The Determination of the Quark-Gluon Mixed Condensate (anti-Q sigma G Q) from Lattice QCD

TL;DR

This paper calculates the quark-gluon mixed condensate using lattice QCD, revealing its significant value and role in QCD operator expansions, and explores its behavior at finite temperature as a chiral order parameter.

Contribution

First lattice QCD determination of the quark-gluon mixed condensate and analysis of its temperature dependence as a chiral order parameter.

Findings

The ratio m_0^2 ≈ 2.5 GeV^2 at the lattice scale.

Large mixed condensate indicates its importance in QCD sum rules.

Finite temperature results show chiral restoration effects.

Abstract

We study the quark-gluon mixed condensate g<\bar{q} sigma G q>, using the SU(3)c lattice QCD with the Kogut-Susskind fermion at the quenched level. We generate 100 gauge configurations on the 16^4 lattice with \beta = 6.0, and perform the measurement of the mixed condensate at 16 points in each gauge configuration for each current quark mass of m_q=21, 36, 52 MeV. Using the 1600 data for each m_q, we find the ratio between the mixed condensate and the quark condensate, m_0^2 = g<\bar{q} sigma G q> / <\bar{q}q> \simeq 2.5 GeV^2 at the lattice scale of 1/a \simeq 2 GeV in the chiral limit. The large value of the mixed condensate suggests its importance in the operator product expansions in QCD. We study also chiral restoration at finite temperature in terms of the mixed condensate, which is another chiral order parameter. We present the lattice QCD results of the mixed condensate at finite temperature.