Light-Quark Mesons and Four-Quark Condensates at Finite Temperature

TL;DR

This paper develops a finite-temperature gap equation analog for four-quark condensates, analyzing their temperature dependence and impact on light-quark meson masses without factorization assumptions.

Contribution

It introduces coupled equations for various four-quark condensates and meson masses at finite temperature, highlighting the violation of factorization near the critical temperature.

Findings

Four-quark condensates' temperature dependence studied.

Factorization violation increases as temperature approaches T_c.

Tensor mesons are sensitive probes of four-quark condensates.

Abstract

We propose an analog of the familiar gap equation for the case of four-quark condensates at finite temperature. The condensates of interest correspond to scalar, vector, psudoscalar, axial vector, and tensor Dirac structures. Working with correlators at zero chemical potential without factorization, we arrive at coupled equations for these four-quark condensates and the masses of certain light-quark mesons. We study the temperature dependence of the four-quark condensates and masses; in one of our models, factorization of the four-quark condensates is shown to be increasingly violated as the temperature is increased toward $T_c$. The 2$^{++}$ tensor mesons a$_2$(1320)-f$_2$(1270) are identified as especially sensitive probes of the four-quark condensates.