# Gauge Boson Masses in the 3-d, SU(2) Gauge-Higgs Model

## TL;DR

This study investigates gauge boson masses in a 3-dimensional SU(2) gauge-Higgs model, revealing phase-dependent mass behaviors and comparing gauge-dependent and gauge-invariant mass measurements through numerical simulations.

## Contribution

It provides the first detailed numerical analysis of gauge boson propagators and masses in the 3D SU(2) gauge-Higgs model, including phase transition effects and lattice size dependence.

## Key findings

- Gauge bosons acquire non-zero masses in both phases.
- W-boson screening mass decreases near the critical temperature.
- Gauge-invariant masses differ significantly from gauge-dependent screening masses.

## Abstract

We study gauge boson propagators in the symmetric and symmetry broken phases of the 3-d, $SU(2)$ gauge-Higgs model. Correlation functions for the gauge fields are calculated in Landau gauge. They are found to decay exponentially at large distances leading to a non-vanishing mass for the gauge bosons. We find that the W-boson screening mass drops in the symmetry broken phase when approaching the critical temperature. In the symmetric phase the screening mass stays small and is independent of the scalar--gauge coupling (the hopping parameter). Numerical results coincide with corresponding calculations performed for the pure gauge theory. We find $m_w = 0.35(1)g^2T $ in this phase which is consistent with analytic calculations based on gap equations. This is, however, significantly smaller than masses extracted from gauge invariant vector boson correlation functions. As internal consistency check we also have calculated correlation functions for gauge invariant operators leading to scalar and vector boson masses. Finite lattice size effects have been systematically analyzed on lattices of size $L^2\times L_z$ with $L=4-24$ and $L_z = 16 - 128$.