From Instantons to Sphalerons: Time-Dependent Periodic Solutions of SU(2)-Higgs Theory

TL;DR

This paper numerically investigates time-dependent periodic solutions in SU(2)-Higgs theory, revealing their connection to instantons and sphalerons and identifying a bifurcation point at higher Higgs masses.

Contribution

It introduces a numerical analysis of periodic solutions in SU(2)-Higgs theory, bridging instantons and sphalerons, and identifies a critical bifurcation point for certain Higgs masses.

Findings

Solutions interpolate between instanton-anti-instanton pairs and sphalerons.

A bifurcation point exists at Higgs masses above 3.091 M_W.

The solutions depend on the period length in Euclidean space.

Abstract

We solve numerically for periodic, spherically symmetric, classical solutions of SU(2)-Higgs theory in four-dimensional Euclidean space. In the limit of short periods the solutions approach tiny instanton-anti-instanton superpositions while, for longer periods, the solutions merge with the static sphaleron. A previously predicted bifurcation point, where two branches of periodic solutions meet, appears for Higgs boson masses larger than $3.091 M_W$.