An all-order discontinuity at the electroweak phase transition

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.

9 pages; misprint corrected, reference and small clarifications added; to appear in Phys.Lett.B

References in corpus (4)

• Masses and Phase Structure in the Ginzburg-Landau Model
• High Temperature Dimensional Reduction and Parity Violation
• Vortex tension as an order parameter in three-dimensional U(1)+Higgs theory
• The Chern-Simons number as an order parameter : classical sphaleron transitions for SU(2)-Higgs field theories for a Higgs mass approximately equal to 120 GeV

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• Confined Vortices in Topologically Massive U(1)$\times$U(1) Theory
• Superconductivity at Any Temperature