Quark Mass Correction to Chiral Separation Effect and Pseudoscalar Condensate

TL;DR

This paper analytically and holographically investigates how quark mass influences the chiral separation effect, revealing scaling relations, medium responses, and potential phase transitions in a finite density and magnetic field environment.

Contribution

It provides the first analytic structure of quark mass corrections to the CSE and confirms it through holographic D3/D7 model analysis, including the discovery of a normalizable mode indicating possible phase formation.

Findings

Quark mass correction to CSE is analytically derived.

Scaling relations of correlators with momentum are established.

Normalizable mode suggests potential spiral phase formation.

Abstract

We derived an analytic structure of the quark mass correction to chiral separation effect (CSE) in small mass regime. We confirmed this structure by a D3/D7 holographic model study in a finite density, finite magnetic field background. The quark mass correction to CSE can be related to correlators of pseudo-scalar condensate, quark number density and quark condensate in static limit. We found scaling relations of these correlators with spatial momentum in the small momentum regime. They characterize medium responses to electric field, inhomogeneous quark mass and chiral shift. Beyond the small momentum regime, we found existence of normalizable mode, which possibly leads to formation of spiral phase. The normalizable mode exists beyond a critical magnetic field, whose magnitude decreases with quark chemical potential.