Ginzburg-Landau Theory of the Electroweak Phase Transition and Analytical Results

TL;DR

This paper explores the electroweak phase transition under strong magnetic fields, connecting it with Ginzburg-Landau theory, and provides analytical solutions for lattice structures, highlighting conditions for energy minima.

Contribution

It establishes a link between electroweak vacuum behavior and superconductivity theory, deriving analytical expressions for lattice solutions near critical magnetic fields.

Findings

Each lattice cell encloses an integer magnetic flux quantum.

Triangular Abrikosov lattice is a local energy minimum when Higgs mass exceeds Z boson mass.

Analytical formulas for lattice observables are derived in terms of a complex lattice parameter.

Abstract

The phase transition of the electroweak vacuum induced by a strong magnetic field is examined, and a connection is made with the Ginzburg-Landau theory of type-II superconductivity. For solutions of the exact nonlinear field equations of the electroweak theory with lattice periodicity in directions perpendicular to the magnetic field, it is proven that, likewise, each lattice cell must enclose an integer number of quanta of magnetic flux. Close to the lower critical magnetic field, a perturbative method developed by MacDowell and the author is used to study properties of the lattice solutions. Analytical expressions for observables are obtained in terms of a complex parameter $\tau$ specifying the lattice and it is shown that the triangular Abrikosov solution constitutes a local minimum of the energy provided $M_H > M_Z$. PACS numbers: 11.15.Kc, 11.15.Ex, 74.60.-w, 05.70.Fh