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\journal{Nuclear Physics A} 

%% need cites for
%% les-houches jet accord
%% lund string model -> perhaps the lund book?
%%

\begin{document}

\begin{frontmatter}
\date{}

\title{Systematic Monte-Carlo studies of dijets at RHIC using the VNI/BMS Parton Cascade}
\author[duke]{C.E.Coleman-Smith}
\ead{cec24@phy.duke.edu}
\author[duke]{B.M\"uller}
\author[duke]{S.A.Bass}
\address[duke]{Department of Physics, Duke University, Durham, NC 27701} 


\begin{abstract} 
  We present a study of the dijet suppression at RHIC using the parton cascade model. We
  examine the modification of the dijet asymmetry $A_j$ and the fragmentation
  distributions $z$ and $j_{T}$ in terms of: $\hat{q}$; the path length of leading and
  sub-leading jets; cuts on the jet energy distributions; jet cone angle and the
  jet-medium interaction mechanism. We have introduced a string hadronization model and
  present hadronic jet fragmentation distributions. We find that $A_j$ is most sensitive to
  $\hat{q}$ and less sensitive to the nature of the jet-medium interaction
  mechanism. The fragmentation distributions show jet modification and
  differentiate between elastic and radiative+elastic modes.
\end{abstract}

\begin{keyword}
  LPM \sep parton cascade \sep jet suppression \sep QGP \sep Quark Matter 2012
\end{keyword}


\end{frontmatter}

Recent measurements showing the strong modification of high energy $E_{t} \sim 100-200$
GeV dijets at the LHC \cite{Aad:2010bu, Chatrchyan:2011sx} in Pb+Pb collisions have
sparked an interest in using dijets to quantify jet modification in hot QCD
matter. Proposed upgrades to the PHENIX experiment, and continuing development of jet
reconstruction at STAR, promise access to dijets in a different kinematic region, $E_{t}
\sim 15-65$ GeV at RHIC. The dijet asymmetry
\begin{equation}
  \label{eqn-aj-define}
A_j = \frac{E_{t,\ell} - E_{t,s}}{E_{t,\ell}+E_{t,s}},
\end{equation}
where $E_{t,\ell}$ is the transverse energy of the leading jet and $E_{t,s}$ is that of
the sub-leading jet, has been successfully reproduced with a variety of
models \cite{Qin:2010mn, Young:2011qx, ColemanSmith:2011wd, He:2011pd}. Recent work by
Renk \cite{Renk:2012cx} has indicated that these results may be insensitive to
the fine details of jet energy loss, suggesting that $A_j$ may be unsuitable for
tomographic purposes. If this is indeed the case are there other more differential dijet
observables for jet measurements at RHIC?

With these issues in mind we have used the VNI/BMS \cite{Geiger:1991nj, Bass:2002fh}      
parton cascade to systematically explore dijet suppression at RHIC energy scales under
controlled medium conditions. We examine the modification of dijets under variation of the
medium radius and temperature, the strong coupling constant and the jet definition in
terms of the Anti-Kt cone angle and the leading jet energy cut. The VNI/BMS parton cascade
model provides access to the full jet/medium development at a fixed temperature and density, and thus fixed $\hat{q}$. We run the
code in a static uniform-medium mode. %Here the medium is modeled as torus of a
%given radius. The dijet propagation lengths are generated as chords centered on uniformly
%sampled hard-collision vertices within this torus.

The full set of results from our systematic analysis can be found in
\cite{ColemanSmith:2012vr}. In this proceeding we outline the model, introduce the
hadronization process and show some selected results from the analysis.

The parton cascade model (PCM) is a Monte-Carlo implementation of the relativistic
Boltzmann transport of quarks and gluons
\begin{equation}
\label{eqn-boltzmann}
p^{\mu} \frac{\partial}{\partial x^{\mu}} F_k(x, p) = \sum_{i}\mathcal{C}_i F_k(x,p).
\end{equation}
The collision term $\mathcal{C}_i$ includes all possible $2\to2$ interactions and
final-state radiation $1 \to n$
\begin{align}
  \label{eqn-pcm-collision}
  \mathcal{C}_i F_k(x,\vec{p}) = \frac{(2 \pi)^4}{2 S_i} \int \prod_{j} d\Gamma_j | \mathcal{M}_i | ^2 
  \delta^4\left(P_{in} - P_{out}\right) D(F_k(x, \vec{p})),
\end{align}
$d\Gamma_j$ is the Lorentz invariant phase space for the process $j$, $D$ is the collision
flux factor and $S_i$ is a process dependent normalization factor. A geometric
interpretation of the total cross-section is used to select pairs of partons for
interaction. Between collisions, the partons propagate along straight line trajectories.

In the VNI/BMS PCM outgoing off-shell partons are brought back on-shell through a medium
modified time-like branching, this includes a Monte-Carlo LPM effect \cite{Zapp:2008af,
  ColemanSmith:2011wd}.

The strong coupling constant is fixed at $\alpha_s = 0.3$. A QGP medium is simulated as a
box of thermal quarks and gluons generated at some fixed temperature. Periodic boundary
conditions are imposed on the box, whose size is selected to be large enough that if a
simulated jet wraps around it will not interact with its own wake.

The partonic contents of jets created by a suitable event generator and evolved down to
$Q_0 = 1$~GeV, in this study PYTHIA 8 \cite{Sjostrand:2006za}, are injected into the
medium. Each sub-jet is evolved separately. The partons propagate for a given distance and
their evolution is recorded. Each particle in the initially inserted jet is marked as
being ``jetty'', this jettiness tag is then iteratively applied to all partons that
interact with an already jetty-labeled parton. %The entire time-evolution of the jet can
%then be reconstructed using a suitable jet finder and jet definition.

We have developed a simple scheme for hadronizing the contents of these jets which follows
the Les Houches accord for particle color labeling. We extract the colors labels of
the initial partons from the event generator, as these parton interact the color labels
are propagated appropriately. Each medium parton is given the next free color label, any
ambiguities in the label forwarding are resolved by assigning the incoming colors to the
outgoing partons randomly. The partons interact through color averaged
cross-sections. After including contributions from the medium the jet is in usually a non
singlet state. We neutralize this color structure by generating a minimal set of thermal
partons with appropriate color labels to render the jet a color singlet. 
The final set of partons is hadronized through the Lund string model \cite{Andersson:1998tv}.

In \figref{fig:had-example} we show a comparison of the partonic and hadronic transverse
and longitudinal momentum distributions for a $100$~GeV quark jet evolved in a box at
$T=0.35$~GeV for $4$~fm/c. The dashed blue curve shows the distributions of the jet partons
along with the associated thermal color-matching partons, these additional partons lead to
an enhancement at small $P_{T}$ and small $z$. Hadronization smooths and softens the
longitudinal momentum distribution, conservation of momentum leads to an associated
constriction of the transverse distribution.

%% figures here
\begin{figure}[htb]
  \centering
  \includegraphics[width=0.4\textwidth]{fig-1.pdf}
  \includegraphics[width=0.4\textwidth]{fig-2.pdf}
  \vspace{-0.4cm}
  \caption{  \label{fig:had-example}(Color Online) Transverse (left) and longitudinal (right) momentum
    distributions for the contents of $100$~GeV quark jet evolved in a box at $T=0.35$~GeV
    for $4$~fm. Partonic distributions are shown as the blue curves, hadronic curves in
    red. The dashed blue curve represents the partonic distributions after the addition of
    the thermal partons required for hadronization }
  \vspace{-0.5cm}
\end{figure}

We consider dijets at RHIC scales $\sqrt{s_{NN}} = 200$~GeV, all jets are
reconstructed with the Anti-Kt algorithm \cite{Cacciari:2008gp}. The following kinematic
cuts were always imposed: the minimum jet cut is set to $p_{t,min} = 5$ GeV,
$\Delta |\eta_{12} | < 1.1$, $\Delta \phi_{12} > \pi / 2$ where $\Delta \eta_{12}$ and
$\Delta \phi_{12}$ are measured between the two reconstructed jets in the event.

\begin{figure}[htb]
  \centering
  \includegraphics[width=0.35\textwidth]{fig-3.pdf}
  \includegraphics[width=0.35\textwidth]{fig-4.pdf}
  %% huh, the vacuum distrib is *probably* partonic, is that a problem?
  \caption{  \label{fig:aj-tvary}(Color Online) Elastic (left) and Elastic+Radiation (right) distributions of $A_j$ as a
    function of the medium temperature, for hadrons. The shaded blue histogram shows the vacuum (PYTHIA) results.}
  \vspace{-0.5cm}
\end{figure}

In \figref{fig:aj-tvary} we show the influence of varying the medium temperature on the
dijet asymmetry $A_{j}$. Recall that perturbative calculations for $\hat{q}$ scale like
$T^3$. The higher temperature $T=0.35$~GeV (green curve, crosses) leads to a strong
increase in the observed asymmetry for both interaction mechanisms. The full simulation
(right panel), including elastic and radiative results, shows a somewhat stronger
asymmetry than the elastic only result. This shift is observed to be strongest at small
jet cone radii, here we have used $R=0.2$. Increasing the cone radius ``recaptures'' the
escaped energy and so tends to reduce the observed asymmetry, see \figref{fig:frag-z} and 
\cite{ColemanSmith:2012vr}.

We plot the longitudinal jet fragmentation $z = \frac{p_{t,h}}{p_{t,jet}} \cos \Delta r$
in \figref{fig:frag-z}, for leading (closed symbols) and sub-leading (open symbols)
dijets. The plots show the vacuum distributions (blue, dashed) and the evolved
distributions (red, solid). Let us first consider the left panel, which shows jets
reconstructed at $R=0.2$. There is a strong peak at $z=1$. The limited phase space for the
vacuum evolution of the jets at RHIC scales frequently gives rise to jets which have not
undergone many splittings. The longitudinal momentum distribution for these jets is
dominated by one or two very hard partons. This peak is diminished by evolution, with a
concomitant enhancement at small $z$ for the evolved jets. Since $z$ is normalized to the
final-state measured jet momentum, the medium induced energy loss is mostly scaled out.

The right hand panel of \figref{fig:frag-z} shows the fragmentation distribution for the
same events but calculated with a much wider jet cone angle $R=1.0$. The peak at $z=1$ is
still just evident in the vacuum distributions. There is a clear separation between the
evolved and vacuum distributions (blue,red). The small $z$ peak is enhanced by medium
induced radiation, forward scattering and the fragmentation process itself (as shown in
\figref{fig:had-example}). These two extremes paint a picture of jets as having a hard
core surrounded by a more diffuse cone of soft partons from medium induced radiation and
forward elastic scattering.

%% frag figures
\begin{figure}[htb]
  \centering
  \includegraphics[width=0.35\textwidth]{fig-5.pdf}
  \includegraphics[width=0.35\textwidth]{fig-6.pdf}
  \vspace{-0.4cm}
  \caption{\label{fig:frag-z}(Color Online) Longitudinal jet fragmentation $z$ distributions for evolved
    (red, solid lines) and vacuum (blue, dashed lines) dijets reconstructed at $R=0.2$
    (left) and $R=1.0$ (right). The (sub-leading, leading) dijet results are shown with (filled,open) symbols.}
\end{figure}

Dijets at RHIC scales are likely to be strongly modified by the presence of the deconfined QGP medium. The observables we have discussed are sensitive to many aspects of this modification and suggest that further jet measurements at RHIC will provide valuable insights into the nature of the QGP.

%% perhaps don't need this
We acknowledge support by DOE grants DE-FG02-05ER41367 and DE-SC0005396. This research was done using computing resources provided by OSG EngageVo funded by NSF award 075335. 

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