Fluctuation and Dissipation of Axial Charge from Massive Quarks

TL;DR

This paper investigates how quark mass influences axial charge fluctuations and dissipation in QCD, revealing different behaviors in free quarks and weakly coupled quark-gluon plasma, with implications for understanding axial charge dynamics.

Contribution

It provides the first detailed comparison of axial charge fluctuation and dissipation in free quarks and QGP, highlighting the impact of quark mass and interactions.

Findings

Axial charge generated by quantum fluctuations in free theory.

Mass term prevents axial charge from reaching thermodynamic limit.

Quark-gluon interactions induce random walk growth of axial charge.

Abstract

In quantum chromodynamics (QCD), axial charge is known to be non-conserved due to chiral anomaly and non-vanishing quark mass. In this paper, we explore the role of quark mass in axial charge fluctuation and dissipation. We present two separate calculations of axial charge correlator, which describe dynamics of axial charge. The first is free quarks at finite temperature. We find that axial charge can be generated through effective quantum fluctuations in free theory. However the fluctuation does not follow a random walk behavior. Due to the presence of axial symmetry breaking mass term, the axial charge also does not settle asymptotically to the thermodynamic limit given by susceptibility. The second calculation is in weakly coupled quark gluon plasma (QGP). We find in the hard thermal loop (HTL) approximation, the quark-gluon interaction leads to random walk growth of axial charge, but dissipation is not visible. We estimate relaxation time scale for axial charge, finding it lies beyond the HTL regime.