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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,
, the chiral anomaly opens an instability
toward the erasure of chiral charge and growth of magnetic helicity. Here the
chemical potential parametrizes the chiral asymmetry and 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 , finding and for a
relativistic plasma at temperature . We argue that the presence of a chiral
asymmetry allows the helicity to grow diffusively for a time until it reaches an equilibrium value , and the chiral asymmetry is partially erased. If the
chiral asymmetry is small, , this avenue for chiral charge
erasure is found to be slower than the chiral magnetic effect for which . This mechanism for chiral charge erasure can be
important for the hypercharge sector of the Standard Model as well as
extensions including gauge interactions, such as asymmetric dark
matter models.Comment: v2- minor additions for clarification; matches JCAP version; 17 pages
+ 8 appendices & refs, 6 figures, 1 tabl
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