Axial Chiral Vortical Effect in a Sphere with finite size effect

TL;DR

This paper studies the axial vortical effect in a rotating sphere with finite size, deriving exact and approximate expressions for axial currents and mass corrections, with implications for heavy ion collision phenomenology.

Contribution

It provides exact solutions for axial currents in a finite spherical geometry and explores mass effects on axial conductivity, extending previous cylindrical models.

Findings

Exact axial current expression inside the sphere matches cylindrical coordinate results.

Mass correction to axial conductivity is linear on the boundary, stronger than quadratic.

Qualitative implications for heavy ion collision phenomenology are discussed.

Abstract

We investigate the axial vortical effect in a uniformly rotating sphere subject to finite size. We use MIT boundary condition to limit the boundary of the sphere. For massless fermions inside the sphere, we obtain the exact axial vector current far from the boundary that matches the expression obtained in cylindrical coordinates in the literature. On the spherical boundary, we find both the longitudinal and transverse(with respect to the rotation axis) components with magnitude depending on the colatitude angle. For massive fermions, we derive an expansion of the axial conductivity far from the boundary to all orders of mass whose leading order term agrees with the mass correction reported in the literature. We also obtain the leading order mass correction on the boundary which is linear, and stronger than the quadratic dependence far from the boundary. The qualitative implications on the phenomenology of heavy ion collisions are speculated.