Restriction on the form of the quark anomalous magnetic moment from lattice QCD results*

Abstract

The quark anomalous magnetic moment (AMM) is dynamically generated through the spontaneous chiral symmetry breaking. It has been revealed that even though its exact form is still unknown, the quark AMM is essential to explore quark matter properties and QCD phase structure under external magnetic fields. In this study, we take three different forms of the quark AMM and investigate its influence on the chiral phase transition under magnetic field. In general, a negative (positive) quark AMM plays the role of magnetic-catalyzer (magnetic-inhibition) for the chiral symmetry breaking. It is found that a constant quark AMM drives an unexpected 1st order chiral phase transition; a quark AMM proportional to the chiral condensate gives a flip of the sign on the chiral condensate; and a quark AMM proportional to the square of chiral condensate suppresses the magnetic enhancement in the chiral condensate at finite temperatures while retaining the chiral crossover phase transition. We also evaluate the intrinsic temperature dependence of the effective AMM form by fitting the effective model result of the chiral condensate to the lattice QCD data, which may have a nontrivial correlation with the chiral phase transition.

Anisotropy and paramagnetism of QCD matter with an anomalous magnetic moment

“…The AMM is widely accepted to account for the IMC, as initially proposed by LQCD results [43]. Recently, the constant AMM and the AMM that is proportional to the chiral condensate have been proven to be inappropriate forms [44]. The AMM that is proportional to the square of the chiral condensate was suggested to yield the chiral condensate as functions of the temperature and magnetic field, which is in excellent agreement with LQCD results [44].…”

“…Recently, the constant AMM and the AMM that is proportional to the chiral condensate have been proven to be inappropriate forms [44]. The AMM that is proportional to the square of the chiral condensate was suggested to yield the chiral condensate as functions of the temperature and magnetic field, which is in excellent agreement with LQCD results [44]. It is believed that the scale of the AMM plays a significant role in introducing the IMC effect in the vicinity of the critical temperature [39,45].…”

“…The paramagnetism of the bulk matter is reproduced and influenced by the scale of the AMM. In the present calculation, the following parameters are adopted: 2 (i = u, d, s) [44]. The quark dynamical mass M as a function of magnetic fields at different temperatures can be obtained by solving the gap equations: equations ( 14), ( 15) and ( 16).…”

“…) is a 3 × 3 matrix in the flavour space, and κ i are the AMMs of the different flavors. The more recent results suggested that the proper form of the AMM would change with the chiral condensate, since it involves the behavior related to the condensate [44]. The potential…”

Mass splitting and spin alignment for $$\phi $$ mesons in a magnetic field in NJL model

“…Considering a different choice of AMMs, like in Ref. [89], may result in a different ρ 00 , which is waiting for more comprehensive studies in the future.…”