Pseudoscalar condensation induced by chiral anomaly and vorticity for massive fermions

TL;DR

This paper derives the pseudoscalar condensate induced by chiral anomaly and vorticity for massive fermions, exploring its implications in heavy ion collisions and connecting theoretical predictions with potential experimental observables.

Contribution

It provides a novel derivation of the pseudoscalar condensate from the Wigner function, including anomaly and vorticity effects, for massive fermions and extended to multiple flavors.

Findings

Pseudoscalar condensate linearly proportional to fermion mass in small mass limit.

Neutral pion and eta meson condensates include anomaly and vorticity contributions.

Possible experimental signatures in heavy ion collisions through collective flow observables.

Abstract

We derive the pseudoscalar condensate induced by anomaly and vorticity from the Wigner function for massive fermions in homogeneous electromagnetic fields. It has an anomaly term and a force-vorticity coupling term. As a mass effect, the pseudoscalar condensate is linearly proportional to the fermion mass in small mass expansion. By a generalization to two-flavor and three-flavor cases, the neutral pion and eta meson condensates are calculated from the Wigner function and have anomaly parts as well as force-vorticity parts, in which the anomaly part of the neutral pion condensate is consistent to the previous result. We also discuss about possible observables of the condensates in heavy ion collisions such as collective flows of neutral pions and eta mesons which may be influenced by the electromagnetic field and vorticity profiles.