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\begin{titlepage}

\noindent
\begin{flushleft}
{\tt DESY 11-066    \hfill    ISSN 0418-9833} \\
\end{flushleft}



\noindent


\vspace{2cm}
\begin{center}
\begin{Large}
Erratum to \\
{\bf   Measurement of \boldmath ${ D^{*\pm}}$ Meson Production and 
Determination of \ftwocc\ at low ${Q^2}$ in 
Deep-Inelastic Scattering at HERA  } \\
Eur. Phys.J.C71 (2011) 1769

\vspace{2cm}

H1 Collaboration

\end{Large}
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\vspace{2cm}


\vspace{1.5cm}

\begin{center}
Submitted to \EJC
\end{center}

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In the extraction of the charm contribution \ftwocc\ to the proton structure 
function $F_2$ in our recent publication~\cite{dstarpaper}, we have not 
properly taken into account the running of the electromagnetic coupling 
$\alpha_{\rm em}$. The measured cross
sections were corrected to the Born level for QED radiation, but not 
for the running of $\alpha_{\rm em}$. This was not taken properly into
account in the extraction of \ftwocc. 

In addition, the cross section predictions of the CASCADE program were
calculated with fixed $\alpha_{\rm em}$. The cross section in the visible range calculated with running $\alpha_{\rm em}$ is $5.63~{\rm nb}$ 
(instead of $5.09~{\rm nb}$ given in~\cite{dstarpaper}). 
The conclusions on the description of the data by CASCADE are unchanged.
The extrapolation factors, defined as the ratio of the full cross section 
$\sigma_{\rm{full}}^{\rm{theo}}$ to the cross section
$\sigma_{\rm{vis}}^{\rm{theo}}$ in the visible phase space of 
the \dstar\ meson, and their uncertainties are changed slightly. The amended
values are shown in figure~\ref{factors} which replaces figure~15 
of~\cite{dstarpaper}. 

The amended values of \ftwocc\ 
%determined from data 
extracted from measured ${ D^{*\pm}}$ cross sections 
with the HVQDIS program and with the CASCADE program 
are lower by about $6$ upto $11\%$ as compared to~\cite{dstarpaper}.  
The corrected values of \ftwocc\ and its uncertainties are given in 
table~\ref{Tab_f2cc} which replaces table~11 of~\cite{dstarpaper}.
The amended \ftwocc\ values are compared
to a measurement based on lifetime information 
determined with the H1 silicon vertex detector~\cite{h1vertex09}
and with theoretical predictions in 
figures~\ref{f2cc_hvqdis},~\ref{f2cc_pdfs} and~\ref{f2cc_scaling}, which
replace figures 16, 17 and 18 of~\cite{dstarpaper}, respectively. 

\begin{thebibliography}{10}

\bibitem{dstarpaper}
F.~D.~Aaron {\it et al.}  [H1 Collaboration],
%``Measurement of D^{*\pm} Meson Production and Determination of F_2^{ccbar}
%at low Q2 in Deep-Inelastic Scattering at HERA,''
\EPJC {\bf 71} (2011) 1769 [arXiv:1106.1028].
%%CITATION = EPHJA,C71,1769;%%

\bibitem{h1vertex09}
F.D.~Aaron {\it et~al.} [H1 Collaboration], 
%``Measurement of the Charm and Beauty Structure Functions using the H1 Vertex Detector at HERA,''
\EPJC {\bf 65} (2010) 89 [arXiv:0907.2643].
%%CITATION = EPHJA,C65,89;%%

\end{thebibliography}

 

\renewcommand{\arraystretch}{1.22}

\begin{table}[htbp]
\begin{center}
{\scriptsize
\begin{tabular}{|d|c|d l|d|l||d l|}
\hline
\multicolumn{1}{| c |}{$$} & 
\multicolumn{1}{ c |}{$$} & 
\multicolumn{2}{ c |}{HVQDIS} &   
\multicolumn{1}{ c |}{$$} &   
\multicolumn{1}{ c ||}{$$} &
\multicolumn{2}{ c |}{CASCADE}    
\\   
\multicolumn{1}{| c |}{\rb{$Q^2\  [{\rm GeV}^2]$}} & 
\multicolumn{1}{ c |}{\rb{$x$}} & 
\multicolumn{1}{ c }{\ftwocc} &   
\multicolumn{1}{ c |}{$\delta_{ext}\ [\%]$} &   
\multicolumn{1}{ c |}{\rb{$\delta_{stat}\ [\%]$}} &   
\multicolumn{1}{ c ||}{\rb{$\delta_{syst}\ [\%]$}} &    
\multicolumn{1}{ c }{\ftwocc} &   
\multicolumn{1}{ c |}{$\delta_{ext}\ [\%]$}    
\\ \hline
% \input{F2cc.amended.all.txt}
% Q2 [GeV]    Bjorken x      F2cc HVQDIS   HVQDIS unc.         stat.err       data sys. err     F2cc Cascade   Cascade unc.

 6.5 & $1.3\cdot 10^{-4}$ & 0.2036 & $ \pm _{8.7} ^{8.5} $ & \pm 6.7 & $ \pm ^{8.1} _{7.6}  $ & 0.1750  & $ \pm _{13.9} ^{13.1} $  \\  
 6.5 & $3.2\cdot 10^{-4}$ & 0.1497 & $ \pm _{3.2} ^{4.3} $ & \pm 5.5 & $ \pm ^{8.1} _{7.6}  $ & 0.1364  & $ \pm _{8.3 } ^{7.5 } $ \\    
 6.5 & $5.0\cdot 10^{-4}$ & 0.1446 & $ \pm _{4.5} ^{4.2} $ & \pm 5.4 & $ \pm ^{7.2} _{7.2}  $ & 0.1305  & $ \pm _{7.3 } ^{7.2 } $ \\    
 6.5 & $8.0\cdot 10^{-4}$ & 0.0979 & $ \pm _{3.4} ^{5.7} $ & \pm 8.1 & $ \pm ^{7.4} _{7.0}  $ & 0.0925  & $ \pm _{5.2 } ^{4.8 } $  \\   
 6.5 & $2.0\cdot 10^{-3}$ & 0.0698 & $ \pm _{7.2} ^{10.8}$ & \pm 8.6 & $ \pm ^{9.8} _{10.5} $ & 0.0812  & $ \pm _{3.1 } ^{2.4 } $  \\[0.2cm]
										      	    		       
12.0 & $3.2\cdot 10^{-4}$ & 0.2711 & $ \pm _{5.6} ^{8.7} $ & \pm 7.7 & $ \pm ^{7.9} _{7.6}  $ & 0.2368  & $ \pm _{10.5} ^{10.0} $  \\  
12.0 & $5.0\cdot 10^{-4}$ & 0.2009 & $ \pm _{2.9} ^{3.1} $ & \pm 6.6 & $ \pm ^{7.2} _{7.0}  $ & 0.1799  & $ \pm _{4.6 } ^{4.7 } $ \\    
12.0 & $8.0\cdot 10^{-4}$ & 0.1605 & $ \pm _{2.3} ^{4.6} $ & \pm 7.8 & $ \pm ^{7.3} _{7.4}  $ & 0.1462  & $ \pm _{4.0 } ^{3.7 } $ \\    
12.0 & $2.0\cdot 10^{-3}$ & 0.1149 & $ \pm _{3.5} ^{6.1} $ & \pm 8.9 & $ \pm ^{7.6} _{7.8}  $ & 0.1093  & $ \pm _{2.1 } ^{2.2 } $  \\   
12.0 & $3.2\cdot 10^{-3}$ & 0.0732 & $ \pm _{7.4} ^{11.6}$ & \pm 12.0& $ \pm ^{9.3} _{10.2} $ & 0.0890  & $ \pm _{5.5 } ^{2.4 } $  \\[0.2cm]   
									              	    		  
20.0 & $5.0\cdot 10^{-4}$ & 0.3019 & $ \pm _{5.0} ^{4.6} $ & \pm 8.8 & $ \pm ^{9.0} _{8.7}  $ & 0.2664  & $ \pm _{7.0 } ^{6.9 } $  \\  
20.0 & $8.0\cdot 10^{-4}$ & 0.2730 & $ \pm _{2.1} ^{3.8} $ & \pm 6.1 & $ \pm ^{7.1} _{7.4}  $ & 0.2538  & $ \pm _{3.7 } ^{3.4 } $ \\    
20.0 & $1.3\cdot 10^{-3}$ & 0.2007 & $ \pm _{2.9} ^{4.0} $ & \pm 8.0 & $ \pm ^{8.4} _{8.1}  $ & 0.1908  & $ \pm _{1.8 } ^{1.5 } $ \\    
20.0 & $3.2\cdot 10^{-3}$ & 0.1283 & $ \pm _{3.5} ^{5.3} $ & \pm 9.3 & $ \pm ^{7.0} _{7.5}  $ & 0.1261  & $ \pm _{1.7 } ^{1.7 } $ \\    
20.0 & $5.0\cdot 10^{-3}$ & 0.0970 & $ \pm _{6.0} ^{13.6}$ & \pm 12.5& $ \pm ^{11.7}_{11.1} $ & 0.1214  & $ \pm _{3.2 } ^{2.9 } $  \\[0.2cm]   
									              	    	    
35.0 & $8.0\cdot 10^{-4}$ & 0.3690 & $ \pm _{3.0} ^{3.6} $ & \pm 8.3 & $ \pm ^{8.2} _{8.0}  $ & 0.3247  & $ \pm _{5.0 } ^{5.0 } $ \\    
35.0 & $1.3\cdot 10^{-3}$ & 0.2993 & $ \pm _{2.4} ^{2.8} $ & \pm 6.7 & $ \pm ^{7.0} _{7.3}  $ & 0.2735  & $ \pm _{2.8 } ^{2.5 } $ \\    
35.0 & $3.2\cdot 10^{-3}$ & 0.1894 & $ \pm _{2.4} ^{3.7} $ & \pm 8.5 & $ \pm ^{7.7} _{7.6}  $ & 0.1767  & $ \pm _{2.3 } ^{2.1 } $  \\   
35.0 & $5.0\cdot 10^{-3}$ & 0.1516 & $ \pm _{2.7} ^{4.2} $ & \pm 9.9 & $ \pm ^{8.4} _{8.6}  $ & 0.1445  & $ \pm _{1.3 } ^{1.2 } $  \\   
35.0 & $8.0\cdot 10^{-3}$ & 0.0799 & $ \pm _{6.5} ^{11.2}$ & \pm 14.9& $ \pm ^{11.8}_{10.5} $ & 0.1046  & $ \pm _{3.6 } ^{4.1 } $  \\[0.2cm]    

60.0 & $1.3\cdot 10^{-3}$ & 0.3659 & $ \pm _{1.5} ^{2.8} $ & \pm 11.3& $ \pm ^{8.2} _{8.2}  $ & 0.3227  & $ \pm _{2.4 } ^{2.4 } $ \\    
60.0 & $3.2\cdot 10^{-3}$ & 0.2843 & $ \pm _{1.3} ^{3.4} $ & \pm 9.5 & $ \pm ^{8.1} _{7.7}  $ & 0.2613  & $ \pm _{1.8 } ^{1.9 } $  \\   
60.0 & $5.0\cdot 10^{-3}$ & 0.1748 & $ \pm _{2.6} ^{3.5} $ & \pm 13.2& $ \pm ^{8.2} _{7.7}  $ & 0.1551  & $ \pm _{1.6 } ^{1.7 } $  \\   
60.0 & $8.0\cdot 10^{-3}$ & 0.1326 & $ \pm _{1.4} ^{5.5} $ & \pm 17.9& $ \pm ^{7.9} _{8.0}  $ & 0.1259  & $ \pm _{2.3 } ^{2.4 } $  \\   
60.0 & $2.0\cdot 10^{-2}$ & 0.0484 & $ \pm _{6.8} ^{10.9}$ & \pm 56.4& $ \pm ^{10.3}_{13.2} $ & 0.0687  & $ \pm _{6.7 } ^{6.5 } $  \\   


\hline
\end{tabular}
}
\end{center}
\caption{\ftwocc\ in bins of $Q^2$ and $x$ extracted from measured 
\dstar\ cross sections
with two different programs, HVQDIS and CASCADE. The extrapolation uncertainty 
$\delta_{ext}$ is determined by varying model parameters within a program. The statistical 
($\delta_{stat}$) and systematic ($\delta_{syst}$) uncertainties arise from the
determination of the \dstar\ cross section and are the same for both programs.}
\label{Tab_f2cc}
\end{table}

\clearpage

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%Figures

\begin{figure}[htbp]
\begin{center}
\includegraphics[width=12cm, angle=0]{d11-066.erratumf1.eps} 
\end{center}
\caption{Extrapolation factors from the visible phase space 
to the total phase space for the \dstar\ meson as determined from 
HVQDIS and CASCADE. The error bars show the extrapolation uncertainty which
is determined by varying the theory parameters listed in 
tables~1 and 2 of~\cite{dstarpaper}.}
\label{factors}
\end{figure}
%%%% 
%%%%
\begin{figure}[htbp]
\begin{center}
\includegraphics[width=12cm, angle=0]{d11-066.erratumf2.eps} 
\end{center}
\caption{\ftwocc\ as derived from \dstar\ data with HVQDIS (points). 
The inner error bars show the statistical uncertainty, the outer error bar the 
statistical and experimental systematic uncertainty added in quadrature. 
The extrapolation uncertainty within the HVQDIS model is shown as
blue band in the bottom of the plots. The outer (orange) band shows the
model uncertainty obtained from the difference in \ftwocc\ 
determined with HVQDIS and CASCADE. The data are compared to the measurement
of \ftwocc\ with the H1 vertex detector~\cite{h1vertex09} (open squares), 
to NLO DGLAP predictions from HVQDIS with two different proton PDFs, and to 
the \ftwocc\ prediction of HERAPDF1.0.}
\label{f2cc_hvqdis}
\end{figure}
%%%% 
%%%%
\begin{figure}[htbp]
\begin{center}
\includegraphics[width=12cm, angle=0]{d11-066.erratumf3.eps} 
\end{center}
\caption{\ftwocc\ as derived from \dstar\ data with HVQDIS (points). 
The inner error bars show the statistical uncertainty, the outer error bar the 
statistical and experimental systematic uncertainty added in quadrature. 
The extrapolation uncertainty within the HVQDIS model is shown as
blue band in the bottom of the plots. The outer (orange) band shows the
model uncertainty obtained from the difference in \ftwocc\ 
determined with HVQDIS and CASCADE. The data are compared to the measurement
of \ftwocc\ with the H1 vertex detector~\cite{h1vertex09} (open squares)
and to predictions from the global PDF fits CT10 (dashed line),
MSTW08 at NNLO (dark dashed-dotted line), NNPDF2.1 (shaded band) and 
ABKM (light dashed-dotted line).}
\label{f2cc_pdfs}
\end{figure}
%%%% 
%%%%
\begin{figure}[htbp]
\begin{center}
\includegraphics[width=12cm,angle=0]{d11-066.erratumf4.eps} 
\end{center}
\caption{\ftwocc\ as a function of $Q^2$ for different $x$, as derived 
from \dstar\ data with HVQDIS (points). The inner
error bars show the statistical uncertainty, the outer error bar the 
total uncertainty, including statistical, experimental systematic, extrapolation
and model uncertainty added in quadrature. 
The data are compared to the measurement
of \ftwocc\ with the H1 vertex detector~\cite{h1vertex09} (open squares), to 
NLO DGLAP predictions from HVQDIS with two different proton PDFs, and to the 
\ftwocc\ prediction of HERAPDF1.0.}
\label{f2cc_scaling}
\end{figure}
%%%%



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