Quark condensate in QCD at nonzero magnetic field and temperature

TL;DR

This paper derives a formula for the quark condensate in QCD considering magnetic fields and temperature, showing its relation to the wave function and matching lattice data for various conditions.

Contribution

It introduces a new expression for the quark condensate accounting for confinement, magnetic field, and temperature effects, validated against lattice data.

Findings

Condensate proportional to the square of the wave function at origin

Good agreement with lattice data for magnetic fields and temperatures

Condensate scales with string tension as σ^{3/2} for light quarks

Abstract

The basic form of the quark condensate for arbitrary values of external magnetic field and temperature, is derived using the field equations with account of confinement. The resulting expression of the chiral condensate is shown to be proportional to square of the singlet $q\bar q$ ground state wave function at origin, $|\phi_0(0)|^2$. For light quarks without magnetic field the condensates are proportional to $\sigma^{3/2}$ ($\sigma$ is the string tension). Numerical results are presented in 5 Tables and shown to be in good agreement with the lattice data, both for nonzero magnetic field $eB$ and temperature $T$ in the range $0 <T < 120$~MeV,~ $0 <eB <4$~GeV$^2$.