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\title{Main sources of uncertainty in quark and gluon fragmentation functions
into hadrons and photons}
\author{Monique Werlen, LAPTH}
\maketitle
In the calculation of inclusive hadron and photon cross sections in $pp$ collisions
with the PHOX programs, NLO event generators (parton level)
for large pt PHOton (hadron or jet) X-sections \cite{phoxfamily},
uncertainties on fragmentation functions (FF) do matter compared
to those from scales and parton distribution functions (PDF) at RHIC
and LHC energies \cite{Arleo:2004gn}.

There are various sources of uncertainties in the
determination of FF from fits to inclusive
cross sections where one assumes a functional form at a scale $M_{F0}$
and evolves it to the scale of the data.
Experimental uncertainties are due to statistical error
(FF with a large momentum fraction z of the parton in $e^+e^-$ data),
systematic, normalization, the probed
z and $Q^2$ range as well as the sensitivity to quark and gluon FF.
Matching theory and data (binning, cuts) may also be an issue.
Theoretical uncertainties come from the choice of the functional form,
the z range of assumptions, the choice of scales, the order of the theory
(leading, next-to-leading NLO, resummation) and further parameters
like PDF and $\alpha_s$.

%\centerline{Quark and gluon fragmentation into hadrons}
NLO fits  to $e^+ e^- \to \pi^0 X$ data from PEP and PETRA
constrain the quark fragmentation into neutral pions while NLO fits to $p p \to \pi^0 X$
from ISR and UA2 constrain the gluon fragmentation \cite{Chiappetta:1992uh}.
%In particular, the strong correlation between gluon
%and sea quark normalization obtained in $e^+ e^-$ fits is different from the one observed
%in $pp$ data where only the gluon normalization is well constrained. There are however
%large uncertainties due to the choice of factorization, renormalization and fragmentation
%scales in $pp$ fits.
%For increased transverse momentum in the $pp$ data, the sensitivity moves to larger z.

BFGW \cite{Bourhis:2000gs} sets of FF into
unidentified charged hadrons have been obtained from LEP and PETRA data
%To be less sensitive to uncertainties due to the choice of renormalization
%and fragmentation scales 
%In fits to $e^+ e^- \to h X$, we 
choosing optimized scales
(a rough approximation of the large z resummation performed later in \cite{Cacciari:2001cw}).
Gluon parameters were quite sensitive to the functional form
chosen for the quark distribution.
A full statistical error analysis is performed 
%Three sets with ruther different gluon shapes
%at large z are compatible with UA1 data.
while estimation of the "theoretical error" embedded in the parametrizations
and  which come from various theoretical assumptions
can be obtained by comparing with different sets: 
There are important discrepancies, specially at large z, with the BKK set 
\cite{Binnewies:1995pt}
%(which is also largely unconstrained by the LEP data due to limited statistics). 
while the very low gluon
FF at $z>0.5$ from the Kretzer set \cite{Kretzer:2000yf} seems unfavored by
UA1 data.

Large scale instabilities (specially at low $\sqrt{s}$ and low $p_T$)
affect the phenomenology of inclusive production of pion \cite{Aurenche:1999nz}.
Theoretical estimates rely on extrapolations
of the FF outside ($0.75-0.9$) of the region where they
are actually constrained ($0.1<z<0.7$) by the data from which they are extracted
\cite{Binoth:2002ym}. 
%The KKP set \cite{Kniehl:2000fe} improves the phenomenology.
%compared to the BKK set. 
%At RHIC energy, uncertainties from scales are important: +-50\% at $p_T= 8$ GeV
%and comparable to uncertainties obtained using different FF. 
%At LHC energy,
%uncertainties from scales are of order of: +-20\% for $p_T> 10$ GeV 
%while  differences from FF sets are dominant.
A preliminary study \cite{inprep} with JETPHOX shows that hadron-jet correlation
at RHIC energy may be used to constrain the FF into hadron in
the high z region. With $p_T(h) > 25$~GeV 
and $p_T (jet) >30$~GeV, 
BFGW is systematically higher than KKP \cite{Kniehl:2000fe} while Kretzer is almost a factor two lower
than BFGW.

%\centerline{Photon FF}

Thanks to recent data from PHENIX and D0 spanning a large $x_T=2p_T/\sqrt{s}$ range,
inclusive prompt photons cross sections from $ \sqrt{s}=23$ GeV to $\sqrt{s}= 1.96$ TeV
are now well understood in the NLO QCD framework \cite{Aurenche:2006vj}.
Photons can be produced either directly or via a FF. The later
become important at low $p_T$ and high $\sqrt{s}$. Uncertainties on the photon
FF are mainly due to the uncertainty on the gluon FF
as quantified by the BFG sets I and II \cite{Bourhis:1997yu}. BFG I
reduce the cross section by up to 10\% (a factor 2.5) at $p_T= 3$GeV
at RHIC (LHC) energy compared to BFG II \cite{Arleo:2004gn}.
A preliminary study \cite{inprep} with JETPHOX  shows that photon-jet correlation
at RHIC energy may be used to constrain the photon FF. 
With the momentum of the jet fixed, varying the momentum of the non
isolated photon allows a direct access to the photon fragmentation at low z,
a region barely accessible in the LEP experiments. 
%However further check is
%needed concerning uncertainties from the scales.

\begin{thebibliography}{99}

\bibitem{phoxfamily}
see http://www.lapp.in2p3.fr/lapth/PHOX\_FAMILY/main.html

\bibitem{Arleo:2004gn}
F.~Arleo et al.,
%``Photon physics in heavy ion collisions at the LHC,''
[arXiv:hep-ph/0311131].

\bibitem{Chiappetta:1992uh}
P.~Chiappetta, M.~Greco, J.~P.~Guillet, S.~Rolli and M.~Werlen,
%``Next-To-Leading Order Determination Of Pion Fragmentation Functions,''
Nucl.\ Phys.\  B412 (1994) 3
[arXiv:hep-ph/9301254].

\bibitem{Bourhis:2000gs}
L.~Bourhis, M.~Fontannaz, J.~P.~Guillet and M.~Werlen,
%``Next-to-leading order determination of fragmentation functions,''
Eur.\ Phys.\ J.\  C19 (2001) 89
[arXiv:hep-ph/0009101].
%%CITATION = EPHJA,C19,89;%%

\bibitem{Cacciari:2001cw}
M.~Cacciari and S.~Catani,
Nucl.\ Phys.\ B 617 (2001) 253.

\bibitem{Binnewies:1995pt}
J.~Binnewies, B.~A.~Kniehl and G.~Kramer,
%``Pion And Kaon Production In E+ E- And E P Collisions At Next-To-Leading
%Order,''
Phys.\ Rev.\  D52 (1995) 4947.
%[arXiv:hep-ph/9503464].
%%CITATION = PHRVA,D52,4947;%%

\bibitem{Kretzer:2000yf}
S.~Kretzer,
%``Fragmentation functions from flavour-inclusive and flavour-tagged e+ e-
%annihilations,''
Phys.\ Rev.\  D62 (2000) 054001
[arXiv:hep-ph/0003177].
%%CITATION = PHRVA,D62,054001;%%

\bibitem{Kniehl:2000fe}
B.~A.~Kniehl, G.~Kramer and B.~Potter,
%``Fragmentation functions for pions, kaons, and protons at  next-to-leading
%order,''
Nucl.\ Phys.\  B582 (2000) 514
%[arXiv:hep-ph/0010289].
%%CITATION = NUPHA,B582,514;%%

\bibitem{Aurenche:1999nz}
P.~Aurenche, M.~Fontannaz, J.~P.~Guillet, B.~A.~Kniehl and M.~Werlen,
%``Large p(T) inclusive pi0 cross-sections and next-to-leading-order QCD
%predictions,''
Eur.\ Phys.\ J.\  C13 (2000) 347
[arXiv:hep-ph/9910252].
%%CITATION = EPHJA,C13,347;%%

\bibitem{Binoth:2002ym}
T.~Binoth, J.~P.~Guillet, E.~Pilon and M.~Werlen,
%``A next-to-leading order study of pion-pair production and comparison with
%E706 data,''
Eur.\ Phys.\ J.\  C24 (2002) 245.
[arXiv:hep-ph/0111043]
%%CITATION = EPHJA,C24,245;%%
\bibitem{Aurenche:2006vj}
P.~Aurenche, M.~Fontannaz, J.~P.~Guillet, E.~Pilon and M.~Werlen,
%``A new critical study of photon production in hadronic collisions,''
Phys.\ Rev.\  D73, 094007 (2006)
[arXiv:hep-ph/0602133].
%%CITATION = PHRVA,D73,094007;%%
\bibitem{Bourhis:1997yu}
L.~Bourhis, M.~Fontannaz and J.~P.~Guillet,
%``Quark and gluon fragmentation functions into photons,''
Eur.\ Phys.\ J.\  C2 (1998) 529
[arXiv:hep-ph/9704447].
%%CITATION = EPHJA,C2,529;%%
\bibitem{inprep}
Z.~Belghobsi, M.~Fontannaz, J.Ph.~Guillet, G.~Heinrich, E.~Pilon and M.~Werlen,
in preparation


\end{thebibliography}

\end{document}


