Weak Scale From the Maximum Entropy Principle

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 $v_h=\mathcal{O}(300\text{GeV})$ 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.

21 pages, 10 figures; references added, version to appear in PTEP (v2)

References in corpus (7)

• The top quark and Higgs boson masses and the stability of the electroweak vacuum
• Higgs boson and Top quark masses as tests of Electroweak Vacuum Stability
• Bare Higgs mass at Planck scale
• Varying the light quark mass: impact on the nuclear force and Big Bang nucleosynthesis
• Solving the Naturalness Problem by Baby Universes in the Lorentzian Multiverse
• Evidence of the Big Fix
• Asymptotically Vanishing Cosmological Constant in the Multiverse

Cited by in corpus (14)

• Euclidean wormholes, baby universes, and their impact on particle physics and cosmology
• Weak Gravity Conjecture, Multiple Point Principle and the Standard Model Landscape
• Eternal Higgs inflation and cosmological constant problem
• Criticality and Inflation of the Gauged B-L Model
• Models of LHC Diphoton Excesses Valid up to the Planck scale
• Reheating-era leptogenesis
• Natural solution to the naturalness problem -- Universe does fine-tuning
• Hubble selection of the weak scale from QCD quantum critical point
• Baby universes in 2d and 4d theories of quantum gravity
• Gravitational waves in models with multicritical-point principle
• Saddle point inflation in string-inspired theory
• Low-energy probes of small CMB amplitude in models of radiative Higgs mechanism
• Possible explanations for fine-tuning of the universe
• Hillclimbing saddle point inflation