夸克-胶子等离子体的η/σel比率：连接剪切粘度与电导率的关键洞察

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本文主要探讨了夸克-胶子等离子体（QGP）在超相对论重离子碰撞实验（uRHIC）中的重要性，特别是在理解强相互作用物质特性方面。焦点集中在两个关键的传输系数：剪切粘度η与熵密度比η/s，以及电导率σel。作者强调了这两个参数在刻画QGP性质中的核心角色，因为它们直接反映了夸克与胶子间的散射速率。文章首先阐述了理论和现象学研究的现状，指出剪切粘度η/s是衡量系统接近理想量子液体状态的重要指标，其最小值1/4π在临界温度Tc附近被观察到。这一比率与QGP的量子色动力学（lQCD）模拟结果相符，预示着高温下的强相互作用物质可能表现出极低的黏性，类似于玻色-爱因斯坦凝聚态。此外，文章探讨了电导率σel与温度的关系，特别提到当将松弛时间调整至适宜范围时，η/s与σel/T的比值可以预测出接近实验数据的结果。作者发现，当温度接近Tc时，η/s/（σel/T）的比例预计会显著增加，大约为20左右，而随着温度上升至4Tc以上，该比值趋于平坦。这表明σel/T在温度依赖性上可能比η/s更强，这是受到lQCD热力学限制的准粒子模型的预期。对比之下，共形理论则预测η/s和σel/T具有类似的温度依赖性，这与实验观测及理论分析存在差异。这些发现对于深入理解QGP的微观结构和动力学行为至关重要，因为它揭示了在极端条件下夸克和胶子相互作用的动态变化。通过对夸克-胶子等离子体剪切粘度η与电导率σel之比的研究，本文不仅提供了新的理论洞察，而且有望指导未来实验设计，以便更精确地测试这些基本物理参数，从而推动我们对强相互作用物质及其在宇宙早期或极端条件下的行为理解。

Physics Letters B 751 (2015) 326–330

Contents lists available at ScienceDirect

Physics Letters B

www.elsevier.com/locate/physletb

Shear viscosity η to electric conductivity σ

ratio for the quark–gluon

plasma

A. Puglisi

a,b

, S. Plumari

a,b

, V. Greco

a,b,∗

Department of Physics and Astronomy, University of Catania, Via S. Soﬁa 64, I-95125 Catania, Italy

Laboratorio Nazionale del Sud, INFN-LNS, Via S. Soﬁa 63, I-95125 Catania, Italy

a r t i c l e i n f o a b s t r a c t

Article history:

Received

12 February 2015

Received

in revised form 11 September

2015

Accepted

26 October 2015

Available

online 28 October 2015

Editor:

J.-P. Blaizot

The transport coeﬃcients of strongly interacting matter are currently subject of intense theoretical and

phenomenological studies due to their relevance for the characterization of the quark–gluon plasma

produced in ultra-relativistic heavy-ion collisions (uRHIC). We discuss the connection between the shear

viscosity to entropy density ratio, η/s, and the electric conductivity, σ

. Once the relaxation time is tuned

to have a minimum value of η/s = 1/4π near the critical temperature T

, one simultaneously predicts

/T very close to recent lQCD data. More generally, we discuss why the ratio of (η/s)/(σ

/T ) supplies

a measure of the quark to gluon scattering rates whose knowledge would allow to signiﬁcantly advance

in the understanding of the QGP phase. We also predict that (η/s)/(σ

/T ), independently on the running

coupling α

(T ), should increase up to about ∼ 20 for T → T

, while it goes down to a nearly ﬂat behavior

around  4for T ≥ 4 T

. Therefore we in general predict a stronger T dependence of σ

/T with respect

to η/s that in a quasi-particle approach is constrained by lQCD thermodynamics. A conformal theory,

instead, predicts a similar T dependence of η/s and σ

/T .

(http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP

Relativistic Heavy Ion Collider (RHIC) at BNL and Large Hadron

Collider (LHC) at CERN have produced a very hot and dense system

of strongly interacting particles as in the Early Universe with tem-

peratures

largely above T

 160 MeV [1–3], the transition tem-

perature

from nuclear matter to the Quark–Gluon Plasma (QGP)

[4–6]. The phenomenological studies by viscous hydrodynamics

[7–10] and parton transport [11–16] of the collective behavior

have shown that the QGP has a very small value of η/s, quite

close to the conjectured lower-bound limit for a strongly interact-

ing

system in the limit of inﬁnite coupling η/s = 1/4π [17]. This

suggests that hot QCD matter could be a nearly perfect ﬂuid with

the smallest η/s ever observed, even less dissipative than the ultra

cold matter created by magnetic traps [18,19]. As for atomic and

molecular systems a minimum in η/s is expected slightly above T

[20,21].

Another

key transport coeﬃcient, yet much less studied, is σ

This transport coeﬃcient represents the linear response of the

system to an applied external electric ﬁeld. Several processes oc-

curring

in uRHIC as well as in the Early Universe are regulated

by the electric conductivity. Indeed HICs are expected to generate

Corresponding author.

E-mail

address: greco@lns.infn.it (V. Greco).

very high electric and magnetic ﬁelds (eE  eB  m

, with m

the pion mass) in the very early stage of the collisions [22,23].

A large value of σ

would determine a relaxation time for the

electromagnetic ﬁeld of the order of ∼ 1–2 fm/c [24,25], which

would be of fundamental importance for the strength of the Chiral-

Magnetic

Effect [26], a signature of the CP violation of the strong

interaction. Also in mass asymmetric collisions, like Cu + Au, the

electric ﬁeld directed from Au to Cu induces a current result-

ing

in charge asymmetric collective ﬂow directly related to σ

[23]. Furthermore the emission rate of soft photons should be di-

rectly

proportional to σ

[27–29]. Despite its relevance there is

yet only a poor theoretical and phenomenological knowledge of

and its temperature dependence. First preliminary studies in

lQCD have extracted only few estimates with large uncertainties

[30,33] and only recently more safe extrapolation has been devel-

oped

[31,32,35].

this Letter, we point out the main elements determining σ

for a QGP plasma and in particular its connection with η. In fact,

while one may expect that the QGP is quite a good conductor due

to the deconﬁnement of color charges, on the other hand, the very

small η/s indicates large scattering rates which can largely damp

the conductivity, especially if the plasma is dominated by gluons

that do not carry any electric charge.

http://dx.doi.org/10.1016/j.physletb.2015.10.070

0370-2693/

SCOAP

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