Physics Letters B 734 (2014) 157–161
Contents lists available at ScienceDirect
Physics Letters B
www.elsevier.com/locate/physletb
Charmonium spectral functions and transport properties of
quark-gluon plasma
Si-xue Qin
∗
, Dirk H. Rischke
Institute for Theoretical Physics, Goethe University, Max-von-Laue-Str. 1, D-60438 Frankfurt am Main, Germany
a r t i c l e i n f o a b s t r a c t
Article history:
Received
13 March 2014
Received
in revised form 30 April 2014
Accepted
19 May 2014
Available
online 23 May 2014
Editor: A.
Ringwald
Keywords:
Charmonium
Quark-gluon
plasma
Transport
properties
Diffusion
coefficient
Spectral
functions
Dyson–Schwinger
equations
Bethe–Salpeter
equation
Nonperturbative
methods
We study vacuum masses of charmonia and the charm-quark diffusion coefficient in the quark-gluon
plasma based on the spectral representation for meson correlators. To calculate the correlators, we
solve the quark gap equation and the inhomogeneous Bethe–Salpeter equation in the rainbow-ladder
approximation. It is found that the ground-state masses of charmonia in the pseudoscalar, scalar, and
vector channels can be well described. For 1.5T
c
< T < 3.0T
c
, the value of the diffusion coefficient D is
comparable with that obtained by lattice QCD and experiments: 3.4 < 2π TD < 5.9. Relating the diffusion
coefficient with the ratio of shear viscosity to entropy density η/s of the quark-gluon plasma, we obtain
values in the range 0.09 < η/s < 0.16.
© 2014 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license
(http://creativecommons.org/licenses/by/3.0/). Funded by SCOAP
3
.
The charmonium system is a bound state of a charmed quark–
anti-quark
pair. The first charmonium state J /ψ was found si-
multaneously
at BNL [1] and at SLAC [2] in 1974. Charmonium
spectroscopy plays an important role [3,4] in understanding the
strong interaction, described by quantum chromodynamics (QCD).
Charm quarks are also produced in hard parton interactions in the
early stage of heavy-ion collisions, e.g. at the Relativistic Heavy
Ion Collider (RHIC) and the Large Hadron Collider (LHC). During
the further evolution of the fireball, these quarks interact with
the quark-gluon plasma (QGP) created in such collisions. The en-
suing
loss of energy of a charm quark is different from the one
experienced by light quarks [5,6]. A comparison of the energy loss
for light quarks with that for heavy ones can provide insight into
properties of the QGP.
Even
in a hot and dense medium, charm quarks can form bound
states with other light or heavy quarks. The formation and dis-
sociation
of these states depends on the properties of the sur-
rounding
medium. For instance, it was proposed [7] that, due to
color screening, the formation of J /ψ is suppressed in the QGP,
which can serve as a signal of the deconfinement phase transition.
*
Corresponding author.
E-mail
addresses: sixueqin@th.physik.uni-frankfurt.de (S.-x. Qin),
drischke@th.physik.uni-frankfurt.de (D.H. Rischke).
More recent calculations within lattice QCD [8–11], however, show
that the J /ψ may actually survive up to temperatures exceeding
the critical temperature T
c
of the deconfinement and chiral phase
transition. Therefore, it is an interesting and meaningful task to
understand charmonium properties in vacuum and medium sys-
tematically.
A
first-principle method to study charmonium properties is lat-
tice
QCD. Within this approach, the charmonium spectrum, includ-
ing
ground, excited, and exotic states, has been computed at zero
temperature, T = 0 [12–14], finding rather good agreement with
experimental data. Transport properties, e.g., the charm quark dif-
fusion
coefficient, which are closely related to charmonium spec-
tral
functions, are also calculable within lattice QCD [15–17]. The
charm quark diffusion coefficient has also been studied within
a T -matrix approach [18–21] and a relativistically covariant ap-
proach
based on QCD sum rules [22].
Assuming
that the interaction between charm quarks can be
described by a potential, one can adopt nonrelativistic potential
models to study charmonium properties [23]. The parameters of
the potential can be adjusted to the vacuum charmonium spec-
trum.
In order to study charmonia at nonzero temperatures, one
can generalize the vacuum potential to a temperature-dependent
one based on models [24] or lattice-QCD results [25]. In this frame-
work,
it is a great challenge to build a faithful connection between
these models and QCD.
http://dx.doi.org/10.1016/j.physletb.2014.05.060
0370-2693/
© 2014 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/3.0/). Funded by
SCOAP
3
.
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