%     \includegraphics[width=0.5\textwidth]{figures/ratdval19.pdf}\includegraphics[width=0.5\textwidth]{figures/ratdval6464.pdf}
%     \caption{Ratio plot for Valence of $xd$ PDF at $Q^2=1.9$ \gevsq (left) and at  $Q^2=M_W^2$ \gevsq (right) }
%     \label{fig:ratdval} 
%   \end{center}
% \end{figure}

% \begin{figure}[]
%   \begin{center}
%     \includegraphics[width=0.5\textwidth]{figures/ratUbar19.pdf}\includegraphics[width=0.5\textwidth]{figures/ratUbar6464.pdf}
%     \caption{Ratio plot for Sea of $U$ PDF at $Q^2=1.9$ \gevsq (left) and at  $Q^2=M_W^2$ \gevsq (right) }
%     \label{fig:ratUbar} 
%   \end{center}
% \end{figure}

% \begin{figure}[]
%   \begin{center}
%     \includegraphics[width=0.5\textwidth]{figures/ratDbar19.pdf}\includegraphics[width=0.5\textwidth]{figures/ratDbar6464.pdf}
%     \caption{Ratio plot for Sea of $D$ PDF at $Q^2=1.9$ \gevsq (left) and at  $Q^2=M_W^2$ \gevsq (right) }
%     \label{fig:ratDbar} 
%   \end{center}
% \end{figure}

% Comparison between HERAPDF1.5 LO, NLO, NNLO sets are shown in Figs.
% ~\ref{fig:gluH}- \ref{fig:DbarH}.
% %~\ref{fig:gluH},\ref{fig:uvalH}, \ref{fig:dvalH}, \ref{fig:UbarH}, \ref{fig:DbarH}.

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{figure}[]
%   \begin{center}
%     \includegraphics[width=0.5\textwidth]{figures/Hglu19.pdf}\includegraphics[width=0.5\textwidth]{figures/Hglu6464.pdf}
%     \caption{Gluon at $Q^2=1.9$ \gevsq (left) and at  $Q^2=M_W^2$ \gevsq (right) }
%     \label{fig:gluH} 
%   \end{center}
% \end{figure}

% \begin{figure}[]
%   \begin{center}
%     \includegraphics[width=0.5\textwidth]{figures/Huval19.pdf}\includegraphics[width=0.5\textwidth]{figures/Huval6464.pdf}
%     \caption{Valence of $xu$ PDF at $Q^2=1.9$ \gevsq (left) and at  $Q^2=M_W^2$ \gevsq (right) }
%     \label{fig:uvalH} 
%   \end{center}
% \end{figure}

% \begin{figure}[]
%   \begin{center}
%     \includegraphics[width=0.5\textwidth]{figures/Hdval19.pdf}\includegraphics[width=0.5\textwidth]{figures/Hdval6464.pdf}
%     \caption{Valence of $xd$ PDF at $Q^2=1.9$ \gevsq (left) and at  $Q^2=M_W^2$ \gevsq (right) }
%     \label{fig:dvalH} 
%   \end{center}
% \end{figure}

% \begin{figure}[]
%   \begin{center}
%     \includegraphics[width=0.5\textwidth]{figures/HUbar19.pdf}\includegraphics[width=0.5\textwidth]{figures/HUbar6464.pdf}
%     \caption{Sea of $U$ PDF at $Q^2=1.9$ \gevsq (left) and at  $Q^2=M_W^2$ \gevsq (right) }
%     \label{fig:UbarH} 
%   \end{center}
% \end{figure}

%  \begin{figure}[]
%   \begin{center}
%     \includegraphics[width=0.5\textwidth]{figures/HDbar19.pdf}\includegraphics[width=0.5\textwidth]{figures/HDbar6464.pdf}
%     \caption{Sea of $D$ PDF at $Q^2=1.9$ \gevsq (left) and at  $Q^2=M_W^2$ \gevsq (right) }
%     \label{fig:DbarH} 
%   \end{center}
% \end{figure}




\end{document}



