Ⅱ-5. Hadron Physics (Theory)

RIKEN Accel. Prog. Rep. 48 (2015)

Chemical equilibration of QCD medium for photon v2 puzzle
A. Monnai∗1∑dNN=[1 + 2vn cos(φ − Ψn )],
dφ2π
n=1

neq
gn2 ,2 q(neqq )1∂µ Ngµ = (ra − rb )ng − ra eq n2gng
neq
1g+ rb eq 2 n2q + rc nq − rc eq nq ng ,(nq )
ng

(2)

(3)

where ra , rb , and rc are the reaction rates. Since pair
production is the only quark numbe-changing process,†∗10.20.2

Condensed from the article in Phys. Rev. C 90, 021901(R)(2014)RIKEN Nishina Centerγ(eq)vvγ22 (eq)γ(c =0.2,=0.2, cca,c=1.5)vvγ22 (c=1.5)
a,cbbγγ(c =0.5,=0.5, cca,c=1.5)
vv22 (c=1.5)
a,cbbγγ(c =2.0,=2.0, cca,c=1.5)
vv22 (c=1.5)
a,cbb

0.15
0.15
0.1
0.1
0.05
0.05
00
0
0

0.5
0.5

11

1.5
1.5

22

2.5
2.5

33p (GeV)
(GeV)
p

3.5
3.5

444.5
4.5

55

TT

(1)

where φ is the azimuthal angle in momentum spaceand Ψn is the n-th harmonic event plane. On the otherhand, direct photon v2 is found to be a few times larger
than hydrodynamic predictions,1,2) which is recognized
as the “photon v2 puzzle.” Of direct photons, thermal photons from the QGP medium are the dominantsource of anisotropy because prompt photons from initial hard processes do not have it intrinsically.
In this work, I have considered the eﬀects of chemical equilibration in the QGP on thermal photon v2 .3)
A heavy-ion system before the collision is described as
the color glass condensate, a state of saturated gluons.
Several early equilibration models indicate that chemical equilibration is slower than thermalization.4) Thisimplies that the quark number at the onset of hydrodynamic evolution is smaller than that under equilibrium. Since photons are coupled to quarks, late chemical equilibration suppresses the emission of thermal
photons in the early stages where ﬂow anisotropy isstill small. Consequently, thermal photon v2 can become eﬀectively large owing to the contribution fromlater times.
I have developed a new (2+1)-dimensional ideal hydrodynamic model and coupled it to the rate equations
for the parton number densities. The number changing processes are (a) g ↔ gg, (b) g ↔ q q̄, and (c)q(q̄) ↔ gq(g q̄). Here, the vanishing net baryon number limit is considered. The relaxation equations are:∂µ Nqµ = 2rb ng − 2rb

0.25
0.25

vvγ2γ2

Discovery of the quark-gluon plasma (QGP), a deconﬁned phase of QCD, at BNL Relativistic Heavy IonCollider and CERN Large Hadron Collider is a milestone in hadron physics. The produced medium is considered to be strongly coupled because the momentum
anisotropy in hadronic spectra is large enough to validate hydrodynamic description. This is quantiﬁed byelliptic ﬂow v2 deﬁned as a Fourier expansion coeﬃcient of the yield N :Fig. 1. Thermal photon v2 with diﬀerent quark chemical
equilibration rates.

chemical equilibration time would be given by τchem =1/rb . Here, the rates are parametrized as ri = ci T .
The equation of state is a hyperbolic interpolation of
those for hadron and parton gases with Nf = 2. The
thermal photon emission rate is also derived from thosefor the hadron and QGP phases.
Figure 1 shows the elliptic ﬂow of thermal photons√
for Au-Au collisions at sN N = 200 GeV with theimpact parameter b = 7 fm. The chemical reaction
parameters are chosen as cb = 0.2, 0.5, and 2.0, whereca,c = 1.5. Thermal photon v2 can be visibly enhancedby late quark chemical equilibration. For the suggested
chemical equilibration time τchem = 2 fm,4) cb = 0.5
follows from T ∼ 0.2 GeV. The dependences on thegluon number-changing processes characterized withra and rc are found to be small as expected. The particle spectrum of thermal photons is not aﬀected muchby chemical non-equilibrium with the current parameter settings. This implies that late quark chemical
equilibration is important to explain the photon v2
problem. It should be noted that the mechanism canalso be an explanation to the large photon v3 recently
observed in the experiments.
Future prospects include the introduction of a dynamical equation of state, improved initial conditions,and chemical equilibration rates. Eﬀects of viscosities
would also be important in quantitative discussion because thermal photons are sensitive to early-time ﬂuid
dynamics where oﬀ-equilibrium corrections are large
because photons can pass through the QCD medium.
References
1) A. Adare et al. [PHENIX Collaboration]: Phys. Rev.
Lett. 109, 122302 (2012).
2) D. Lohner [ALICE Collaboration]: J. Phys. Conf. Ser.
446, 012028 (2013).
3) A. Monnai: Phys. Rev. C 90, 021901 (2014).
4) A. Monnai and B. Müller: arXiv:1403.7310 [hep-ph].

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