Chiral charge erasure via thermal fluctuations of magnetic helicity

We consider a relativistic plasma of fermions coupled to an Abelian gauge field and carrying a chiral charge asymmetry, which might arise in the early Universe through baryogenesis. It is known that on large length scales, lambda greater than or similar to 1/(alpha mu(5)), the chiral anomaly opens an instability toward the erasure of chiral charge and growth of magnetic helicity. Here the chemical potential mu(5) parametrizes the chiral asymmetry and alpha is the fine-structure constant. We study the process of chiral charge erasure through the thermal fluctuations of magnetic helicity and contrast with the well-studied phenomenon of Chern-Simons number diffusion. Through the fluctuation-dissipation theorem we estimate the amplitude and time scale of helicity fluctuations on the length scale lambda, finding delta H similar to lambda T and tau similar to alpha lambda T-3(2) for a relativistic plasma at temperature T. We argue that the presence of a chiral asymmetry allows the helicity to grow diffusively for a time t similar to T-3/(alpha(5)mu(4)(5)) until it reaches an equilibrium value H similar to mu T-5(2)/alpha, and the chiral asymmetry is partially erased. If the chiral asymmetry is small, mu(5) < T/alpha, this avenue for chiral charge erasure is found to be slower than the chiral magnetic effect for which t similar to T/(alpha(3)mu(2)(5)). This mechanism for chiral charge erasure can be important for the hypercharge sector of the Standard Model as well as extensions including U(1) gauge interactions, such as asymmetric dark matter models.