The lifetime of the electroweak vacuum and sensitivity to Planck scale physics

TL;DR

This paper investigates how Planck-scale physics can drastically influence the lifetime of the electroweak vacuum, challenging previous assumptions that it vastly exceeds the universe's age, by including all contributions to the tunneling process.

Contribution

It provides a comprehensive, non-approximated analysis of the Higgs potential's vacuum stability, emphasizing the significant impact of Planck-scale operators on tunneling rates.

Findings

Planck-scale operators can significantly alter vacuum decay rates.

The Higgs potential's instability point is near the Planck scale.

Non-perturbative effects may enhance tunneling despite suppression by the Planck scale.

Abstract

If the Standard Model (SM) is valid up to extremely high energy scales, then the Higgs potential becomes unstable at approximately $10^{11}$ GeV. However, calculations of the lifetime of the SM vacuum have shown that it vastly exceeds the age of the Universe. It was pointed out by two of us (VB,EM) that these calculations are extremely sensitive to effects from Planck scale higher-dimensional operators and, without knowledge of these operators, firm conclusions about the lifetime of the SM vacuum cannot be drawn. The previous paper used analytical approximations to the potential and, except for Higgs contributions, ignored loop corrections to the bounce action. In this work, we do not rely on any analytical approximations and consider all contributions to the bounce action, confirming the earlier result. It is surprising that the Planck scale operators can have such a large effect when the instability is at $10^{11}$ GeV. There are two reasons for the size of this effect. In typical tunneling calculations, the value of the field at the center of the critical bubble is much larger than the point of the instability; in the SM case, this turns out to be numerically within an order of magnitude of the Planck scale. In addition, tunneling is an inherently non-perturbative phenomenon, and may not be as strongly suppressed by inverse powers of the Planck scale. We include effective $\Phi^6$ and $\Phi^8$ Planck-scale operators and show that they can have an enormous effect on the tunneling rate.