# Critical Higgs Mass and Temperature Dependence of Gauge Boson Masses in the SU(2) Gauge-Higgs Model

## TL;DR

This study investigates the finite-temperature behavior of the SU(2) Gauge-Higgs model, identifying a critical Higgs mass where the electroweak phase transition shifts from first order to a crossover, and analyzes gauge boson masses near this critical point.

## Contribution

It provides a detailed analysis of the Higgs-mass dependence of the electroweak phase transition and compares gauge boson screening masses with theoretical predictions.

## Key findings

- Electroweak phase transition weakens with increasing Higgs mass.
- Transition becomes a crossover above approximately 75.4 GeV.
- W-boson screening masses align with gap equation predictions near the critical Higgs mass.

## Abstract

We study the effective 3-D SU(2) Gauge-Higgs model at finite temperature for Higgs-masses in the range from $60$ GeV up to $100$ GeV. The first order electroweak phase transition weakens with increasing Higgs-mass and terminates at a critical end-point. For Higgs-mass values larger than about $m_{H,c}=75.4(6)$ GeV the thermodynamic signature of the transition is described by a crossover. Close to this Higgs-mass value we investigate the vector boson propagator in Landau gauge. The calculated W-boson screening masses are compared with predictions based on gap equations.