# Lepton asymmetry rate from quantum field theory: NLO in the hierarchical limit

## TL;DR

This paper derives a relation between lepton asymmetry generation rates and finite-temperature correlation functions, providing a NLO calculation in the hierarchical sterile neutrino mass limit relevant for leptogenesis.

## Contribution

It introduces a master formula linking asymmetry rates to a three-point spectral function, valid to all orders in SM couplings, and computes NLO corrections in the non-relativistic regime.

## Key findings

- NLO corrections are approximately 4% or less.
- Derived a universal relation for asymmetry rates in hierarchical neutrino models.
- Validated the master formula's applicability to all orders in SM gauge and Yukawa couplings.

## Abstract

The rates for generating a matter-antimatter asymmetry in extensions of the Standard Model (SM) containing right-handed neutrinos are the most interesting and least trivial coefficients in the rate equations for baryogenesis through thermal leptogenesis. We obtain a relation of these rates to finite-temperature real-time correlation functions, similar to the Kubo formulas for transport coefficients. Then we consider the case of hierarchical masses for the sterile neutrinos. At leading order in their Yukawa couplings we find a simple master formula which relates the rates to a single finite temperature three-point spectral function. It is valid to all orders in $g$,where $g$ denotes a SM gauge or quark Yukawa coupling. We use it to compute the rate for generating a matter-antimatter asymmetry at next-to-leading order in g in the non-relativistic regime. The corrections are of order $g ^ 2$, and they amount to 4% or less.