Effective mass of W-boson in a magnetic field

TL;DR

This paper derives a simple formula for the effective mass of W-bosons in a magnetic field, demonstrating the stability of the spectrum near the critical field strength through analytical calculations.

Contribution

It provides a novel, simplified representation of the W-boson polarization tensor in a magnetic field and analyzes its implications for spectrum stability.

Findings

Effective mass squared remains positive at the instability threshold.

Derived a formula analogous to Demeur's for electrons in QED.

Confirmed the stability of the W-boson spectrum near critical magnetic field.

Abstract

Simple representation for the average value of the W-boson one-loop polarization tensor in a magnetic field B=const, calculated in the ground state of the tree-level spectrum, is derived. It corresponds to Demeur's formula for electron in QED. The energy of this state, describing effective particle mass, is computed by solving the Schwinger-Dyson equation. As application, we investigate the effective mass squared at the threshold of the tree-level instability, $B \to B_c = m^2/e$, and show that it is positive. In this way the stability of the W-boson spectrum is established. Some peculiarities of the results obtained and other applications are discussed.