Quark Condensate in a Weak Magnetic Field

TL;DR

This paper revises the theoretical series expansion for the quark condensate in a weak magnetic field at low temperatures, resolving inconsistencies in previous one-loop calculations and providing a more accurate representation.

Contribution

It introduces an alternative method to derive the series expansion for the quark condensate in weak magnetic fields, clarifying the correct published results.

Findings

Identifies inconsistencies in previous one-loop series.

Derives an arbitrary-order series expansion in H/T^2.

Determines the correct series representation for the quark condensate.

Abstract

The low-temperature representation for the quark condensate in a weak magnetic field $H$ is known up to two-loop order. Remarkably, at one-loop order, the published series for the quark condensate in the chiral limit and $H \ll T^2$ are inconsistent. Using an alternative representation for the kinematical Bose functions, we derive the series to arbitrary order in $H/T^2$, and also determine which of the published results is correct.