Skyrme Sphalerons of an O(3)-sigma Model and the Calculation of Transition Rates at Finite Temperature

TL;DR

This paper investigates how a Skyrme term influences sphaleron solutions and transition rates at finite temperature in an O(3)-sigma model, providing explicit calculations of fluctuation measures and transition regimes.

Contribution

It introduces a method to compute fluctuation measures with a Skyrme term and analyzes its effect on transition rates and temperature regimes in the model.

Findings

Skyrme term modifies the fluctuation measure factor.

Transition rates depend on Skyrme coupling strength.

Crossover temperature range shifts due to the Skyrme term.

Abstract

The reduced O(3)-sigma model with an O(3)->O(2) symmetry breaking potential is considered with an additional Skyrmionic term, i.e. a totally antisymmetric quartic term in the field derivatives. This Skyrme term does not affect the classical static equations of motionwhich, however, allow an unstable sphaleron solution. Quantum fluctuations around the static classical solution are considered for the determination of the rate of thermally induced transitions between topologically distinct vacua mediated by the sphaleron. The main technical effect of the Skyrme term is to produce an extra measure factor in one of the fluctuation path integrals which is therefore evaluated using a measure-modified Fourier-Matsubara decomposition (this being one of the few cases permitting this explicit calculation). The resulting transition rate is valid in a temperature region different from that of the original Skyrme-less model, and the crossover from transitions dominated by thermal fluctuations to those dominated by tunneling at the lower limit of this range depends on the strength of the Skyrme coupling.