The Sphaleron Rate at the Electroweak Crossover

TL;DR

This paper calculates the sphaleron transition rate during the electroweak crossover in the Standard Model using lattice simulations, filling a gap in intermediate temperature regime understanding relevant for Leptogenesis.

Contribution

It provides the first lattice-based calculation of the sphaleron rate across the electroweak crossover with physical Higgs masses, using advanced simulation techniques.

Findings

Sphaleron rate is quantitatively determined during the crossover.

Results are relevant for Leptogenesis scenarios.

The study bridges the gap between high and low-temperature sphaleron rate estimates.

Abstract

The baryon number is violated in the Standard Model by non-perturbative sphaleron transitions. At temperatures above the electroweak scale, the rate of the sphaleron transitions is unsuppressed and has been accurately measured using effective theories on the lattice. At temperatures substantially below the electroweak scale, the Higgs field expectation value is large and the sphaleron rate is strongly suppressed. Here analytical estimates are sufficient. The sphaleron rate, however, has not been calculated in the intermediate temperature range with physical Standard Model parameters. In this work we use an effective electroweak theory on the lattice with multicanonical and real-time simulation methods to calculate the sphaleron rate through the electroweak crossover at Higgs masses of 115 GeV and 160 GeV. The results are significant e.g. for Leptogenesis scenarios.