Standard Model Higgs field and energy scale of gravity

TL;DR

This paper explores the connection between the Higgs field's potential with a second minimum at high energy scales and the Planck scale of gravity, suggesting a link to spacetime foam and wormhole solutions.

Contribution

It proposes that the ultrahigh vacuum expectation value of the Higgs field is proportional to the Planck energy scale, integrating concepts of quantum gravity with Standard Model parameters.

Findings

Ultrahigh Higgs vacuum expectation value is proportional to the Planck energy scale.

Existence of wormhole solutions imposes a lower bound on the Higgs vacuum expectation value.

The lower bound is approximately equal to the Planck energy.

Abstract

The effective potential of the Higgs scalar field in the Standard Model may have a second degenerate minimum at an ultrahigh vacuum expectation value. This second minimum then determines, by radiative corrections, the values of the top-quark and Higgs-boson masses at the standard minimum corresponding to the electroweak energy scale. An argument is presented that this ultrahigh vacuum expectation value is proportional to the energy scale of gravity, E_{Planck} \equiv \sqrt{\hbar c^5/G_N}, considered to be characteristic of a spacetime foam. In the context of a simple model, the existence of kink-type wormhole solutions places a lower bound on the ultrahigh vacuum expectation value and this lower bound is of the order of E_{Planck}.