A remark on sphaleron erasure of baryon asymmetry

TL;DR

The paper addresses how the baryon asymmetry surviving after a period of full thermal equilibrium depends on lepton flavor asymmetries in the early universe. It uses a finite-temperature effective potential with chemical potentials and gauge fields to derive the baryon number as a function of conserved charges, yielding leading-order flavour-dependent corrections parameterized by $f_1$ and $f_2$ in the relation $B = f_0 \sum_i X_i + \sum_i X_i \left( f_1 \frac{m_i^2}{T^2} + f_2 h_i^2 \right)$. The main result is an explicit expression for $B$ with $n_F=3$ and $n_S=1$, including the limits $\phi \gg T$ and $\phi \ll T$ where $f_1$ and $f_2$ take specific values; in the symmetric phase $f_2$ matches previous results and $f_2$ reduces to $f_1/4$ in the low-$\phi$ regime. The work clarifies how flavor, Yukawa couplings, and the electroweak phase structure affect residual $B$ and provides a framework for precise cosmological predictions with higher-order corrections forthcoming.

Abstract

We complete an existing result for how the baryon asymmetry left over after a period of full thermal equilibrium depends on different lepton asymmetries.