Lattice QCD study for the Quark-Gluon Mixed Condensate (anti-Q sigma G Q)

TL;DR

This study uses lattice QCD to measure the quark-gluon mixed condensate, revealing its significant role in QCD operator product expansions and providing a quantitative ratio to the quark condensate.

Contribution

First lattice QCD calculation of the quark-gluon mixed condensate ratio, demonstrating its importance in chiral symmetry breaking and QCD sum rules.

Findings

Ratio m_0^2 ≈ 2.5 GeV^2 at 1/a ≈ 2 GeV

Large mixed condensate impacts operator product expansions

Quantitative data at multiple quark masses

Abstract

We study the quark-gluon mixed condensate g<\bar{q} sigma G q>, which is another chiral order parameter, using the SU(3)c lattice QCD with the Kogut-Susskind(KS) fermion at the quenched level. We generate 100 gauge configurations on the 16^4 lattice with \beta = 6.0, and measure the mixed condensate at 16 points in each gauge configuration for each current-quark mass of m_q=21, 36, 52 MeV. From 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.