NJL模型中搜索QCD相变点的规范方法

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"在NJL模型的规范方法中搜索QCD相变点" 这篇研究文章主要探讨了在量子色动力学（Quantum Chromodynamics, QCD）中的相变点，特别是在有限温度和密度条件下的相变现象。研究人员采用Nambu-Jona-Lasinio (NJL)模型作为QCD的有效模型，利用典范方法来研究李-杨零点（Lee-Yang zeros），这是寻找相变点的重要工具。NJL模型是一个简化模型，它在不考虑胶子的情况下，通过四费米子相互作用来描述夸克的行为，这对于理解非微扰QCD现象尤其有用。规范方法在有限密度下处理QCD时，能够避免在晶格QCD（Lattice QCD）中常见的符号问题。晶格QCD是一种数值方法，通过在四维空间-时间网格上离散化QCD来求解，但在包含费米子时，尤其是在非零化学势下，会出现符号问题，使得计算变得极其困难。本文提出的方法通过有限自由度的李-杨零点外推至无限自由度情况，成功地确定了相变点，这为QCD的实际晶格模拟提供了新的途径。李-杨零点是复数场中的特殊点，当系统的参数变化时，如温度或密度，它们的位置会移动，当这些零点接近实轴时，通常标志着相变的发生。通过这种方式，研究者可以在NJL模型中寻找和识别相变的迹象，这对于理解和预测QCD在极端条件下的行为至关重要，例如在宇宙早期的高温度和密度环境，或者在中子星内部等极端物理环境中。此外，文章还提到了关键词" Imaginary chemical potential"，这指的是在处理有限密度问题时，通过引入虚部的化学势来解决符号问题的一种技术。虽然实际物理系统中的化学势是实数，但虚部化学势在数学上允许研究者避开符号问题，并间接获取关于实部化学势的信息。这篇研究通过NJL模型和典范方法，为理解和模拟QCD在有限温度和密度下的相变提供了新策略，对于深化我们对基本粒子物理学的理解以及解决QCD计算中的实际挑战具有重要意义。

Physics Letters B 795 (2019) 548–553

Contents lists available at ScienceDirect

Physics Letters B

www.elsevier.com/locate/physletb

Search of QCD phase transition points in the canonical approach

of the NJL model

Masayuki Wakayama

a,b,c,∗

, Atsushi Hosaka

a,d

Research Center for Nuclear Physics (RCNP), Osaka University, Ibaraki, Osaka 567-0047, Japan

Center for Extreme Nuclear Matters (CENuM), Korea University, Seoul 02841, Republic of Korea

Department of Physics, Pukyong National University (PKNU), Busan 48513, Republic of Korea

Advanced Science Research Center, Japan Atomic Energy Agency (JAEA), Tokai 319-1195, Japan

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

Article history:

Received

3 June 2019

Received

in revised form 26 June 2019

Accepted

2 July 2019

Available

online 3 July 2019

Editor:

J.-P. Blaizot

Keywords:

QCD

phase

Finite

density

Canonical

approach

Imaginary

chemical potential

Nambu-Jona-Lasinio

model

We study the Lee-Yang zeros in the canonical approach to search phase transition points at ﬁnite

temperature and density in the Nambu-Jona-Lasinio (NJL) model as an effective model of QCD. The

canonical approach is a promising method to avoid the sign problem in lattice QCD at ﬁnite density.

We ﬁnd that a set of Lee-Yang zeros computed with ﬁnite degrees of freedom can be extrapolated to

those with inﬁnite degrees of freedom, providing the correct phase transition point. We propose the

present method as a useful method for actual lattice simulations for QCD.

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

1. Introduction

The role of Quantum Chromodynamics (QCD), the theory of the

strong interaction, at ﬁnite temperature and density is increas-

ing

as it provides basic inputs in the fundamental questions such

as the matter generation in the early universe, the formation of

galaxies and stars, and mysterious stellar objects such as neu-

tron

stars and black holes. Especially, the latter objects are under

active discussions due to the recent observation of gravitational

waves [1,2] and black holes [3]. Experimentally, those problems

are approached by the high energy accelerators at such as J-PARC

(KEK/JAEA), FAIR (GSI) and NICA (JINR), which will be expected to

operate in the near future. Theoretically, lattice QCD is known as a

unique method for the ﬁrst principle calculations of QCD.

However,

lattice QCD suffers from the sign problem at ﬁ-

nite

density. Many methods have been proposed toward avoid-

ing

the sign problem. Meanwhile, a method called the canonical

approach [4] has been recently developed rapidly with multiple-

precision

arithmetic [5–18]. In the canonical approach, physical

quantities are calculated at pure imaginary chemical potentials, in

Corresponding author at: Research Center for Nuclear Physics (RCNP), Osaka

University, Ibaraki, Osaka 567-0047, Japan.

E-mail

address: wakayama@rcnp.osaka-u.ac.jp (M. Wakayama).

which the sign problem does not exist. Information at physical real

ﬁnite chemical potentials is extracted. The canonical approach can

predict physical observable such as particle distributions in heavy

ion collisions and reveal the phase structure at high densities.

Ref. [18], one of the present authors studied the so-called

Lee-Yang zeros (LYZs), which are zeros of grand canonical parti-

tion

functions as functions of the fugacity parameter. LYZs provide

us with various information on phase transitions [19,20]. However,

numerical simulations can be only available with ﬁnite degrees

of freedom, which should be extrapolated to the real situation

with inﬁnite degrees of freedom. Currently, such an extrapolation

method is not known.

attack this problem, we propose to study in an effective

model of QCD, the Nambu-Jona-Lasinio (NJL) model [21,22]. Be-

cause

phase properties are known well in the model e.g. [23,

24],

we can study exclusively the effect of ﬁnite degrees of free-

dom.

We show how the LYZs with ﬁnite degrees of freedom are

smoothly extrapolated to those with inﬁnite degrees of freedom.

Moreover, we also study an additional approximation for the num-

ber

density as a function of imaginary chemical potential which

has been used in the lattice simulations [14–18]. Taking into ac-

count

the two features, phase transition points are well deter-

mined

from the data of ﬁnite degrees of freedom.

will begin, in Sec. 2, by brieﬂy describing the canonical

approach in the NJL model. In Sec. 3, we introduce LYZs and a

https://doi.org/10.1016/j.physletb.2019.07.006

0370-2693/

SCOAP

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