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%     Proceedings of the 24th Winter Workshop on Nuclear Dynamics        %|
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\title{Understanding Jet Energy Loss with \\ 
Angular Correlation Studies in PHENIX} 
\authors{
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{J. A. Hanks for the PHENIX Collaboration$^1$ %
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{\normalsize
\hspace*{-8pt}$^1$ Department of Physics, Columbia University, \\ 
New York, NY 10027, USA\\[0.2ex] 
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}}
 
\abstract{Angular correlation studies provide powerful insight into the 
energy loss of hard scattered partons as they traverse the partonic medium 
produced in heavy ion collisions at RHIC. These results are generally compared 
to jet correlations in p+p collsisions where all correlation strength is 
attributed to vacuum fragmentation. Strong modification to di-jet correlations 
has been observed in A+A collisions at RHIC, most notably for the away side 
jet. Many different effects, including the opacity of the medium, its response 
to energy deposited by partons as they propagate, and modifications to the 
parton fragmentation, are involved in producing the final correlation 
stuctures. Understanding the interplay between these various effects is 
essential to developing a complete picture of the medium. Measurements of jet 
correlations involving direct photons provide a unique probe of jet 
fragmentation effects, as photons are not strongly interacting. Additionally, 
systematic studies of the away side structure as a function of $p_{T}$, as 
well as attempts to include additional high $p_{T}$ trigger requirements, can 
help to distinguish different energy loss mechanisms. We discuss recent 
PHENIX results from these detailed studies of jet correlations in A+A and p+p 
collisions.
}

\keyword{correlations,jets,} 
\PACS{25.75.Gz}
 
\begin{document}
 
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\section{Introduction}\label{intro}

In heavy ion collisions at RHIC we observe a significant modification of jets 
as a result of their interaction with the medium \cite{bib1}. We are able to measure 
such modifications through two particle angular correlations, where the large 
background can be dealt with using statistical subtraction methods \cite{bib2}. We can 
perform these correlation measurements over a large range of momentum for both the 
trigger and associated particles to study the observed modification as a function of both.\\
The modification of the away-side jet appears in two ways. The first is in the form of a 
supression of the di-jet at $\pi$, which we will refer to as the the "head" region. This 
suppression can be described well at high $p_{T}$ in terms of energy loss \cite{bib3}. The 
second is in the form of an enhancement away from $\pi$, in the "shoulder" region, thought 
to be do to medium response. There are several models which attempt to explain how this 
enhancement is produced. One possibility is that the jet propogates faster than the speed 
of sound in the medium, producing a mach cone \cite{bib4}. Another is that the jet is 
propagating faster than the speed of light in the medium, producing cherenkov radiation 
\cite{bib5}. Finally, the jet propagation may be coulpled with the collective flow, causing 
it to be deflected away from $\pi$ \cite{bib6}. These various scenarios can be tested by 
studying the position of the shoulder peaks as a function of $p_{T}$ and centrality \cite{bib3}, 
as well the reaction plane dependence.\\
Much information can be gained from these di-hadron studies, however there are inherent 
limitations to how well energy loss can be understood through these measurements, both as a 
result of the surface bias introduced by the trigger requirement \cite{bib7}, as well as the 
fact that both the trigger and associated hadrons will experience modification due to the 
medium. These difficulties can, at least in part, be overcome by measuring correlations of 
hadrons with direct photons, which do not interact with the medium.


\section{Away-side Jet Modification}\label{awayside}

There are several methods in PHENIX for studying the modification of the away-side jet. To 
understand the interplay between the head and shoulder regions the away-side can be decomposed 
into three sections: the head region, centered around $\Detla\phi = \pi$ and ranging from 
$\pi - \pi/6$ to $\pi + \pi/6$; and the two shoulder regions, in the range 
$\pi/6 < |\Delta\phi - \pi | < \pi/2$. This allows us to study how these various regions evolve. 
To measure the positions of the shoulder regions there are two fitting procedures that are used. 
The first uses two gaussians seperated by a distance D, as shown in equation (1).

\begin{equation}

J(\Delta\phi)_{away-side} = A(e^{\frac{(\Delta\phi -\pi + D)^{2}}{2\sigma^{2}}} + 
e^{\frac{(\Delta\phi -\pi - D)^{2}}{2\sigma^{2}}})

\end{equation}

The second includes a third gaussian, representing the head contribution, which is fixed by the 
p+p width, and centered at $\pi$, as shown in equation (2).

\begin{equation}

J(\Delta\phi)_{away-side} = A(e^{\frac{(\Delta\phi - \pi + D)^{2}}{2\sigma^{2}}} + 
e^{\frac{(\Delta\phi - \pi - D)^{2}}{2\sigma^{2}}})
+ Be^{\frac{(\Delta\phi - \pi)^{2}}{2\sigma_{pp}^{2}}}

\end{equation}

And illustration of both the head/shoulder decomposition and the two fitting methods is shown in 
figure \ref{fig:decomp}.\\
Studying the dependence of the head and shoulder regions on both the trigger and associated 
$p_{T}$ reveals that there is an enhancement of the shoulder yield at low associated $p_{T}$ 
which persists as we go to higher trigger momentum. This gives the shoulder a softer spectral 
shape, making it appear more bulk-like. We also find that the head is suppressed at intermediate 
to high associated $p_{T}$, for all trigger $p_{T}$ bins \cite{bib3}. Using the decomposition 
of the head and shoulder regions also allows us to compare them directly by looking at the ratio 
of the integrated yields, $R_{HS}$, as described by equation (3).

\begin{equation}

R_{HS} = (\integral_{head}d\Delta\phi \frac{1}{N_{trig}}\frac{dN}{d\Delta\phi})/
(\integral_{shoulder}d\Delta\phi \frac{1}{N_{trig}}\frac{dN}{d\Delta\phi})

\end{equation}

We find that the shoulder dominates at low partner momentum, up to $p_{T} \approx 4GeV/c$, 
while as the trigger $p_{T}$ is increased this ratio becomes consistent with the p+p measurement 
when the partner $p_{T}$ is greater than $4GeV/c$ \cite{bib3}.\\
The two fitting methods can be used to extract the D parameter, which is a measure of the 
separation between the shoulder peaks, and study it's dependence on the momentum of either 
hadron. We find that the peak positions show minimal dependence on the either the trigger or 
partner $p_{T}$, as shown in figure \ref{fig:shoulder_position} \cite{bib3}. This poses a 
challenge for models such as cherenkov radiation which predict a $p_{T}$ dependence.\\
It is also possible to use particle ID to measure these types of correlations for baryons and 
mesons seperately to determine how the modification observed depends on species. The results show 
a similar shape to the away side correlations for both. Additionally, the ratio of baryons to 
mesons in the away side yields shows a similar centrality dependence to that of the bulk, which 
is incompatible with vacuum fragmentation \cite{bib8}. These observations place a tight constraint on models 
attempting to describe baryons and mesons together, and provides further evidence for the idea 
that the shoulder region is dominated by medium response.\\


\section{$\gamma$-h and h-$\gamma$}\label{photons}

Correlations between hardons and photons can go even futher to improve our understanding of 
the various affects leading to both the energy loss of the jet, as well as the medium response, 
since the photons remain unmodified. $\gamma$-jet correlations, where the near-side parton 
fragments all of it's energy into the photon via compton scattering, which is then unmodified. 
This allows us to measure the initial parton energy by measuring the photon energy, and therefore 
measure the amount of energy loss the parton goes through in the medium. Additionally, di-jet 
measurements will be dominated by jets produced near the surface, leading to a geometric bias 
which adds further complications when trying to understand energy loss effects.


\end{document}
