\title{AKK update: Improvements from New Theoretical Input and Experimental Data}

\author{S.\ Albino, B.\ A.\ Kniehl, G.\ Kramer}

\affiliation{{II.} Institut f\"ur Theoretische Physik, Universit\"at Hamburg,\\
             Luruper Chaussee 149, 22761 Hamburg, Germany}

We present results from a forthcoming publication presenting an update
of the previous AKK fragmentation function (FF) sets for charged
pions, charged kaons, (anti)protons, neutral kaons and (anti)lambdas
with additional theoretical and experimental input.

We incorporate hadron mass effects \cite{Albino:2005gd}, and fit the
hadron mass in the case of the e+e- calculation which also has the
effects of subtracting out other low $\sqrt{s}$ and small $x$ effects
beyond the fixed order approach, such as higher twist, small $x$
logarithms, etc. In the case of the baryons, the fitted masses are
about 1\% above the true masses, which is consistent with scenarios in
which the baryons are produced mainly from direct partonic
fragmentation with a small contribution from decays from slightly
heavier resonances.  A greater excess is found for the pion mass,
suggesting contributions to the sample from decays of heavier
particles such as $\rho(770)$. Charged and neutral kaon masses are
significantly below their true masses.  A possible explanation for
this is that there are significant contributions from complicated
decay channels, such that the direct partonic fragmentation approach
is insufficient. For this reason we do not impose SU(2) isospin
symmetry of $u$ and $d$ quarks between charged and neutral kaons,
which we do for pions.  We implement large $x$ resummation in the
quark coefficient function of $e^+ e^-$ reactions using the results
from Ref.\ \cite{Cacciari:2001cw}, since this is a simple improvement
which modifies the cross section over the whole range in $x$ that we
constrain.  Large $x$ resummation is also implemented in the DGLAP
evolution of the FFs \cite{Albino:2007ns}.  This results in a
significant improvement in the fit for charged kaons, (anti)protons
and (anti)lambdas, while $chi^2$ is essentially unchanged for neutral
kaons and charged pions.

In addition to the constraints of the previous AKK fit, we impose
further constraints on the charge-sign unidentified FFs from the data
for single inclusive production of identified particles from RHIC
\cite{Arsene:2007jd,Adler:2003pb,Adams:2006nd,Adams:2006uz,Abelev:2006cs},
the Tevatron \cite{Acosta:2005pk} ($p_T \geq 2$GeV) and
electron-positron reactions below the Z pole mass and in the range
$0.05<x<0.1$.  While the untagged measurements from electron-positron
reactions provide excellent constraints for the sums of the
charge-sign unidentified FFs for quarks of the same electroweak
charges, they do not constrain the remaining degrees of freedom at
all. As in the previous AKK fit, these were constrained using quark
tagged data, while in the new AKK fit additional constraints are
provided by the data from RHIC.  These data are also much more
sensitive to gluon fragmentation and impose (exclusively) new
constraints on the charge-sign assymetry FFs.  Normalization errors
were treated as systematic effects, i.e.\ these errors were
incorporated via a correlation matrix. Their weights were fitted
analytically and independently of the fit in order to further
ascertain the quality of the fit, and were typically found to lie in
the reasonable range of 0 -- 2.

While the results for the fitted masses suggest that the baryons are
the best candidates for studying direct partonic fragmentation, there
unfortunately exist some inconsistencies between the calculation and
the measurements of the inclusive production of these particles at
RHIC: The description of the STAR data for
$\Lambda/\overline{\Lambda}$ fails, while the contribution from the
initial protons' valence $d$ quarks to the charge-sign assymetry for
$p/\overline{p}$ from STAR is negative. Furthermore, while the
contributions to the production from the fragmentations of the valence
and sea quarks of the initial protons for the data from RHIC exhibited
the expected behaviour, the contribution from the valence $d$ quark
fragmentation to the charge-sign assymetry in (anti)proton production
is negative. All these issues would be better understood in the
context of an error analysis of the FFs.

We compared our sets to the recent DSS \cite{deFlorian:2007aj} / DSV
\cite{deFlorian:1997zj} and HKNS \cite{Hirai:2007cx} ones, and
typically found reasonable agreement for favoured FFs but not for
unfavoured, and large discrepancies exist at large $x$ in some cases.

Future hadron identifed data from BaBar, CLEO, HERA and RHIC will help
to clarify these issues and significantly reduce the large
uncertainties in much of the FF degrees of freedom.

\bibitem{Albino:2005gd}
S.~Albino, B.~A.~Kniehl, G.~Kramer and W.~Ochs,
Phys.\ Rev.\ D 73 (2006) 054020;
%\bibitem{Albino:2005gg}
Phys.\ Rev.\ Lett.\ 95 (2005) 232002.

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

\bibitem{Albino:2007ns}
S.~Albino, B.~A.~Kniehl and G.~Kramer,
arXiv:0711.1086 [hep-ph].

\bibitem{Arsene:2007jd}
BRAHMS Collaboration, I.~Arsene {\it et al.},
Phys.\ Rev.\ Lett.\ 98 (2007) 252001.

\bibitem{Adler:2003pb}
PHENIX Collaboration, S.~S.~Adler {\it et al.},
Phys.\ Rev.\ Lett.\ 91 (2003) 241803.

\bibitem{Adams:2006nd}
STAR Collaboration, J.~Adams {\it et al.},
Phys.\ Lett.\ B 637 (2006) 161.

\bibitem{Adams:2006uz}
STAR Collaboration, J.~Adams {\it et al.},
Phys.\ Rev.\ Lett.\ 97 (2006) 152302.

\bibitem{Abelev:2006cs}
STAR Collaboration, B.~I.~Abelev {\it et al.},
Phys.\ Rev.\ C 75 (2007) 064901.

\bibitem{Acosta:2005pk}
CDF Collaboration, D.~E.~Acosta {\it et al.},
Phys.\ Rev.\ D 72 (2005) 052001.

\bibitem{deFlorian:2007aj}
D.~de Florian, R.~Sassot and M.~Stratmann
Phys.\ Rev.\ D 75 (2007) 114010;
%\bibitem{de Florian:2007hc}
%D.~de Florian, R.~Sassot and M.~Stratmann,
Phys.\ Rev.\ D 76 (2007) 074033.

\bibitem{deFlorian:1997zj}
D.~de Florian, M.~Stratmann and W.~Vogelsang,
Phys.\ Rev.\ D 57 (1998) 5811.

\bibitem{Hirai:2007cx}
M.~Hirai, S.~Kumano, T.~H.~Nagai and K.~Sudoh,
Phys.\ Rev.\ D 75 (2007) 094009.
