Critical value of symmetry breaking parameter in the phase transition of decay rate

TL;DR

This paper investigates the phase transition in decay rates of (3+1)-dimensional field theories with symmetry breaking, identifying bounds for the critical symmetry breaking parameter and emphasizing the role of continuum states in transition type determination.

Contribution

It provides the first bounds for the critical symmetry breaking parameter in (3+1) dimensions and highlights the importance of continuum states near sphalerons.

Findings

Bounds for critical symmetry breaking parameter are established.

Continuum states influence the transition type in higher dimensions.

Criteria for sharp first-order transition are applied successfully.

Abstract

Phase transition of decay rate from quantum tunneling to thermal activity regimes is investigated in (3+1)-dimensional field theories with symmetry breaking term $f\phi$. By applying the two independent criteria for the sharp first-order transition to the same model, the upper and lower bounds of critical value of the symmetry breaking parameter are obtained. Unlike two dimensional case continuum states of the fluctuation operator near sphaleron solution play an important role to determine the type of transition.