The Study of Chiral Restoration using the Quark-Gluon Mixed Condensate g<\bar{q} \sigma G q> in Lattice QCD at Finite Temperature

TL;DR

This study investigates the behavior of the quark-gluon mixed condensate and the quark condensate at finite temperature using lattice QCD, revealing their simultaneous vanishing at the critical temperature and suggesting a linked chiral restoration process.

Contribution

First lattice QCD analysis of the thermal behavior of g<ar{q} \sigma G q> and <ar{q}q> near T_c, showing their correlated critical behavior and temperature independence of their ratio.

Findings

Both condensates vanish around T_c 280 MeV.

The ratio m_0^2 remains nearly constant near T_c.

Thermal effects on condensates are weak except near T_c.

Abstract

The quark-gluon mixed condensate g<\bar{q} \sigma G q> is studied using SU(3)c lattice QCD with the Kogut-Susskind fermion at the quenched level. Using the lattices as \beta = 6.0 with 16^3 * N_t (N_t=16,12,10,8,6,4), \beta = 6.1 with 20^3 * N_t (N_t=20,12,10,8,6) and \beta = 6.2 with 24^3 * N_t (N_t=24,16,12,10,8) in high statistics of 100-1000 gauge configurations, we perform accurate measurement of the thermal effects on g<\bar{q} \sigma G q> as well as <\bar{q}q> in the chiral limit. We find that the thermal effects on both the condensates are very weak except for the vicinity of T_c, while both the condensates suddenly vanish around T_c \simeq 280 MeV, which indicates strong chiral restoration near T_c. We also find that the ratio m_0^2 = g<\bar{q} \sigma G q>/ <\bar{q}q> is almost independent of the temperature even in the very vicinity of T_c, which means that these two different condensates obey the same critical behavior. This nontrivial similarity between them would impose constraints on the chiral structure of the QCD vacuum near T_c.