Chiral Charge Erasure via Thermal Fluctuations of Magnetic Helicity

Abstract

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, $\lambda \gtrsim 1/(\alpha {\mu }_5)$, 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 $\delta \mathcal{H}\sim \lambda T$ and $\tau \sim \alpha {\lambda }^3{T}^2$ 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 $t\sim T^3/({\alpha }^5{\mu }_5^4)$ until it reaches an equilibrium value $\mathcal{H}\sim {\mu }_5{T}^2/\alpha$, 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 $t\sim T/({\alpha }^3{\mu }_5^2)$. This mechanism for chiral charge erasure can be important for the hypercharge sector of the Standard Model as well as extensions including $\mathrm{U}(1)$ gauge interactions, such as asymmetric dark matter models.

Comments: v2- minor additions for clarification; matches JCAP version; 17 pages + 8 appendices & refs, 6 figures, 1 table