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

TL;DR

The paper addresses the critical Higgs mass $m_{H,c}$ at which the finite-temperature electroweak transition in the 3-D SU(2) Gauge-Higgs model changes from first order to a crossover, and studies infrared properties via W-boson screening masses. Using lattice simulations at fixed $\beta=9.0$ across five $\lambda_3$ values mapping to $m_H$ in the range $59.2$–$98.5$ GeV, the authors analyze Fisher and Lee-Yang zeros of the partition function to locate the end-point and compute the W-boson propagator in Landau gauge near the critical region. They find $m_{H,c}=75.4(6)$ GeV, with a first-order transition for $m_H < m_{H,c}$ and a crossover for larger $m_H$, and report a W-boson screening mass of $m_W \approx 0.161(3)$ in the high-temperature phase that increases in the Higgs phase with a power-law form $m_W = 0.161 + a (\kappa - \kappa_c)^\beta$ where $\beta \approx 0.4$, in qualitative agreement with gap-equation predictions. The work clarifies the phase structure in this effective model and provides insights into high-temperature gauge dynamics relevant to early-universe phenomenology and baryogenesis, while validating gap-equation approaches for infrared behavior.

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.

Figures (4)

• Figure 1: cv_max.eps
• Figure 2: l_im.eps
• Figure 3: fitconst.eps
• Figure 4: mass_w.eps