Ring diagrams and electroweak phase transition in a magnetic field

TL;DR

This paper studies the electroweak phase transition in a magnetic field within the Standard Model, highlighting the roles of fermions and W-bosons, and finds a first-order transition at extremely high magnetic fields.

Contribution

It provides a detailed analysis of the electroweak phase transition including ring diagrams and magnetic fields, with specific focus on the effects of fermions and W-bosons.

Findings

Phase transition is of first order at magnetic fields 10^{23}-10^{24} G.

The effective potential remains real at high temperatures.

Baryogenesis conditions are not satisfied in these magnetic fields.

Abstract

Electroweak phase transition in a magnetic field is investigated within the one-loop and ring diagram contributions to the effective potential in the minimal Standard Model. All fundamental fermions and bosons are included with their actual values of masses and the Higgs boson mass is considered in the range $75 GeV \leq m_H \leq 115 GeV$. The effective potential is real at sufficiently high temperature. The important role of fermions and $W$-bosons in symmetry behaviour is observed. It is found that the phase transition for the field strengths $10^{23} - 10^{24}$G is of first order but the baryogenesis condition is not satisfied. The comparison with the hypermagnetic field case is done.