Physical Degrees of Freedom in Higgs Models

TL;DR

This paper critically examines the Higgs mechanism, revealing a conceptual inconsistency in how physical degrees of freedom are identified before and after the phase transition, challenging standard perturbative explanations.

Contribution

It demonstrates that the standard account of the Higgs mechanism incorrectly equates unphysical and physical degrees of freedom across phases, highlighting a fundamental inconsistency.

Findings

Longitudinal gauge boson degrees of freedom are effectively 'created' at the phase transition.

Standard perturbative Higgs models cannot fully explain the physical degrees of freedom involved.

A discrepancy exists in the count of physical degrees of freedom before and after the phase transition.

Abstract

Despite the clear-cut prediction and subsequent experimental detection of the weak interaction bosons, the Higgs sector of the standard model of elementary particle physics has long remained one of its most obscure features. Here, it is demonstrated through a very basic argument that standard accounts of the Higgs mechanism suffer from a serious conceptual consistency problem, in that they incorrectly identify physical degrees of freedom. The point at issue, is that the reasoning which leads to a removal of the unphysical excitation modes is valid in both phases of the theory - i.e. both after and before the phase transition occurs. Consistently removing unphysical degrees of freedom implies a discrepancy in the number of physical degrees of freedom. In particular, the longitudinally polarized, massive gauge boson degrees of freedom do not have physical counterparts before the phase transition and are thus effectively "created ex nihilio" at the transition, within the context of ordinary Higgs models. Possible scenarios for removing the discrepancy are briefly considered. The results obtained here strongly indicate that although standard, perturbative formulations of the Higgs mechanism provide a convenient parametrization of electroweak physics over a certain range of scales, they cannot provide a sensible explanation of all relevant physical degrees of freedom involved.