Weak Scale From the Maximum Entropy Principle

TL;DR

This paper explores the maximum entropy principle in the multiverse context, showing that the weak scale naturally aligns with the observed value around 300 GeV when considering the universe's final radiation entropy.

Contribution

It demonstrates that the weak scale maximizes the universe's final radiation entropy within the maximum entropy principle framework, linking it to fundamental constants and cosmological parameters.

Findings

The weak scale is near 300 GeV when maximizing final radiation entropy.

The weak scale is related to the electron Yukawa coupling, BBN temperature, and Planck mass.

The maximum entropy principle constrains the Higgs expectation value to observed levels.

Abstract

The theory of multiverse and wormholes suggests that the parameters of the Standard Model are fixed in such a way that the radiation of the $S^{3}$ universe at the final stage $S_{rad}$ becomes maximum, which we call the maximum entropy principle. Although it is difficult to confirm this principle generally, for a few parameters of the Standard Model, we can check whether $S_{rad}$ actually becomes maximum at the observed values. In this paper, we regard $S_{rad}$ at the final stage as a function of the weak scale ( the Higgs expectation value ) $v_{h}$, and show that it becomes maximum around $v_{h}={\cal{O}}(300\text{GeV})$ when the dimensionless couplings in the Standard Model, that is, the Higgs self coupling, the gauge couplings, and the Yukawa couplings are fixed. Roughly speaking, we find that the weak scale is given by \begin{equation} v_{h}\sim\frac{T_{BBN}^{2}}{M_{pl}y_{e}^{5}},\nonumber\end{equation} where $y_{e}$ is the Yukawa coupling of electron, $T_{BBN}$ is the temperature where the Big Bang Nucleosynthesis starts and $M_{pl}$ is the Planck mass.