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\title{Study of Charm Fragmentation in DIS at H1}

\begin{document}
\maketitle

The process of charm fragmentation is studied using $D^{*\pm}$ meson 
production in deep-inelastic scattering as measured by the H1 detector 
at HERA collider~\cite{preliminary}. Two different methods are used for the definition 
of the observable approximating the fraction of the four-momentum of 
the  $D^{*\pm}$ meson with respect to the charm quark. 
The momentum of the charm quark is approximated in the 
$\gamma^{*}p$-rest-frame either by the momentum of the jet including 
the $D^{*\pm}$ meson or by the momentum of a suitably defined hemisphere which 
includes the $D^{*\pm}$ meson.\\

The visible phase space of this analysis is given by cuts on the photon
virtuality $2<Q^{2}<100$ GeV$^{2}$, event inelasticity $0.05<y<0.7$ and 
$D^{*\pm}$ meson phase space $1.5<P_{\rm T}(D^{*\pm})<15$ GeV, 
$|\eta(D^{*\pm})|<1.5$. In addition a $D^{*\pm}$ jet with $E_{\rm T}^{*}>3$ GeV 
in $\gamma^{*}p$-rest-frame is required in order to have hard scale for the events.
The fractional energy distributions of $D^{*}$ mesons, corrected for detector 
effects, are used to extract parameters for the Kartvelishvili and Peterson 
fragmentation functions within the framework of leading order + parton shower 
QCD models RAPGAP 3.1 and CASCADE 1.2 with string fragmentation and particle 
decays as implemented in PYTHIA, as well as for the next-to-leading order QCD
calculation in the fixed flavour scheme HVQDIS~\cite{hvqdis}.\\

The fragmentation parameters extracted using both observables are in good 
agreement with each other. Further more the value of Peterson parameter 
$\varepsilon$, extracted for the PYTHIA parameter setting~\cite{ALEPH-steering},
is in agreement the ALEPH tuned value of $\varepsilon= 0.04$, supporting the
hypothesis of fragmentation universality between $e^{+}e^{-}$ and $ep$.\\

Finally, the fragmentation of charm produced close to the kinematic threshold
is studied. The description of this sample by the QCD models and NLO 
calculation is not good, and the extracted fragmentation parameters are 
significantly different from the parameters fitted to the nominal 
sample with a hard scale. This can be interpreted as a hint of inadequacies of 
the QCD models and possibly of insufficient flexibility of the simple 
parametrisations used for the fragmentation function in the phase space 
region close to kinematic threshold.  

\begin{thebibliography}{99}

\bibitem{preliminary}
[H1 Collaboration], 
http://www-h1.desy.de/h1/www/publications/htmlsplit/H1prelim-05-074.long.html\\
More up to date version will be released soon.

\bibitem{hvqdis} 
B.W.~Harris and J.~Smith, 
Nucl.\ Phys.\ B {\bf 452} (1995) 109,
Phys.\ Lett.\ B {\bf 353} (1995) 535
   
 
\bibitem{ALEPH-steering}
S.~Schael {\it et al.}  [ALEPH Collaboration],
``Bose-Einstein correlations in W-pair decays with an event-mixing
technique,''
Phys.\ Lett.\  B {\bf 606} (2005) 265

\end{thebibliography}  

\end{document}
