Spinning Electroweak Sphalerons

TL;DR

This paper provides numerical evidence for stationary spinning sphalerons in the Weinberg-Salam theory, revealing a family of solutions with electric charge, monopole-antimonopole pairs, and potential implications for topological transitions.

Contribution

It introduces the existence of spinning sphalerons with electric charge and monopole structures, expanding the understanding of topological transitions in electroweak theory.

Findings

Spinning sphalerons exist for all mixing angles and Higgs masses.

They carry electric charge proportional to angular momentum.

Their action decreases with increasing angular momentum.

Abstract

We present numerical evidence for the existence of stationary spinning generalizations for the static sphaleron in the Weinberg-Salam theory. Our results suggest that, for any value of the mixing angle $\thetw$ and for any Higgs mass, the spinning sphalerons comprise a family labeled by their angular momentum $J$. For $\thetw\neq 0$ they possess an electric charge $Q=eJ$ where $e$ is the electron charge. Inside they contain a monopole-antimonopole pair and a spinning loop of electric current, and for large $J$ they show a Regge-type behavior. It is likely that these sphalerons mediate the topological transitions in sectors with $J\neq 0$, thus enlarging the number of transition channels. Their action {\it decreases} with $J$, which may considerably affect the total transition rate.