Fluctuation and dissipation of axial charge from massive quarks

In quantum chromodynamics, axial charge is known to be nonconserved due to chiral anomaly and nonvanishing quark mass. In this paper, we explore the role of quark mass in axial charge fluctuation and dissipation. We present two separate calculations of the axial charge correlator, which describe dynamics of axial charge. The first is free quarks at a 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. Because of the presence of an 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 a weakly coupled quark gluon plasma. We find in the hard thermal loop (HTL) approximation, the quark-gluon interaction leads to random walk growth of the axial charge, but dissipation is not visible. We estimate the relaxation timescale for the axial charge, finding it lies beyond the HTL regime.