Weyl-invariant Einstein-Cartan gravity: unifying the strong CP and hierarchy puzzles

TL;DR

This paper proposes a Weyl-invariant Einstein-Cartan gravity model combined with the Standard Model, introducing a single axion-like scalar that addresses the strong CP problem and links to the smallness of the cosmological constant and Higgs mass.

Contribution

It introduces a minimal Weyl-invariant Einstein-Cartan framework with a unique scalar field that unifies solutions to the strong CP problem and hierarchy puzzles.

Findings

Identifies a scalar with axion-like properties solving the strong CP problem.

Explains the smallness of the cosmological constant via tiny gauge couplings.

Suggests the Higgs mass and Majorana leptons could be computable from fundamental parameters.

Abstract

We show that the minimal Weyl-invariant Einstein-Cartan gravity in combination with the Standard Model of particle physics contains just one extra scalar degree of freedom (in addition to the graviton and the Standard Model fields) with the properties of an axion-like particle which can solve the strong CP-problem. The smallness of this particle's mass as well as of the cosmological constant is ensured by tiny values of the gauge coupling constants of the local Lorentz group. The tree value of the Higgs boson mass and that of Majorana leptons (if added to the Standard Model to solve the neutrino mass, baryogenesis and dark matter problems) are very small or vanishing, opening the possibility of their computability in terms of the fundamental parameters of the theory due to nonperturbative effects.