Spinning electroweak sphalerons

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 ${\ensuremath{\theta}}_{\mathrm{W}}$ and for any Higgs mass, the spinning sphalerons comprise a family labeled by their angular momentum $J$. For ${\ensuremath{\theta}}_{\mathrm{W}}\ensuremath{\ne}0$ 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 $J$, a Regge-type behavior. It is likely that these sphalerons mediate the topological transitions in sectors with $J\ensuremath{\ne}0$, thus enlarging the number of transition channels. Their action decreases with $J$, which may considerably affect the total transition rate.