Ⅱ-5. Hadron Physics (Theory)

RIKEN Accel. Prog. Rep. 47 (2014)

Quark contribution for center domain in heavy ion collisions†K. Kashiwa∗1 and A. Monnai∗1where T is temperature, a and b are color indices, B4
is the forth Bernoulli polynomial, Nf is the numberof ﬂavors. qa is deﬁned by the classical part of theabtime-like component of the vector potential (Acl=4)ab(2πT /g)qa δ , where g is the gauge coupling.
The overall eﬀective potential4) is shown in Fig. 1.
One can see that the three minima have the same freeenergy in the pure gauge case while imbalance is induced as the number of ﬂavors increases. We label thethree states as ν = 0, 1 and 2 corresponding to thefact that Polyakov loop at the minima can be written
as Φ = exp(2πiν/3) in the high temperature limit.
The emergence of the stable (ν = 0) and themetastable (ν = 1, 2) states is important because pressure imbalance among the domains can lead to longer
mean free path. Schematic pictures of parton scattering with diﬀerent number of ﬂavors/temperatures aresummarized in Fig. 2; (a) In the pure gauge system, thetypical mean free path is characterized by the domain
size. (b) When the system has small number of ﬂavors, the stable domains expand while the metastableones shrink, leading to the longer mean free path onaverage. (c) Domain percolation can occur as the temperature further increases. (d) Finally, the metastable†∗1

Condensed from the article in Phys. Rev. D 89, 011501(R)(2014)RIKEN Nishina Center

Nf = 440
Nf = 0F/TThe quark-gluon plasma (QGP) is characterized bylarge color opacity and near-perfect ﬂuidity in highenergy heavy ion experiments at the Relativistic Heavy
Ion Collider (RHIC) and the Large Hadron Collider(LHC). While hydrodynamic analyses have been quite
successful in quantitative description of the hot media1) , there are continuing debates on the origin ofﬂuidity. It is recently proposed that center domain
structure can be the key to the problem2) . QCD hasSU(3) symmetry, and the Polyakov-loop potential has
three minima in the QGP phase. Since the color glasscondensate, a description of pre-collision state, implies
that the typical correlation length on the transverse
plane is characterized by the inverse of saturation scalein heavy ion collisions, a domain structure can appear
in the hot medium. This indicates a short mean freepath as the domains are separated by energy barrier.
In the present work, we introduce quark contribution
to the center domain picture3) . We consider the gluonand quark perturbative one-loop eﬀective potentials:
δab )2π 2 T 4 ∑(Fg =B4 (|qa − qb |mod 1 ), (1)1−33a,b)4π 2 Nf T 4 ∑ (��1 ��
Ff = −,(2)B4 �qa + �32 mod 1aNf = 2−5−0.50q0.5Fig. 1. Dimensionless eﬀective potentials as a function of qfor the number of ﬂavors Nf = 0, 2 and 4.

Fig. 2. Schematic pictures of the Nf dependence of thecenter domain structure and parton scattering.

states vanish completely and the system can become
weakly coupled above the topological critical temperature deﬁned as Tcri = T (P1 = P2 = 0) where Pν is thepressure. The increase in shear viscosity from RHICto LHC temperatures is roughly estimated as ∼ 1.5-1.6
in our model, which is in agreement with the hydrodynamic implication from experimental data ∼ 1.75) .
We developed a model that can provide a bridgefrom hydrodynamic to perturbative QCD pictures. A
new critical temperature is proposed, which implies
that the medium can suddenly lose ﬂuidity in heavy
ion collisions of very high energies. Future prospects
include investigation on the system size dependence.
References
1) B. Schenke et al., Phys. Rev. Lett. 106, 042301 (2011).
2) M. Asakawa et al., Phys. Rev. Lett. 110, 202301 (2013).
3) K. Kashiwa and A. Monnai, Phys. Rev. D 89,011501(R) (2014).
4) V. M. Belyaev et al., Phys. Lett. B 277, 331 (1992).
5) C. Gale et al., Phys. Rev. Lett. 110, 012302 (2013).

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