Dependence of the critical temperature on the Higgs field reparametrization

TL;DR

This paper demonstrates that the choice of Higgs field parametrization influences the calculated critical temperature and thermodynamic properties in the Higgs mechanism, despite the reparametrization symmetry of the Lagrangian.

Contribution

It reveals that different Higgs field parametrizations lead to varying expressions for the Higgs mass and critical temperature, highlighting a dependence previously overlooked.

Findings

Different parametrizations yield distinct Higgs mass expressions.

Critical temperatures vary from zero to a maximum depending on the parametrization.

Thermodynamical quantities are affected by the choice of Higgs field representation.

Abstract

We show that, despite of the reparametrization symmetry of the Lagrangian describing the interaction between a scalar field and gauge vector bosons, the dynamics of the Higgs mechanism is really affected by the representation gauge chosen for the Higgs field. Actually, we find that, varying the parametrization for the two degrees of freedom of the complex scalar field, we obtain different expressions for the Higgs mass: in its turn this entails different expressions for the critical temperatures, ranging from zero to a maximum value, as well as different expressions for other basic thermodynamical quantities.