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\Title{Theoretical perspectives on the heavy ion LHC program}
\bigskip\bigskip
%+\addtocontents{toc}{{\it K. Zapp}}
%+\label{ZappStart}
\begin{raggedright}
{\it Korinna Zapp\index{Zapp, K.}\\
Institute for Particle Physics Phenomenology\\
Durham University}
\bigskip\bigskip
\end{raggedright}
\section{Introduction}
One of the most important discoveries at \textsc{Rhic} is a
centrality dependent suppression of large transverse momentum
hadrons~\cite{Adams:2005dq,Adcox:2004mh}. This phenomenon -- although established on the basis of
single-inclusive hadrons -- is known as `jet quenching' and is commonly interpreted as being due to
radiative energy loss (i.e.\ QCD bremsstrahlung) of energetic partons in the dense and hot QCD
matter produced in ultra-relativistic collisions of heavy nuclei.
\section{Analytical approaches}
There are several analytical calculations of non-Abelian
bremsstrahlung~\cite{Baier:1996sk,Zakharov:1998sv,Gyulassy:2000er,Wiedemann:2000za,Zhang:2003yn,
Arnold:2000dr}. Despite the different approaches and techniques these calculations have a few things
in common. Firstly, they find that the phenomenology is dominated be an interference that
can be understood as the non-Abelian analogue of the Landau-Pomerantchuk-Migdal (LPM) effect.
Secondly, they operate in a particular kinematical limit, namely the eikonal limit in which the
radiating particle's energy is asymptotically large. This has important consequences, for instance
in that there is no collisional energy loss. In this limit the action of the medium on the fast
parton is characterised by the transport coefficient $\hat q$. Finally, all analytical calculations
consider the radiation of a single gluon that is then iterated probabilistically. Apart from
neglecting possible interferences this does not do justice to the well-known QCD jet evolution.
Consequently, these approaches are suitable for describing single inclusive observables, but not for
more exclusive observables and jets. An study comparing the different calculations in the same
set-up found that they all describe the \textsc{Rhic} hadron
suppression data equally well, albeit with very different transport
coefficients~\cite{Bass:2008rv}. A detailed investigation by the TECHQM collaboration concluded
that this is due to the fact that the kinematical situation in the experiments is far from the
eikonal limit and therefore the models are pushed outside their region of
validity~\cite{Armesto:2011ht}.
\section{Jet Quenching at the LHC}
Measurements of the single-inclusive hadron spectra at the \textsc{Lhc} have shown a similar
amount of suppression as at \textsc{Rhic}, but a different transverse momentum dependence (which is
at least partly caused by the different shape of the underlying
spectrum)~\cite{Aamodt:2010jd,CMS:2012aa}. At the \textsc{Lhc} also properties of reconstructed jets
in heavy ion collisions are accessible and have been measured. For instance, a large transverse
momentum asymmetry was found in di-jet events, while the azimuthal angle between the two jets
remains unchanged~\cite{Aad:2010bu,Chatrchyan:2011sx}. The missing momentum is carried by soft
particles far away from the jet axis~\cite{Chatrchyan:2011sx}. Furthermore, the intra-jet
fragmentation functions are largely unmodified at intermediate and large momentum
fractions~\cite{ATLAS:ffncs,Chatrchyan:2012gw}. All these observations indicate that the jets lose
energy and transverse momentum because soft components get transported outside the jet cone while
the hard core is not altered. This interpretation is supported by a simple formation time
argument~\cite{CasalderreySolana:2010eh}: The formation time of medium induced (bremsstrahlung)
emissions is given by $\tau_\mathrm{med} = \sqrt{2 \omega/\hat q}$, where $\omega$ is the emitted
gluon's energy. The angle of the emitted gluon with respect to the radiating parton can be estimated
as $\theta_\mathrm{med} \approx (2\hat q)^{1/4}/\omega^{3/4}$, i.e.\ soft gluons decohere first and
at large angles. At the same time the formation time of hard emissions from normal (vacuum) QCD
evolution is parametrically of the form $\tau_\mathrm{vac} = 2 \omega/k_\perp^2$, where $k_\perp$ is
the transverse momentum of the radiated gluon. This means that the formation of hard gluons is
delayed by a boost factor and thus protected from interactions in the medium.
\smallskip
On the theoretical side technical advances have been made, for instance various calculations have
been equipped with more realistic models for the medium. They generally agree at least
qualitatively with the hadron suppression
data~\cite{Chen:2011vt,Horowitz:2011cv,Majumder:2011uk,Zakharov:2011dq}, but the conceptual issues
have not been resolved. In order to make progress jet-medium interactions need to be formulated in
more general non-eikonal kinematics. Then, however, elastic and inelastic interactions
cannot be unambiguously separated any more and the ambiguity between the two needs to be resolved.
Multi-gluon emissions have to be formulated consistently treating all sources of radiation (vacuum
and medium-induced) on equal footing and keeping the interference responsible for the LPM-effect.
Also the back-reaction of the jet on the medium has to be understood and modelled. Moreover, in
order to obtain credible results all aspects of the calculation need to be controlled and
uncertainties quantified.
\section{Monte Carlo models}
As Monte Carlo codes are widely used in particle physics to simulate complex
multi-particle final states, it seems plausible that at least some of these problems can be solved
with Monte Carlos. However, one thing to keep in mind is that Monte Carlo models relying on
analytical results to simulate medium-induced gluon emissions also inherit the conceptual
weaknesses. Still, Monte Carlo techniques can be used to exploit approaches that cannot be treated
analytically.
\smallskip
The established Monte Carlo models for jet quenching are HIJING~\cite{Deng:2010mv},
HYDJET++/PYQUEN~\cite{Lokhtin:2008xi}, JEWEL~\cite{Zapp:2011ek},
Q-PYTHIA/Q-HERWIG~\cite{Armesto:2009fj,Armesto:2009ab}, YaJEM~\cite{Renk:2009nz} and
MARTINI~\cite{Schenke:2009gb}. Some of them are based on analytical results while others build on
new ideas. They all include some form of jet evolution and produce final states that can in
principle be compared to jet measurements. Although the Monte Carlo models typically succeed in
reproducing for instance the di-jet asymmetry at least qualitatively, no consistent picture has
emerged yet as it is sometimes unclear to what extent all aspects of the modelling are controlled.
\section{Conclusions}
Jet quenching measurements at the \textsc{Lhc} indicate that the hard core of the jets stays intact
while soft modes get transported to large angles. This picture supports the interpretation that
perturbative, coherent gluon bremsstrahlung is responsible for the observed modification of jets.
However, detailed comparisons of theory predictions and data suffer from large systematic theory
uncertainties. Therefore, in order to make the most of the \textsc{Lhc} data, new developments on
the theory side are necessary. Also, with a wealth of jet data new theory tools such as Monte Carlo
codes are needed. Monte Carlo models are starting to overcome the limitations of analytical
calculations, but most of them still don't provide a controlled and consistent framework.
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\end{thebibliography}
\end{document}
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