QCD $\theta$-vacuum in a Uniform Magnetic Field

TL;DR

This paper investigates how a uniform magnetic field influences the topological properties of QCD's $ heta$-vacuum using chiral perturbation theory, revealing field-dependent enhancements and suppressions of topological susceptibility and cumulants.

Contribution

It provides the first detailed analysis of the magnetic field effects on topological observables in the $ heta$-vacuum within two-flavor chiral perturbation theory.

Findings

Topological susceptibility is enhanced by magnetic fields.

Fourth cumulant is suppressed at weak fields and enhanced at larger fields when $ heta=0$.

Topological density increases for all magnetic fields.

Abstract

We study the $\theta$-vacuum of QCD using two-flavor chiral perturbation theory ($\chi$PT) in the presence of a uniform, background magnetic field calculating the magnetic field-dependent free energy density, the topological density, the topological susceptibility and the fourth cumulant at one-loop order. We find that the topological susceptibility is enhanced by the magnetic field while the fourth topological cumulant is diminished at weak fields and enhanced at larger fields when $\theta=0$. However, in the QCD vacuum with $\theta\neq 0$, the topological susceptibility can be either monotonically enhanced or diminished relative to their $\theta$-vacuum values. The fourth cumulant also exhibits monotonic enhancement or suppression except for regions of $\theta$ near $0$ and $2\pi$, where it is both diminished and enhanced. Finally, the topological density is enhanced for all magnetic fields with its relative shift being identical to the relative shift of the up and down quark condensates in the $\theta$-vacuum.