Basis invariant description of chemical equilibrium with implications for a recent axionic leptogenesis model

TL;DR

This paper develops a basis-invariant framework for describing chemical equilibrium in time-dependent backgrounds relevant to axion leptogenesis, revealing new insights into baryon asymmetry generation and gauge boson behavior.

Contribution

It introduces a basis-invariant method for analyzing chemical equilibrium in dynamic backgrounds, accounting for anomaly measure changes, with applications to axion leptogenesis models.

Findings

At high temperatures, sphaleron processes are less efficient in generating B-L asymmetry.

The smallness of sphaleron rates controls B-L production in certain regimes.

Gauge boson dispersion relations are modified at subleading order.

Abstract

We provide a systematic treatment of chemical equilibrium in the presence of a specific type of time dependent background. The type of time dependent background we consider appears, for example, in recently proposed axion/Majoron leptogenesis models [1,2]. In describing the chemical equilibrium we use quantities which are invariant under redefinition of fermion phases (we refer to this redefinition as a change of basis for short), and therefore it is a basis invariant treatment. The change of the anomaly terms due to the change of the path integral measure [3,4] under a basis change is taken into account. We find it is useful to go back and forth between different bases, and there are insights which can be more easily obtained in one basis rather than another. A toy model is provided to illustrate the ideas. For the axion leptogenesis model [1], our result suggests that at $T > 10^{13}$ GeV , when sphaleron processes decouple, and $\Gamma_{B+L} << H < \Gamma_L$ (where $H$ is the Hubble parameter at temperature $T$ and $\Gamma_L$ is the $\Delta L = 2$ lepton number violating interaction rate), the amount of $B-L$ created is controlled by the smallness of the sphaleron interaction rate, $\Gamma_{B+L}$. Therefore it is not as efficient as described. In addition, we notice an interesting modification of gauge boson dispersion relations at subleading order.