Zero temperature lattice Weinberg - Salam model for the values of the cutoff $\Lambda \sim 1$ TeV

TL;DR

This study numerically investigates the zero-temperature lattice Weinberg-Salam model at high cutoff values around 1 TeV, revealing nonperturbative effects and monopole percolation phenomena near the cutoff scale.

Contribution

It provides the first numerical analysis of the lattice Weinberg-Salam model at large cutoffs, highlighting nonperturbative effects and monopole behavior near 1 TeV.

Findings

Fluctuational region begins above 0.8 TeV cutoff.

Nambu monopoles percolate at cutoff > 1 TeV.

Scalar condensate definitions deviate from expected values in the fluctuational region.

Abstract

The lattice Weinberg - Salam model at zero temperature is investigated numerically. We consider the model for the following values of the coupling constants: the Weinberg angle $\theta_W \sim 30^o$, the fine structure constant $\alpha \sim 1/150$, the Higgs mass $M_H \sim 150$ GeV. We find that the fluctuational region begins at the values of the cutoff $\Lambda$ above about 0.8 TeV. In this region the average distance between Nambu monopoles is close to their sizes. At $\Lambda > 1$ TeV the Nambu monopole currents percolate. Within the fluctuational region the considered definitions of the scalar field condensate give values that differ from the expected one $2 M_Z/g_z$. We consider the given results as an indication that the nonperturbative effects may be present in the Weinberg - Salam model at the large values of the cutoff. Our numerical results were obtained on the lattices of sizes up to $16^3\times 32$.