An all-order discontinuity at the electroweak phase transition

TL;DR

The paper introduces a gauge-invariant Green's function capable of distinguishing between the symmetric and broken phases of the electroweak theory at all perturbative orders, highlighting potential non-perturbative effects.

Contribution

It defines a novel non-local Green's function that can differentiate phases in the electroweak theory beyond perturbation theory, challenging existing assumptions about phase continuity.

Findings

Green's function distinguishes phases at all orders

Implication of possible non-perturbative effects

Potential for lattice simulation studies

Abstract

We define a non-local gauge-invariant Green's function which can distinguish between the symmetric (confinement) and broken (Higgs) phases of the hot SU(2)xU(1) electroweak theory to all orders in the perturbative expansion. It is related to the coupling of the Chern-Simons number to a massless Abelian gauge field. The result implies either that there is a way to distinguish between the phases, even though the macroscopic thermodynamical properties of the system have been observed to be smoothly connected, or that the perturbative Coleman-Hill theorem on which the argument is based, is circumvented by non-perturbative effects. We point out that this question could in principle be studied with three-dimensional lattice simulations.