Acoustic phonons in a magnetized vacuum? First-principle lattice results on the mass spectrum of the electroweak model in a strong magnetic field

TL;DR

This study uses lattice Monte Carlo simulations to analyze the mass spectrum of the electroweak model's bosonic sector under extremely strong magnetic fields, revealing a nearly massless mode linked to vortex lattice vibrations.

Contribution

First-principles lattice results demonstrating the behavior of electroweak boson masses and the emergence of a Goldstone phonon mode in a strong magnetic field.

Findings

The lightest W boson component becomes nearly massless in the intermediate vortex phase.

Higgs and Z boson masses remain finite across all phases and transitions.

A Goldstone acoustic phonon mode is associated with vortex lattice vibrations.

Abstract

We use numerical Monte Carlo simulations to determine the mass spectrum of the bosonic sector of the electroweak model in an external magnetic field of the electroweak-scale strength ($10^{20}\,{\rm T}$) at zero temperature. It is known that as the magnetic field gets stronger, the electroweak vacuum undergoes two consecutive crossover-type transitions, passing from (i) the conventional symmetry-broken homogeneous phase to (ii) an intermediate inhomogeneous vortex phase characterized by a (superconducting) condensate of electrically charged $W$ bosons and then to (iii) a homogeneous phase with a restored electroweak symmetry. We show that the spin component of the $W$ boson aligned with the direction of the magnetic field is the lightest excitation in all three phases. Its mass continuously decreases in the low-field broken phase and becomes very small in the intermediate phase. We argue that this nearly massless excitation corresponds to a Goldstone acoustic phonon mode associated with vibrations of the lattice of electroweak vortices. In the high-field symmetry-restored phase, where the vortices disappear, the lightest $W$ mass rises again. Neither Higgs nor $Z$ boson masses vanish across all studied phases and crossover transitions.