Nambu monopoles in lattice Electroweak theory

TL;DR

This paper investigates Nambu monopoles in lattice electroweak theory, revealing their physical relevance, phase transition role, and the limitations of current lattice models in predicting their density.

Contribution

It provides the first numerical analysis of Nambu monopoles in realistic lattice electroweak theory, highlighting their physical significance and the need for models including TeV-scale physics.

Findings

Nambu monopoles are physically relevant objects in lattice electroweak theory.

Their percolation probability acts as an order parameter for phase transition.

Current lattice models cannot accurately predict monopole density due to ultraviolet cutoff dependence.

Abstract

We considered the lattice electroweak theory at realistic values of $\alpha$ and $\theta_W$ and for large values of the Higgs mass. We investigated numerically the properties of topological objects that are identified with quantum Nambu monopoles. We have found that the action density near the Nambu monopole worldlines exceeds the density averaged over the lattice in the physical region of the phase diagram. Moreover, their percolation probability is found to be an order parameter for the transition between the symmetric and the broken phases. Therefore, these monopoles indeed appear as real physical objects. However, we have found that their density on the lattice increases with increasing ultraviolet cutoff. Thus we conclude, that the conventional lattice electroweak theory is not able to predict the density of Nambu monopoles. This means that the description of Nambu monopole physics based on the lattice Weinberg - Salam model with finite ultraviolet cutoff is incomplete. We expect that the correct description may be obtained only within the lattice theory that involves the description of TeV - scale physics.