Effective constraint potential in lattice Weinberg - Salam model

TL;DR

This paper studies the phase transition and continuum physics of the lattice Weinberg-Salam model without fermions, analyzing the effective potential and renormalized fine structure constant near the Higgs phase transition.

Contribution

It introduces the use of the effective constraint potential to investigate phase transitions and compares non-perturbative results with perturbative estimates in the lattice Weinberg-Salam model.

Findings

Effective potential analysis reveals the nature of the phase transition.

Renormalized fine structure constant matches perturbative estimates near the transition.

Identifies the region where continuum physics can be approximated.

Abstract

We investigate lattice Weinberg - Salam model without fermions for the value of the Weinberg angle $\theta_W \sim 30^o$, and bare fine structure constant around $\alpha \sim 1/150$. We consider the value of the scalar self coupling corresponding to bare Higgs mass around 150 GeV. The effective constraint potential for the zero momentum scalar field is used in order to investigate phenomena existing in the vicinity of the phase transition between the physical Higgs phase and the unphysical symmetric phase of the lattice model. This is the region of the phase diagram, where the continuum physics is to be approached. We compare the above mentioned effective potential (calculated in selected gauges) with the effective potential for the value of the scalar field at a fixed space - time point. We also calculate the renormalized fine structure constant using the correlator of Polyakov lines and compare it with the one - loop perturbative estimate.