Chiral Charge Erasure via Thermal Fluctuations of Magnetic Helicity

TL;DR

This paper investigates how thermal fluctuations of magnetic helicity can erase chiral charge asymmetry in a relativistic plasma, providing estimates for fluctuation amplitudes, timescales, and implications for early Universe physics.

Contribution

It introduces a novel analysis of chiral charge erasure via magnetic helicity fluctuations, contrasting it with Chern-Simons diffusion, and estimates relevant timescales and conditions.

Findings

Helicity fluctuations have amplitude ~ λ T and timescale ~ α λ^3 T^2.

Chiral asymmetry can be partially erased over a diffusive timescale ~ T^3/ (α^5 μ_5^4).

The erasure process is slower than the chiral magnetic effect for small μ_5.

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 ${\rm U}(1)$ gauge interactions, such as asymmetric dark matter models.