Upper bound on the cutoff in the Standard Model

TL;DR

This paper investigates the upper bound of the cutoff in lattice Electroweak theory, finding it around 1.4 TeV for certain parameters, and discusses the implications of topological defects and phase transitions on the continuum limit.

Contribution

It provides numerical estimates of the cutoff limit in lattice Electroweak models, highlighting the role of topological defects and phase structure near the transition.

Findings

Upper bound on cutoff is approximately 1.4 TeV at infinite scalar coupling.

Topological defects dominate near the phase transition, indicating a non-trivial vacuum.

Previous studies suggest a cutoff limit around 1.5 TeV.

Abstract

The main objective of this presentation is to point out that the Upper bound on the cutoff in lattice Electroweak theory is still unknown. The consideration of the continuum theory is based on the perturbation expansion around trivial vacuum. The internal structure of the lattice Weinberg - Salam model may appear to be more complicated especially in the region of the phase diagram close to the phase transition between the physical Higgs phase and the unphysical symmetric phase of the lattice model, where the continuum physics is to be approached. We represent the results of our numerical investigation of the quenched model at infinite bare scalar self coupling $\lambda$. These results demonstrate that at $\lambda = \infty$ the upper bound on the cutoff is around $\frac{\pi}{a} = 1.4$ Tev. The preliminary results for finite $\lambda$ are also presented. Basing on these results we cannot yet make a definite conclusion on the maximal value of the cutoff admitted in the lattice model, although we have found that the cutoff cannot exceed the value around $1.4 \pm 0.2$ Tev for a certain particular choice of the couplings ($\lambda = 0.009$, $\beta = 12$, $\theta_W = 30^o$) for the lattices of sizes up to $12^3\times16$. We also observe that the topological defects, which are to be identified with quantum Nambu monopoles, dominate in vacuum in the vicinity of the transition. This indicates that the vacuum of the model is different from the trivial one. In addition we remind the results of the previous numerical investigations of the SU(2) gauge - Higgs model, where the maximal reported value of the cutoff was around 1.5 Tev.