Space-time variation of the electron-to-proton mass ratio in a Weyl model

TL;DR

This paper investigates a Weyl tensor-based model to explain observed space-time variations in the electron-to-proton mass ratio, but finds it incompatible with existing experimental bounds, ruling out this approach.

Contribution

It introduces a phenomenological model linking fermion masses to the Weyl tensor and tests its viability against experimental constraints.

Findings

Model's free parameters are incompatible with bounds from equivalence principle tests.

Variation of fermion masses via Weyl coupling is not a viable explanation.

The proposed model cannot account for observed mass ratio variations.

Abstract

Seeking a possible explanation for recent data indicating a space-time variation of the electron-to-proton mass ratio within the Milky Way, we consider a phenomenological model where the effective fermion masses depend on the local value of the Weyl tensor. We contrast the required values of the model's free parameters with bounds obtained from modern tests on the violation of the Weak Equivalence Principle and we find that these quantities are incompatible. This result indicates that the variation of nucleon and electron masses through a coupling with the Weyl tensor is not a viable model.