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\begin{titlepage}

\noindent
\begin{flushleft}
{\tt H1-prelim-13-171,\ ZEUS-prel-13-002} \\
{\tt June 26, 2013}                  \\

{\bf Draft version 0.3} \\
\end{flushleft}

\vspace{1cm}

\vspace{3.5cm}
\begin{center}
\begin{Large}
\boldmath
{\bf Combination of D* Differential Cross Section Measurements in Deep-Inelastic \boldmath $ep$ Scattering at HERA 
}
\unboldmath
\vspace{2cm}

H1 and ZEUS Collaborations

\end{Large}
\end{center}

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\begin{abstract}
\noindent

H1 and ZEUS have recently published differential cross sections for D* 
production from their respective final data sets, in a very similar phase 
space. These cross sections are combined at the visible cross section level, 
taking into account all relevant correlations, thereby 
significantly reducing the uncertainties. NLO QCD predictions are compared
to the results.

\end{abstract}
\vspace{1.5cm}
\begin{center}
%Submitted to \EPJC
\end{center}
\end{titlepage}
%\newpage
%\input{./authlist_h1zeus_oct2012.tex}
\newpage
%\input{./includes/Introduction}
\section{Introduction}

Measurements of open charm production in deep-inelastic electron\footnote{In this note `electron' is used to denote both electron and positron if not otherwise stated. }-proton scattering (DIS) at HERA provide important input for stringent tests of the theory of strong interactions, quantum chromodynamics ({QCD}).

H1 \cite{h1dstar_hera2,h1dstarhighQ2} and ZEUS \cite{zeusdstar_hera2} have 
recently published measurements of differential cross sections for $D^*$ 
production from the final HERA II sets, in a similar limited phase space. 
This also includes extrapolations 
to the full phase space, i.e. the charm contributions to the proton structure 
functions, which have partially already been combined \cite{HERAcharmcomb} 
with measurements from other charm production processes 
\cite{h196,zeusdstar97,h1gluon,zd97,h1f2c,zd00,h1dmesons,h1vertex05,
h1ltt_hera1,h1dstar_hera1,zeusdmesons,zd0dp,zmu,h1ltt_hera2,zeusdpluslambda,
h1cbjets} and used to measure the charm quark mass and to improve predictions 
for $W$ and $Z$ production at LHC \cite{HERAcharmcomb}.

This note addresses the combination of cross sections for $D^*$ 
\cite{h1dstar_hera2,h1dstarhighQ2,zeusdstar_hera2} at visible level,
such that one consistent data set is obtained, which can be compared directly 
to differential NLO cross section predictions without the need for 
extrapolation. 
The combination is based on the procedure described 
in \cite{glazov,H1comb,DIScomb}, including a full treatment of the correlated 
uncertainties, similar to the one used for the combinations at 
structure function level \cite{HERAcharmcomb}. This yields a significant 
reduction of the overall uncertainty of the measurements. 

In general, the analysis of fully reconstructed $D^*$ mesons yields the best 
signal-to-background ratio for charm production. 
However, the branching ratios are small and the phase space of charm 
production accessible with $D^*$ mesons is restricted
because all products from the $D^*$ meson decay have to be measured.
For the details of the experimental analysis, the reader is referred
to the previous work \cite{h1dstar_hera2,h1dstarhighQ2,zeusdstar_hera2}.

Combinations are made for the cross sections in terms of the virtuality, 
$Q^2$, of the exchanged photon, the inelasticity $y$, the transverse momenta, 
$p_T^{D^*}$, and pseudorapidities, $\eta^{D^*}$, of the outgoing $D^*$ mesons, 
and the fragmentation variable $z^{D^*}= (E^{D^*}-p_Z^{D^*})/(2E_e y)$, where 
$E_e$ is the 
incoming electron energy.
The double differential cross sections in $Q^2$ and $y$ are also combined.

The massive fixed-flavour-number-scheme (FFNS) is used for theory predictions 
throughout this note, since it is the only scheme for which fully differential 
calculations \cite{hvqdis} are available at next-to-leading order (NLO).



\section{Combination of H1 and ZEUS measurements}
\label{Sect:combination}
%\input{./includes/Data}
%\input{./includes/Extrapolation}
%\input{./includes/Interpolation}
%\input{./includes/Theory}
\subsection{Theoretical predictions}
\label{sect:theory}

QCD predictions from charm production for all distributions were obtained at 
next-to-leading order in QCD ($O(\alpha_s)^2$) using HVQDIS \cite{hvqdis} in 
the 3-flavour FFNS scheme.

The following parameters are used in the calculations and the 
corresponding variations are used to estimate the associated uncertainties
\begin{itemize}
 \item {\bf pole mass of the charm quark} $m_c=1.5 \pm 0.15$ GeV;
 \item {\bf renormalisation and factorisation scales}
  $\mu_f=\mu_r=\sqrt{Q^2+4m_c^2}$, varied simultaneously  up or down by
  a factor of two for the extrapolation from $Q^2<100$ GeV$^2$ to 
$Q^2<1000$ GeV$^2$, for which only the shape was relevant, and varied 
independently by the same factor for the absolute predictions, with the 
restriction that the difference between the two scales never exceeds a 
factor 2.
 \item {\bf strong coupling constant} $\alpha_s^{n_f=3}(M_Z) = 0.105 \pm 0.002$,
 corresponding to $\alpha_s^{n_f=5}(M_Z) = 0.116 \pm 0.002$;
\item {\bf the proton structure} is described by a series of {FFNS} variants of the HERAPDF1.0 set~\cite{DIScomb} 
at NLO, evaluated for $m_c=1.5\pm0.15$~GeV, for  $\alpha_s^{n_f=3}(M_Z) = 0.105 \pm 0.002$, and for different scales. Charm data are not included in these fits.
%For estimating the uncertainties of the NLO calculations~\cite{hvqdis} due to 
%the respective
%choice of the scales, $\alpha_s$, and $m_c$, the appropriate PDF set is used. 
The effects of the PDF uncertainties are calculated according to the
HERAPDF1.0  prescription~\cite{DIScomb}.
\item {\bf charm fragmentation} is treated as detailed in \cite{HERAcharmcomb}.
\end{itemize}

The small beauty contribution needs a detailed treatment of $b$ hadron to $D^*$ 
decays and is therefore obtained from the RAPGAP \cite{rapgap} MC, renormalized
to independent measurements as detailed 
in \cite{h1dstar_hera2,zeusdstar_hera2}.
The sum of the HVQDIS charm and scaled RAPGAP beauty predictions will be 
referred to as NLO predictions in the following. 
  

%\input{./includes/Combination}
\subsection{Combination method}
\label{sect:combine}
Both measurements to be combined are already corrected to Born level (using 
running $\alpha$) and include both the charm and beauty 
contributions to $D^*$ production. 
The total expected beauty contribution is small ($\sim 3\%$).
The overall phase space for the combined cross sections is given by
\begin{itemize}
\item $5< Q^2 < 1000$ GeV$^2$,
\item $0.02<y<0.7$,
\item $1.5<P_T^{D^*}<20$ GeV,
\item $|\eta^{D^*}|<1.5$.
\end{itemize}
In order to make the input data sets compatible to this phase space and 
with each other, some small modifications are applied before the combination.
From the two sets of measurements in \cite{h1dstar_hera2}, the one 
compatible with the cuts on $p_T^{D^*}$ and $\eta^{D^*}$ quoted above is chosen.
Since this measurement extends only up to $Q^2 < 100$ GeV$^2$ it was 
extrapolated to $Q^2 <1000$ GeV$^2$ using the shape of the HVQDIS \cite{hvqdis}
prediction,
normalized to the measurement of the cross section between $100$ and $1000$
GeV$^2$ taken from \cite{h1dstarhighQ2}.
In order to cope with some differences in the binning for the $Q^2$ 
distribution between \cite{zeusdstar_hera2} and 
\cite{h1dstar_hera2,h1dstarhighQ2}, the first two $Q^2$ bins from 
\cite{h1dstar_hera2} were combined, and the highest $Q^2$ bins from 
\cite{zeusdstar_hera2} and \cite{h1dstarhighQ2} were obtained 
from an integral of the double differential cross sections, which have a 
common binning. For the data from \cite{h1dstar_hera2}, 
the $D^*$ branching ratio was updated to the latest PDG value \cite{PDG12}.

The combination of the data sets uses the $\chi^2$ minimisation method 
developed for the 
combination of inclusive DIS cross sections~\cite{glazov,DIScomb}, as 
implemented in HERAverager \cite{HERAAverager}.
The $\chi^2$ function is defined as described in \cite{HERAcharmcomb}
and takes into account the correlated 
systematic uncertainties for the H1 and ZEUS cross section measurements.
The statistical uncertainaties are treated as uncorrelated, while most of the 
systematic uncertainties are treated as point-to-point correlated. 
Asymmetric systematic uncertainties are symmetrised before performing the 
combination.
Except for the branching ratio uncertainty, which is treated as correlated, 
all systematic uncertainties are treated as independent between 
H1 and ZEUS. 
Each combined point consists of the combination of exactly two measurements.

Since the data are statistically correlated between the different 
distributions, each distribution was combined separately. 
The individual data sets as well as the results of the combination are shown
in Figs. \ref{fig:q2} to \ref{fig:q2y}.  
The combinations in the different variables have a $\chi^2$ probability 
varying between 
15\% and 86\%, i.e. the two data sets are consistent.

%\input{./includes/Results}
\section{Combined D* Cross Sections}
\label{sect:results}

The combined cross sections as a function of $Q^2$, $y$, $p_T$, $\eta$ and $z$,
and the double differential cross sections in $Q^2$ and $y$ 
are shown in Figs. \ref{fig:q2th} to \ref{fig:q2yth} and compared to NLO 
predictions.

In general the predictions describe the data very well. The data reach a 
precision of about 5\% over a large fraction of the measurede phase space,
while the typical theory uncertainty ranges from 30\% at low $Q^2$ to 10\%
at high $Q^2$. NNLO calculations would therefore be very helpful to match 
the data precision. 

Both in the single differential and in the double differential distributions
the central theory prediction shows a somewhat softer $y$ distribution than 
the data. The central prediction for $z^{D^*}$ is a bit wider than the 
measured distribution.%\input{./includes/Predictions}
%\input{./includes/QCD}
%\input{./includes/Conclusion}
\section{Conclusions}
\label{sect:conclude}
Measurements of D* production in deep-inelastic $ep$ scattering by the 
H1 and ZEUS experiments are 
combined at the vsisble cross section level, 
accounting for the systematic correlations. 
The data sets were found to be consistent, and the combined sets exhibits 
significantly reduced uncertainties.
The combined data are compared to NLO QCD predictions.
The predictions describe the 
data very well, but also give some hints for possible future improvements.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section*{Acknowledgements}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

We are grateful to the HERA machine group whose outstanding
efforts have made these experiments possible.
We appreciate the contributions to the construction and maintenance of the H1 and ZEUS detectors of many people who are not listed as authors.
We thank our funding agencies for financial 
support, the DESY technical staff for continuous assistance and the 
DESY directorate for their support and for the hospitality they 
extended to the non-DESY members of the collaborations. 

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\input{./includes/References}
\noindent
\begin{flushleft}
\begin{thebibliography}{99}%{References}
\bibitem{h1dstarhighQ2}

  F.~D.~Aaron {\it et al.}  [H1 Collaboration],
  % ``Measurement of the D*+- Meson Production Cross Section and F(2)**(c c-bar), at High Q**2, in ep Scattering at HERA,''
  \Journal{Phys.~Lett.}{B686}{2010}{91} [arXiv:0911.3989].
  %% CITATION = PHLTA,B686,91;%%

 
\bibitem{h1dstar_hera2} 
  F.~D.~Aaron  {\it et al.}  [H1 Collaboration],
  \Journal{Eur.~Phys.~J.}{C71}{2011}{1769} [arXiv:1106.1028].
% Riemersma {\it et al.} inclusive FFNS calculation

\bibitem{zeusdstar_hera2}
H.~Abramowicz {\it et al.} [ZEUS Collaboration], 
%Measurement of D^*\pm Production in Deep Inelastic Scattering at HERA
DESY-13-054, accepted by JHEP .


\bibitem{HERAcharmcomb}
F.D.~Aaron  {\it et al.}  [H1 and ZEUS Collaborations],
%Combination and QCD Analysis of Charm Production Cross Section Measurements 
%in Deep-Inelastic ep Scattering at HERA
\EPJC {\bf 73} (2013) 2311 [arXiv:1106.1028].

\bibitem{h196}
 C.~Adloff {\it et al.} [H1 Collaboration], 
  % ``Inclusive D0 and D*+- production in deep inelastic e p scattering at HERA'',
  \Journal{Z.Phys}{C72}{1996}{593} [hep-ex/9607012].
  %% CITATION = ZEPYA,C72,593;%%

\bibitem{zeusdstar97}
  J.~Breitweg {\it et al.} [ZEUS Collaboration],  
  % ``D* Production in Deep Inelastic Scattering at HERA'',
  \Journal{Phys.~Lett.}{B407}{1997}{402} [hep-ex/9706009].
  %% CITATION = PHLTA,B407,402;%%

\bibitem{h1gluon}
  C.~Adloff {\it et al.} [H1 Collaboration],
  % ``Measurement of D* meson cross-sections at HERA and determination of the gluon density in the proton using NLO QCD,''
  \Journal{Nucl.~Phys.}{B545}{1999}{21} [hep-ex/9812023].
  %% CITATION = NUPHA,B545,21;%%

\bibitem{zd97}
  J.~Breitweg {\it et al.} [ZEUS Collaboration],
  % ``Measurement of D*+- production and the charm contribution to F2 in  deep
  % inelastic scattering at HERA,''
  \Journal{Eur.~Phys.~J.}{C12}{2000}{35} [hep-ex/9908012].

\bibitem{h1f2c}
  C.~Adloff {\it et al.} [H1 Collaboration],
  % ``Measurement of D*+- meson production and F2(c) in deep inelastic scattering at HERA,''
  \Journal{Phys.~Lett.}{B528}{2002}{199} [hep-ex/0108039].
  %% CITATION = PHLTA,B528,199;%%

\bibitem{zd00}
  S.~Chekanov {\it et al.}  [ZEUS Collaboration],
  % ``Measurement of D*+- production in deep inelastic e+- p scattering at
  %HERA,''
  \Journal{Phys.~Rev.}{D69}{2004}{012004} [hep-ex/0308068].

\bibitem{h1dmesons}
  A.~Aktas {\it et al.} [H1 Collaboration],
  % ``Inclusive production of D+, D0, D+(s) and D*+ mesons in deep inelastic scattering at HERA,''
  \Journal{Eur.~Phys.~J.}{C38}{2005}{447} [hep-ex/0408149].
  %% CITATION = EPHJA,C38,447;%%

\bibitem{h1vertex05}
  A.~Aktas {\it et al.}  [H1 Collaboration],
  % ``Measurement of F2($c \bar{c}$) and F2($b \bar{b}$) at high $Q^{2}$ using the H1 vertex detector at HERA,''
  \Journal{Eur.~Phys.~J.}{C40}{2005}{349} [hep-ex/0411046].
  %% CITATION = EPHJA,C40,349;%%

\bibitem{h1ltt_hera1}
  A.~Aktas {\it et al.}  [H1 Collaboration],
  % ``Measurement of F2(c anti-c) and F2(b anti-b) at low Q**2 and x using  the H1 vertex detector at HERA,''
   \Journal{Eur.~Phys.~J.}{C45}{2006}{23} [hep-ex/0507081].
   %% CITATION = EPHJA,C45,23;%%

%\bibitem{znote}
%S.~Chekanov, S.~Robins, M.~Wing
%"Measurement of D* Cross Sections and the Charm Structure Function of the Proton in DIS at HERA'', ZEUS Note 05-016.

\bibitem{h1dstar_hera1}
  A.~Aktas {\it et al.}  [H1 Collaboration],
  % ``Production of D*+- Mesons with Dijets in Deep-Inelastic Scattering at HERA,''
  \Journal{Eur.~Phys.~J.}{C51}{2007}{271} [hep-ex/0701023].
  %% CITATION = EPHJA,C51,271;%%

\bibitem{zeusdmesons}
  S.~Chekanov {\it et al.}  [ZEUS Collaboration],
  % ``Measurement of D mesons production in deep inelastic scattering at HERA,''
  \Journal{JHEP}{0707}{2007}{074} [arXiv:0704.3562].
  %% CITATION = JHEPA,0707,074;%%

\bibitem{zd0dp}
  S.~Chekanov {\it et al.} [ZEUS Collaboration], 
  % ``Measurement of D+- and D0 production in deep inelastic scattering using a lifetime tag at HERA'',
   \Journal{Eur.~Phys.~J.}{C63}{2009}{171} [arXiv:0812.3775].
   %% CITATION = EPHJA,C63,171;%%

\bibitem{zmu}
  S.~Chekanov {\it et al.} [ZEUS Collaboration],
  % ``Measurement of charm and beauty production in deep inelastic ep scattering from decays into muons at HERA,''
   \Journal{Eur.~Phys.~J.}{C65}{2010}{65} [arXiv:0904.3487].
   %% CITATION = EPHJA,C65,65;%%

\bibitem{h1ltt_hera2}
  F.~D.~Aaron {\it et al.} [H1 Collaboration], 
  % ``Measurement of the Charm and Beauty Structure Functions using the H1 Vertex Detector at HERA,''
   \Journal{Eur.~Phys.~J.}{C65}{2010}{89} [arXiv:0907.2643].
   %% CITATION = EPHJA,C65,89;%%


\bibitem{zeusdpluslambda}
  H.~Abramowicz {\it et al.} [ZEUS Collaboration],
  % ``Measurement of $D^+$ and $\Lambda_{c}^{+}$ production in deep inelastic scattering at HERA,''
  \Journal{JHEP}{1011}{2010}{009} [arXiv:1007.1945].
  %% CITATION = JHEPA,1011,009;%%

\bibitem{h1cbjets}
  F.~D.~Aaron {\it et al.}  [H1 Collaboration],
  % ``Measurement of Charm and Beauty Jets in Deep Inelastic Scattering at %HERA,''
  \Journal{Eur.~Phys.~J.}{C71}{2011}{1509} [arXiv:1008.1731].
  %% CITATION = EPHJA,C71,1509;%%


%\bibitem{riemersma}
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%  E.~Laenen {\it et al.},
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%  %%CITATION = PHLTA,B291,325;%%
%  \\
%  %\bibitem{Laenen:1992zk}
%  E. Laenen {\it et al.},
%  %E.~Laenen, S.~Riemersma, J.~Smith and W.~L.~van Neerven,
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%  %  \NPB {\bf 392} (1993) 162, 229;
%  %%CITATION = NUPHA,B392,162;%%
%  %\bibitem{Laenen:1992xs}
%  \\
%  E. Laenen {\it et al.},
%  %{\it ibid.}~229;
%  %E.~Laenen, S.~Riemersma, J.~Smith and W.~L.~van Neerven,
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%  \Journal{Nucl.~Phys.}{B392}{1993}{229};
%  %%CITATION = NUPHA,B392,229;%%
%  \\
%%\bibitem{Riemersma:1994hv}
%  S.~Riemersma, J.~Smith and W.~L.~van Neerven,
%  %``Rates for inclusive deep inelastic electroproduction of charm quarks at HERA,''
%  \Journal{Phys.~Lett.}{B347}{1995}{143} [hep-ph/9411431].
%  %%CITATION = HEP-PH/9411431;%%
%
%\bibitem{abm11}
%  % \bibitem{Alekhin:2012ig}
%  S.~Alekhin, J.~Blumlein and S.~Moch,
%  %``Parton Distribution Functions and Benchmark Cross Sections at NNLO,''
%  \Journal{Phys.~Rev.}{D86}{2012}{054009} [arXiv:1202.2281].
%  %%CITATION = ARXIV:1202.2281;%%  S.~Alekhin, J.~Bl\"umlein and S.~Moch,
%
%% GJR 2008 PDF
%\bibitem{gjr}
%  M.~Gl\"uck {\it et al.},
%  % P.~Jimenez-Delgado,E.~Reya, C.Schuck Phys. Lett. 
%  \Journal{Phys.~Lett.}{B664}{2008}{133} [arXiv:0801.3618].
%
%% CT10F3 series, including FFNS variant of CTEQ 5
%\bibitem{ct10f3}
%  H.~L.~Lai {\it et al.},
%  \Journal{Phys.~Rev.}{D82}{2010}{074024} [arXiv:1007.2241].
%
%
%% MSTW08 TR-VFNS PDF
%\bibitem{mstw08f3}
%  A.~D.~Martin {\it et al.},
%  % W.~J.~Stirling, R.~S.~Thorne, G. Watt, Eur. Phys. J. \
%  \Journal{Eur.~Phys.~J.}{C70}{2010}{51} [arXiv:1007.2624].
%
%%% VFNS references
%
%\bibitem{zmvfns}
%G.~C.~Collins and W.~-K.~Tung,
%\Journal{Nucl. Phys.}{B278}{1986}{934}.
%
%\bibitem{acot} 
%  % \bibitem{Aivazis:1993kh}
%  M.~A.~G.~Aivazis, F.~I.~Olness and W.~-K.~Tung,
%  %``Leptoproduction of heavy quarks. 1. General formalism and kinematics of charged current and neutral current production processes,''
%  \Journal{Phys.~Rev.}{D50}{1994}{3085} [hep-ph/9312318];
%  %%CITATION = HEP-PH/9312318;%%
%  \\
%  % \bibitem{Aivazis:1993pi}
%  M.~A.~G.~Aivazis {\it el al.},
%  % M.~A.~G.~Aivazis, J.~C.~Collins, F.~I.~Olness and W.~-K.~Tung,
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%  \Journal{Phys.~Rev.}{D50}{1994}{3102} [hep-ph/9312319].
%  %%CITATION = HEP-PH/9312319;%%
%
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%\bibitem{bmsn}
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%  M.~Buza, {\it et al.},
%  %%% >>> et al:  Y.~Matiounine, J.~Smith, R.~Migneron and W.~L.~van Neerven,
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%  %%CITATION = HEP-PH/9601302;%%
%% CTEQ6.6 ACOT scheme
%
%\bibitem{s_acot_chi} 
%%\bibitem{Collins:1998rz}
%  J.~C.~Collins,
%  %``Hard scattering factorization with heavy quarks: A General treatment,''
%  \Journal{Phys.~Rev.}{D58}{1998}{094002} [hep-ph/9806259];
%  %%CITATION = HEP-PH/9806259;%%
%  \\
%  % \bibitem{Kramer:2000hn}
%  M.~Kramer, F.~I.~Olness, and D.~E.~Soper,
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%  %%CITATION = HEP-PH/0003035;%%
%  \\
%  % \bibitem{Tung:2001mv}
%  W.~-K.~Tung, S.~Kretzer and C.~Schmidt,
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%  %%CITATION = HEP-PH/0110247;%%
%
%\bibitem{rt_std} 
%  R.~S.~Thorne,
%  % ``A Variable-flavor number scheme for NNLO,''
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%  %% CITATION = PHRVA,D73,054019;%%
%  \\
%  A.~D.~Martin {\it et al.},
%  %%% >>> et al.:  , W.~J.~Stirling, R.~S.~Thorne and G.~Watt,
%  % ``Parton distributions for the LHC,''
%  \Journal{Eur.~Phys.~J.}{C63}{2009}{189} [arXiv:0901.0002].
%  %% CITATION = EPHJA,C63,189;%%
%
%% FONLL VFNS scheme
%\bibitem{FONLL}
%  S. Forte {\it et al.},
%  \Journal{Nucl.~Phys.}{B834}{2010}{116} [arXiv:1001.2312].  
%
%
%\bibitem{fonllb_and_c}
%  R.~D.~Ball {\it et al.} [NNPDF Collaboration],
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%  \\
%  R.~D.~Ball {\it el al.} [NNPDF Collaboration],
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%
%\bibitem{rt_opt} 
% R.~S.~Thorne,
% %``The Effect of Changes of Variable Flavour Number Scheme on PDFs and
% %Predicted Cross Sections,''
% arXiv:1201.6180.
% %%CITATION = ARXIV:1201.6180;%%
%
\bibitem{glazov}
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\bibitem{DIScomb}
%\bibitem{Aaron:2009aa}
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%% ABKM FFNS running mass scheme
%\bibitem{ABKMMSbar}
%  S.~Alekhin and S.~Moch,
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%
%%F_L Contribution is small:
%\bibitem{daum_fl}
%  K. Daum {\it et al.},
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%
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%\bibitem{CTEQNNLO}
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%  %M.~Guzzi, P.~M.~Nadolsky, H.~-L.~Lai and C.~-P.~Yuan,
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%  \Journal{Phys.~Rev.}{D86}{2012}{053005}  [arXiv:1108.5112].
%  %%CITATION = ARXIV:1108.5112;%%  
%
%% F2c definition for MSTW
%\bibitem{MSTWF2}
%  % \bibitem{Chuvakin:1999nx}
%  A.~Chuvakin, J.~Smith and W.~L.~van Neerven,
%  %``Comparison between variable flavor number schemes for charm quark electroproduction,''
%  \Journal{Phys.~Rev.}{D61}{2000}{096004} [hep-ph/9910250].
%  %% CITATION = HEP-PH/9910250;%%
%  
%% charm mass has large effect on W/Z cross sections at LHC
%%\bibitem{Tungmass} W.K. Tung {\it el al.}, JHEP0702 (2007) 053 [hep-ph/0611254].
%
% HVQDIS differential FFNS calculation
\bibitem{hvqdis}
  % \bibitem{Harris:1997zq}
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  %%CITATION = HEP-PH/9706334;%%

%\bibitem{pdg}
%  K.~Nakamura {\it et al.} [Particle Data Group],
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%
%% Running mass
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%  \\
%  K.~Chetyrkin and M.~Steinhauser,
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%  \\
%  K.~Melnikov and T.~v.~Ritbergen,
%  \Journal{Nucl.~Phys.}{B482}{2000}{99} [hep-ph/9912391].
%
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%
%%\bibitem{Kawamura} H. Kawamura, N.A. Lo Presti, S. Moch and A. Vogt [arXiv:1205.5727].
%
%
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%\bibitem{h1}
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%  \\
%  I.~Abt {\it et al.} [H1 Collaboration],
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%  \\
%  R.~D.~Appuhn {\it et al.} [H1 SPACAL Group],
%  \Journal{Nucl.~Instrum.~Meth.}{A386}{1997}{397}.
%
%\bibitem{zeus}
%  U.~Holm (ed.) [ZEUS Collaboration],
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%
%
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%\bibitem{H1cst}
%  D.~Pitzl {\it et al.},
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%  %%CITATION = NUIMA,A454,334;%%
%
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%\bibitem{ZEUSmvd}
%A. Polini \etal, \Journal{Nucl. Instr. and Meth.}{A581}{2007}{656}.
%
%\bibitem{heracles}
%  A.~Kwiatkowski, H.~Spiesberger and H.~J.~Mohring,
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%
%\bibitem{h1frag}
%%\bibitem{Aaron:2008ac}
%  F.~D.~Aaron {\it et al.} [H1 Collaboration],
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%  %%CITATION = ARXIV:0808.1003;
%
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%\bibitem{cacciari} 
%M.~Cacciari, P.~Nason and C.~Oleari, 
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%
%\bibitem{belle}
%  % \bibitem{Seuster:2005tr}
%  R.~Seuster {\it et al.} [Belle Collaboration],
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%  %%CITATION = HEP-EX/0506068;%%
%
%\bibitem{ptkink} %REFERENCES ON PTKINK 
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%  N.~E.~Adam {\it et al.} [Cleo Collaboration],
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%
%\bibitem{webpage}
% % H1 and ZEUS collaboration, ``Combined HERA heavy flavour results'', 
%The input data sets and the combined data together with the full correlation information is provided at the URL
%  \url{http://www.desy.de/h1zeus}
%  \\
% % {\special{ps: 1 0 0 setrgbcolor}  title of web-page added, to be adjusted!
% %   Please make sure the web-page exists and has the proper title
% %   before submitting the article to arXiv!\black}
%
%\bibitem{ref:HERAPDF1.5}
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%  \\
%  V.~Radescu, Proceedings of the 35$^{\text{th}}$ International Conference of High Energy Physics, Proceedings of Science, POS (ICHEP 2010) 168.
%
%% CT10  S-ACOT GM-VFNS 
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%  P. Nadolsky {\it et al.},
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%  arXiv:1206.3321. 
%  % Progress in CTEQ-TEA PDF analysis
%
%% ABKM08 and BMSN 
%\bibitem{abkm}
%  S.~Alekhin {\it et al.},
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%  \\
%  S.~Alekhin and S.~Moch, arXiv:1107.0469. 
%
%%\bibitem{abkm09msbar} 
% %S.~Alekhin, J.~Blumlein, S.~Klein and S.~Moch,
% %``The 3, 4, and 5-flavor NNLO Parton from Deep-Inelastic-Scattering Data and at Hadron Colliders,''
%% Phys.\ Rev.\ D {\bf 81} (2010) 014032
%% [arXiv:0908.2766].
% %%CITATION = ARXIV:0908.2766;%%
%% \\
%% S. Alekhin, S.~Moch, arXiv:1107.0469. 
%
%\bibitem{herafitter}
%  HERAFitter-0.2.1, \url{http://projects.hepforge.org/herafitter}.
% 
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%  \\
%  A.~Vogt, S.~Moch and J.~Vermaseren,
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%
%\bibitem{qcdnum}
%  % \bibitem{Botje:2010ay}
%  M.~Botje,
%  %``QCDNUM: Fast QCD Evolution and Convolution,''
%  \Journal{Comput.~Phys.~Commun.}{182}{2011}{490} [arXiv:1005.1481],
%  %%CITATION = ARXIV:1005.1481;%%
%  \url{http://www.nikhef.nl/~h24/qcdnum/index.html}.
%
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%\bibitem{fsnu}
%  D.~Mason {\it et al.} [NuTeV Collaboration],
%  \Journal{Phys.~Rev.~Lett.}{99}{2007}{192001}. 
%
%
%\bibitem{fsatlas}
%%\bibitem{Aad:2012sb}
%  G.~Aad {\it et al.} [ATLAS Collaboration],
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%  \Journal{Phys.~Rev.~Lett.}{109}{2012}{012001}
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%
%%\bibitem{acot_zm} \red{Reference for the ZERO MASS SCHEME in ACOT (HERAFITTER)}
%\bibitem{openqcdrad}
%  S. Alekhin, ``OPENQCDRAD-1.5'',\\
%  \url{http://www-zeuthen.desy.de/~alekhin/OPENQCDRAD}.
%  \\
%
%% FONLL VFNS scheme
%%\bibitem{FONLL} S. Forte {\it el al.}, \NPB {\bf 834} (2010) 116 [arXiv:1001.2312].  
%
%\bibitem{adlm}
%  S. Alekhin \etal, arXiv:1209.0436.
%
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%  \\
%%  {\special{ps: 1 0 0 setrgbcolor} Is there no poublication? Do we have to give the version number?\black}
%
%\bibitem{applgrid}
%  % \bibitem{Carli:2010rw}
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%  % T.~Carli, D.~Clements, A.~Cooper-Sarkar, C.~Gwenlan, G.~P.~Salam, F.~Siegert, P.~Starovoitov and M.~Sutton,
%  %``A posteriori inclusion of parton density functions in NLO QCD final-state calculations at hadron colliders: The APPLGRID Project,''
%  \Journal{Eur.~Phys.~J.}{C66}{2010}{503} [arXiv:0911.2985].
%  %%CITATION = ARXIV:0911.2985;%%
%  \\
% % {\special{ps: 1 0 0 setrgbcolor} So we need to give the title ``APPLGRID'' here? Version number needed?\black}
%
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\end{thebibliography}
\end{flushleft}
%\include{./includes/Tables}
%\include{./includes/Figures}
\newpage
\begin{figure}[h]
\center
\epsfig{file=H1prelim-13-171.fig1.eps,width=1.0\textwidth}
\caption{Differential $D^*$ production cross section as a function of $Q^2$. 
The triangles 
and open squares are the cross sections before combination, shown with a 
small horizontal offset for better visibility. 
The filled points are the combined cross sections. The inner 
error bars indicate the statistical uncertainties before combination, and the 
uncorrelated part of the uncertainties after combination.
The outer error bars represent the total uncertainties.
The bottom part shows the ratio of these cross sections with respect to the 
central value of the combined cross sections.}
\label{fig:q2} 
\end{figure}

\newpage
\begin{figure}[h]
\center
\epsfig{file=H1prelim-13-171.fig2.eps,width=1.0\textwidth}
\caption{Differential $D^*$ production cross section as a function of $y$. 
The triangles 
and open squares are the cross sections before combination, shown with a 
small horizontal offset for better visibility. 
The filled points are the combined cross sections. The inner 
error bars indicate the statistical uncertainties before combination, and the 
uncorrelated part of the uncertainties after combination.
The outer error bars represent the total uncertainties.
%The bottom part shows the ratio of these cross sections with respect to the 
%central value of the combined cross sections.
}
\label{fig:y} 
\end{figure}

\newpage
\begin{figure}[h]
\center
\epsfig{file=H1prelim-13-171.fig3.eps,width=1.0\textwidth}
\caption{Differential cross section as a function of $p_T$. The triangles 
and open squares are the cross sections before combination, shown with a 
small horizontal offset for better visibility. 
The filled points are the combined cross sections. The inner 
error bars indicate the statistical uncertainties before combination, and the 
uncorrelated part of the uncertainties after combination.
The outer error bars represent the total uncertainties.
The bottom part shows the ratio of these cross sections with respect to the 
central value of the combined cross sections.}
\label{fig:pt} 
\end{figure}

\newpage
\begin{figure}[h]
\center
\epsfig{file=H1prelim-13-171.fig4.eps,width=1.0\textwidth}
\caption{Differential $D^*$ production cross section as a function of $\eta$. 
The triangles 
and open squares are the cross sections before combination, shown with a 
small horizontal offset for better visibility. 
The filled points are the combined cross sections. The inner 
error bars indicate the statistical uncertainties before combination, and the 
uncorrelated part of the uncertainties after combination.
The outer error bars represent the total uncertainties.
%The bottom part shows the ratio of these cross sections with respect to the 
%central value of the combined cross sections.
}
\label{fig:eta} 
\end{figure}

\newpage
\begin{figure}[h]
\center
\epsfig{file=H1prelim-13-171.fig5.eps,width=1.0\textwidth}
\caption{Differential $D^*$ production cross section as a function of $z$. 
The triangles 
and open squares are the cross sections before combination, shown with a 
small horizontal offset for better visibility. 
The filled diamonds are the combined cross sections. The inner 
error bars indicate the statistical uncertainties before combination, and the 
uncorrelated part of the uncertainties after combination.
The outer error bars represent the total uncertainties.
%The bottom part shows the ratio of these cross sections with respect to the 
%central value of the combined cross sections.
}
\label{fig:z} 
\end{figure}

\newpage
\begin{figure}[h]
\center
\epsfig{file=H1prelim-13-171.fig6.eps,width=1.0\textwidth}
\caption{Double differential $D^*$ production 
cross sections as a function of $Q^2$ and $y$. 
The triangles 
and open squares are the cross sections before combination, shown with a 
small horizontal offset for better visibility. 
The filled points are the combined cross sections. The inner 
error bars indicate the statistical uncertainties before combination, and the 
uncorrelated part of the uncertainties after combination.
The outer error bars represent the total uncertainties.
%The bottom part shows the ratio of these cross sections with respect to the 
%central value of the combined cross sections.
}
\label{fig:q2y} 
\end{figure}

\newpage
\begin{figure}[h]
\center
\epsfig{file=H1prelim-13-171.fig7.eps,width=1.0\textwidth}
\caption{Differential $D^*$ production cross section as a function of $Q^2$.
The data points are the combined cross sections. The inner 
error bars indicate the uncorrelated part of the uncertainties.
The outer error bars represent the total uncertainties.
Also shown are the NLO predictions from HVQDIS (including the beauty 
contribution as obtained from RAPGAP, normalized to independent 
data sets), and their uncertainty band.
The bottom part shows the ratio of these cross sections with respect to the 
%central value of the NLO theory.}
central value of the combined cross sections.}
\label{fig:q2th} 
\end{figure}

\newpage
\begin{figure}[h]
\center
\epsfig{file=H1prelim-13-171.fig8.eps,width=1.0\textwidth}
\caption{Differential $D^*$ production cross section as a function of $y$.
The data points are the combined cross sections. The inner 
error bars indicate the uncorrelated part of the uncertainties.
The outer error bars represent the total uncertainties.
Also shown are the NLO predictions from HVQDIS (including the beauty 
contribution as obtained from RAPGAP, normalized to independent 
data sets), and their uncertainty band.
%The bottom part shows the ratio of these cross sections with respect to the 
%central value of the NLO theory.
}
\label{fig:yth} 
\end{figure}

\newpage
\begin{figure}[h]
\center
\epsfig{file=H1prelim-13-171.fig9.eps,width=1.0\textwidth}
\caption{Differential $D^*$ production cross section as a function of $p_T$.
The data points are the combined cross sections. The inner 
error bars indicate the uncorrelated part of the uncertainties.
The outer error bars represent the total uncertainties.
Also shown are the NLO predictions from HVQDIS (including the beauty 
contribution as obtained from RAPGAP, normalized to independent 
data sets), and their uncertainty band.
The bottom part shows the ratio of these cross sections with respect to the 
%central value of the NLO theory.}
central value of the combined cross sections.}
\label{fig:ptth} 
\end{figure}

\newpage
\begin{figure}[h]
\center
\epsfig{file=H1prelim-13-171.fig10.eps,width=1.0\textwidth}
\caption{Differential $D^*$ production cross section as a function of $\eta$.
The data points are the combined cross sections. The inner 
error bars indicate the uncorrelated part of the uncertainties.
The outer error bars represent the total uncertainties.
Also shown are the NLO predictions from HVQDIS (including the beauty 
contribution as obtained from RAPGAP, normalized to independent 
data sets), and their uncertainty band.
%The bottom part shows the ratio of these cross sections with respect to the 
%central value of the NLO theory.
}
\label{fig:etath} 
\end{figure}

\newpage
\begin{figure}[h]
\center
\epsfig{file=H1prelim-13-171.fig11.eps,width=1.0\textwidth}
\caption{Differential $D^*$ production cross section as a function of $z$.
The data points are the combined cross sections. The inner 
error bars indicate the uncorrelated part of the uncertainties.
The outer error bars represent the total uncertainties.
Also shown are the NLO predictions from HVQDIS (including the beauty 
contribution as obtained from RAPGAP, normalized to independent 
data sets), and their uncertainty band.
%The bottom part shows the ratio of these cross sections with respect to the 
%central value of the NLO theory.
}
\label{fig:zth} 
\end{figure}

\newpage
\begin{figure}[h]
\center
\epsfig{file=H1prelim-13-171.fig12.eps,width=1.0\textwidth}
\caption{Double differential $D^*$ production cross section as a function 
of $Q^2$ and $y$.
The data points are the combined cross sections. The inner 
error bars indicate the uncorrelated part of the uncertainties.
The outer error bars represent the total uncertainties.
Also shown are the NLO predictions from HVQDIS (including the beauty 
contribution as obtained from RAPGAP, normalized to independent 
data sets), and their uncertainty band.
%The bottom part shows the ratio of these cross sections with respect to the 
%central value of the NLO theory.
}
\label{fig:q2yth} 
\end{figure}


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