Evolution of the Primordial Axial Charge across Cosmic Times

We investigate collisional decay of the axial charge in an electron-photon plasma at temperatures 10 MeV–100 GeV. We demonstrate that the decay rate of the axial charge is first order in the fine-structure constant ${\mathrm{\Gamma }}_{\text{flip}}\propto \alpha m_e^2/T$ and thus orders of magnitude greater than the naive estimate which has been in use for decades. This counterintuitive result arises through infrared divergences regularized at high temperature by environmental effects. The decay of axial charge plays an important role in the problems of leptogenesis and cosmic magnetogenesis.

Figure 1

The $t$-channel Compton scattering (a) and electron-positron annihilation (b) with the chirality flip in the intermediate state contributing to the chirality equilibration rate. Although naively they are of the second order in $\alpha$, their amplitudes contain infrared singularities. Regularization of these singularities leads to the result which is of the first order in $\alpha$.

Figure 2

One of the $1\leftrightarrow 2$ collinear processes with chirality flip of the incoming electron (states with different chiralities are shown in different colors). Although for massless particles the process has a finite phase space, it is very sensitive to any modification of the particles’ dispersion relations. This leads to an uncertainty in the probability of such a process which is addressed in Ref. [41].

Figure 3

Chirality flipping rates due to different processes in comparison to the Hubble expansion rate $H(T)=T^2/M_{*}$ as functions of temperature.