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%{\small \it Rencontre de Moriond, QCD and Hadronic Interactions, La Thuile (Italy), March 8--15, 2008}

%\textbf{Oral}
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\begin{center}{\bf Issues of fragmentation function and medium effects in single inclusive production and two particle correlations in p-p and A+A collisions}\end{center}

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\centerline{ {\bf M.~J.~Tannenbaum}$^{\rm a}$ }

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\centerline{$^{\rm a}$Physics Department, 510c, Brookhaven National Laboratory} \centerline{Upton, N.Y., 11973-5000, U.S.A., {\it mjt@bnl.gov}}
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  Hard-scattering of point-like constituents (or partons) in p-p collisions was discovered at the CERN-ISR in 1972 by measurements utilizing inclusive single or pairs of hadrons with large transverse momentum ($p_T$). Due to the steeply falling power-law ${p}_T$  spectrum of the hard-scattered partons, the inclusive single particle (e.g. $\pi^0$) $p_{T_t}$ spectrum from jet fragmentation of a parton with $\hat{p}_{T_t}$ is dominated by trigger fragments with large $\mean{z_t}\sim 0.7-0.8$, where $z_t=p_{T_t}/\hat{p}_{T_t}$ is the fragmentation variable. It was generally assumed, following Feynman, Field and Fox~[1], as shown by data from the CERN-ISR experiments, that the $p_{T_a}$ distribution of away side hadrons from a single particle trigger [with $p_{T_t}$], corrected for $\mean{z_t}$, would be the same as that from a jet-trigger and follow the same fragmentation function as observed in $e^+ e^-$  or DIS. PHENIX~[2] attempted to measure the fragmentation function from the away side $x_E\sim p_{T_a}/p_{T_t}$ distribution of charged particles triggered by a $\pi^0$ in p-p collisions and showed by explicit calculation that the $x_E$ distribution is actually quite insensitive to the fragmentation function.  A new formula 
for the distribution of an associated
away-side particle with transverse momentum $p_{T_a}$, which is
presumed to be a fragment of an away-jet with $\hat{p}_{T_a}$, with exponential fragmentation function $D(z)=Be^{-bz}$, 
triggered by a particle with transverse momentum $p_{T_t}$,
presumably from a trigger-side jet with $\hat{p}_{T_t}$, invariant cross section, $Ed^3\sigma/dp^3=A\hat{p}_{T_t}^{-n}$, was
given~[2]: \  ${dP_{p_{T_a}}/dx_E}|_{p_{T_t}}\approx
{{\langle{m}\rangle}\over\hat{x}_h} {(n-1)\over
{(1+ {x_E /{\hat{x}_h}})^{n}}}$   \quad , 
which relates $x_E$, the ratio of the transverse
momenta of the measured particles, to $\hat{x}_h=\hat{p}_{T_a}/\hat{p}_{T_t}$,
the ratio of the transverse momenta of the away-side to
trigger-side jets, where $\langle m\rangle$ is the mean
multiplicity of particles in the away jet. Many analyses of the
away-jet $p_{T_a}$ distributions in Au+Au collisions are
available; but these tend to describe the effect of the medium
with the variable $I_{AA}(x_E)$, the ratio of the $x_E$
distribution in A+A collisions to that in p-p collisions, which
typically shows an enhancement at low values of $x_E$ and a
suppression at higher values of $x_E$. Such behavior could be
explained as a decrease in $\hat{x}_h$ in A+A collisions due to
energy loss of the away jet in the medium. Fits of the above
formula to the available data will be presented to establish
whether: a) the away-jets simply lose energy; b) some of the
away-jets lose energy, others punch-through without losing
energy; etc. \hfill\break
\hspace*{60pt} Measurements of direct single $\gamma$ production in p-p and Au+Au are also discussed. Fragmentation photons in p-p collisions, if they exist, can be eliminated by isolation cuts, although, at the ISR and at RHIC, measurements of correlations to a direct single $\gamma$ show very little activity, if any, on the same side. In contrast to triggers with $\pi^0$ which are the fragments of jets, away-side correlations for direct single $\gamma$'s which are direct participants in 2-2 hard scattering should measure the fragmentation function of the away side jet, modulo $k_T$ smearing. This fragmentation function can be plotted conventionally as a function of $x_E$ or as a function of $\xi=\ln(1/x_E)$ as suggested for jets at the LHC[3] 

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\parindent=0pt \textbf{References}

[1] R.~P.~Feynman, R.~D.~Field, and G.~C.~Fox, Nucl. Phys. B {\bf 128}\ (1977)~1--65.

[2] S.~S.~Adler, et al., PHENIX Collaboration, Phys. Rev. D {\bf 74}\ (2006)~072002. Latest results for $\pi^0$ suppression in Au+Au are given in A.~Adare, et al., PHENIX Collaboration, arXiv:0801.1665,0801.4020. Latest results for direct photon production in p-p are given in S.~S.~Adler, et al., PHENIX Collaboration, Phys. Rev. Lett. {\bf 98}\ (2007)~012002.  

[3] N.~Borghini and U.~A.~Wiedemann, {\tt hep-ph/0506218}.
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