Quark condensates and magnetization in chiral perturbation theory in a uniform magnetic field

TL;DR

This paper uses chiral perturbation theory to analyze how a uniform magnetic field affects QCD vacuum properties, including quark condensates and magnetization, providing improved theoretical predictions aligned with lattice QCD results.

Contribution

It extends previous two-flavor analyses to three-flavor chiral perturbation theory, offering more accurate calculations of quark condensates and vacuum magnetization in magnetic fields.

Findings

Three-flavor results improve upon two-flavor predictions.

QCD vacuum exhibits paramagnetism under magnetic fields.

Theoretical results agree with lattice QCD up to certain magnetic field strengths.

Abstract

We reconsider the problem of calculating the vacuum free energy (density) of QCD and the shift of the quark condensates in the presence of a uniform background magnetic field using two-and-three-flavor chiral perturbation theory ($\chi$PT). Using the free energy, we calculate the degenerate, light quark condensates in the two-flavor case and the up, down and strange quark condensates in the three-flavor case. We also use the vacuum free energy to calculate the (renormalized) magnetization of the QCD vacuum, which shows that it is paramagnetic. We find that the three-flavor light-quark condensates and (renormalized) magnetization are improvements on the two-flavor results. We also find that the average light quark condensate is in agreement with the lattice up to $eB=0.2 {\rm\ GeV^{2}}$, and the (renormalized) magnetization is in agreement up to $eB=0.3 {\rm\ GeV^{2}}$, while three-flavor $\chi$PT, which gives a non-zero shift in the difference between the light quark condensates unlike two-flavor $\chi$PT, underestimates the difference compared to lattice QCD.