Anomalous Pseudoscalar-Photon Vertex In and Out of Equilibrium

TL;DR

This paper investigates how the anomalous pseudoscalar-photon vertex behaves in and out of equilibrium within a quark model, revealing medium-induced modifications and potential for enhanced isospin breaking during rapid chiral transitions.

Contribution

It provides a detailed analysis of the in-medium modifications of the pseudoscalar-photon vertex, especially during out-of-equilibrium chiral phase transitions, highlighting the impact on isospin breaking and pion condensate formation.

Findings

Equilibrium vertex vanishes near the chiral transition in the chiral limit.

Out-of-equilibrium chiral transition significantly alters the vertex and quark propagators.

Potential enhancement of isospin breaking and neutral pion condensate formation.

Abstract

The anomalous pseudoscalar-photon vertex is studied in real time in and out of equilibrium in a constituent quark model. The goal is to understand the in-medium modifications of this vertex, exploring the possibility of enhanced isospin breaking by electromagnetic effects as well as the formation of neutral pion condensates in a rapid chiral phase transition in peripheral, ultrarelativistic heavy-ion collisions. In equilibrium the effective vertex is afflicted by infrared and collinear singularities that require hard thermal loop (HTL) and width corrections of the quark propagator. The resummed effective equilibrium vertex vanishes near the chiral transition in the chiral limit. In a strongly out of equilibrium chiral phase transition we find that the chiral condensate drastically modifies the quark propagators and the effective vertex. The ensuing dynamics for the neutral pion results in a potential enhancement of isospin breaking and the formation of $\pi^0$ condensates. While the anomaly equation and the axial Ward identity are not modified by the medium in or out of equilibrium, the effective real-time pseudoscalar-photon vertex is sensitive to low energy physics.