FIAS Scientific Report 2011 - Frankfurt Institute for Advanced Studies ...

The phase structure of a chiral model with dilatons in hot and dense matter
Collaborators: C. Sasaki 1 , I. Mishustin 1,2
1 Frankfurt Institute for Advanced Studies, 2 Kurchatov Institute, Russian Research Center, Moscow, Russia
In this work we have studied thermodynamics and the phase structure of a QCD-like model whose degrees of
freedom are constituent quarks and gluons. Both chiral and scale symmetries are implemented in the model
by introducing mean fields representing ¯qq and GµνG µν . These symmetries are dynamically broken at low
temperature and density. The model thus mimics the features of QCD in the strong coupling region, i.e. the
spontaneous breaking of chiral symmetry and trace anomaly. The results suggest that a system in deconfined
phase develops gradually with increasing temperature/density toward weakly-interacting quark-gluon matter
composed of almost massless quarks and gluons. Our model improves the standard linear sigma model by
introducing missing gluons and EoS, energy density in particular, shows a good agreement with the expected
high-temperature (see Fig. 1 left).
The condensates of the sigma and dilaton fields are dynamically linked via their gap equations. How strong
they are correlated depends crucially on the sigma-meson mass mσ chosen in vacuum (see Fig. 1 right). We
found that a large mσ∼ 1 GeV is consistent with the lattice result regarding the thermal behavior of the gluon
condensate. This further leads to the chiral phase transition which takes place almost simultaneously with the
deconfinement transition at µ∼ 0. At finite µ these two transitions are expected to be separated.
The present model can also be applied to a non-equilibrium system, where the time evolution of the gluon
condensate is described by the equation of motion for the dilaton. On the other hand, in several models with
Polyakov loops it is unclear how the kinetic term of the Polyakov loop dynamically emerges since the Polyakov
loop by itself does not represent a field but a character of the SU(3) color group. It would be interesting to
explore non-equilibrium dynamics along this line.
E/T 4
14
12
10
8
6
4
2
m σ =600 MeV
900 MeV
Lattice (cont. estimate)
Stefan-Boltzmann
0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8
T/Tchiral T [GeV]
0.35
0.3
0.25
0.2
0.15
0.1
0.05
m σ =infinity
m σ =1.2 GeV
m σ =2.0 GeV
m σ =3.0 GeV
0
0 0.2 0.4 0.6 0.8 1
µ [GeV]
Figure 1: (Left) The scaled energy density at µ = 0. (Right) The phase diagram of our model for several mσ .
Related publication in 2011:
1) C. Sasaki and I. Mishustin, The phase structure of a chiral model with dilatons in hot and dense matter,
arXiv:1110.3498 [hep-ph], accepted for publication in Physical Review C.
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