Pis’ma v ZhETF, vol. 112, iss. 7, pp. 435 - 436
© 2020 October 10
Collective nuclear vibrations and initial state shape fluctuations
in central Pb + Pb collisions: resolving the v2 to v3 puzzle
B.G.Zakharov1)
L. D. Landau Institute for Theoretical Physics, 117334 Moscow, Russia
Submitted 17 August 2020
Resubmitted 17 August 2020
Accepted 1 September 2020
DOI: 10.31857/S1234567820190015
The results of experiments on the heavy ion collisions
v2 flow coefficients in the ultra-central (b → 0) Pb+ Pb
at RHIC and LHC give a lot of evidences for formation
collisions at the LHC energies. For central collisions, at
of the quark-gluon plasma (QGP) in the initial stage
b = 0, the anisotropy of the initial fireball geometry
of nuclear collisions (at the proper time τ0 ∼ 0.5-1 fm)
originates completely from the fluctuations. The hydro-
which flows as an almost ideal fluid. The most effec-
dynamic calculations show [3, 2] that for small central-
tive constraints on the QGP viscosity come from the
ities in each event the vn for n ≤ 3 to good accuracy
hydrodynamic analysis of the azimuthal dependence of
satisfy the linear response relation
the hadron spectra which is characterized by the Fourier
coefficients vn
vn ≈ knǫn,
(2)
{
}
dN
N
∑
where ǫn are the Fourier coefficients characterizing the
=
1+
2vncos[n (φ - Ψn)]
,
(1)
dφ
2π
anisotropy of the initial fireball entropy distribution,
n=1
ρs(ρ), in the transverse plane defined as [4]
where N is hadron multiplicity in a certain pT and ra-
∫
dρρneinφρs(ρ)
pidity bin, Ψn are the event reaction plane angles. For
ǫn =
∫
(3)
smooth initial conditions at midrapidity (y = 0) in the
dρρnρs(ρ)
Fourier series (1) only the terms with n = 2k survive.
Here it is assumed that the transverse vector ρ is calcu-
And the azimuthal anisotropy appears only for noncen-
∫
lated in the tranverse c.m. frame, i.e.,
dρρρs(ρ) = 0.
tral collisions due to the almond shape of the overlap
The hydrodynamic calculations give k2/k3 > 1, and
region of the colliding nuclei in the transverse plane.
this ratio grows with increase of the QGP viscosity.
The event plane (for each n) in this case coincides with
On the other hand, the MCG calculations show that
the true reaction plane and Ψn = 0. In the presence
at b = 0 ǫ2 and ǫ3 are close to each other (and are
of fluctuations of the initial QGP entropy, all the flow
∼ 0.1 for Pb+ Pb collisions). This leads to prediction
coefficients vn become nonzero. The fluctuations of the
that v2/v3 > 1. But experimentally it was observed that
initial fireball entropy is a combined effect of the fluc-
v2 is close to v3 in the ultra-central 2.76 and 5.02 TeV
tuations of the nucleon positions in the colliding nu-
Pb + Pb collisions [5, 6]. Since the hydrodynamic pre-
clei and fluctuations of the entropy production for a
diction for k2/k3 seems to be very reliable, this situation
given geometry of the nuclear positions. The most pop-
looks very puzzling (it is called in the literature v2-to-v2
ular method for evaluation of the initial entropy distri-
puzzle). This leads to a serious tension for the hydrody-
bution for event-by-event simulation of AA-collisions is
namic paradigm of heavy ion collisions.
the Monte-Carlo (MC) wounded nucleon Glauber model
There were several attempts to resolve the v2-to-v2
[1 and references therein]. The even-by-event hydrody-
puzzle by modifying: the initial conditions [7, 8], the vis-
namic modeling with the MC Glauber (MCG) model
cosity coefficients [9], and the QGP equation of state of
initial conditions has been quite successful in descrip-
[10]. However, these attempts have not been successful.
tion of a vast body of experimental data on the flow co-
The common feature of all previous analyses devoted to
efficients in AA-collisions obtained at RHIC and LHC.
the v2-to-v2 puzzle is the use of the Woods-Saxon (WS)
However, in the last years it was found that the hydro-
nuclear distribution for sampling the nucleon positions
dynamical models fail to describe simultaneously v2 and
in the MC simulations of Pb + Pb collisions. In fact,
1)e-mail: bgz@itp.ac.ru
this is an universal choice in the physics of high-energy
Письма в ЖЭТФ том 112 вып. 7 - 8
2020
435
436
B.G.Zakharov
heavy ion collisions. However, the MC sampling of nu-
quantum version the ratio ǫ2/ǫ3 becomes substantially
cleon positions with the WS distribution completely ig-
smaller than that for ordinary WS distribution. The
nores the collective nature of the long range fluctua-
magnitude of the obtained ǫ2/ǫ3 is small enough to re-
tions of the nucleon positions. It is well known that
solve the v2-to-v2 puzzle.
the long range 3D fluctuations of the nuclear density
This work was partly supported by the Russian
have a collective nature and are closely related to the
Foundation for Basic Research grant 18-02-40069mega.
giant nuclear resonances [11] (for more recent reviews
Full text of the paper is published in JETP Letters
see [12, 13]). The major vibration mode of the spherical
journal. DOI: 10.1134/S0021364020190029
208Pb nucleus corresponds to excitation of the isoscalar
giant quadrupole resonance [11]. These collective quan-
tum effects are completely lost if one samples the nuclear
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H. Niemi, G. S. Denicol, H. Holopainen, and P. Huovi-
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∑A
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2mNEc〈r2L〉
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=
,
(4)
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〈0|F+LFL|0〉q
L(2L + 1)〈r2L-2〉
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Письма в ЖЭТФ том 112 вып. 7 - 8
2020