CP violation and gravity as the weakest force

TL;DR

This paper explores how CP violation influences the 'gravity as the weakest force' conjecture, suggesting a new ultraviolet scale bound and implications for the consistency of CP-conserving theories with quantum gravity.

Contribution

It introduces a novel bound on the ultraviolet scale involving CP violation and discusses its implications for the consistency of CP conservation in quantum gravity frameworks.

Findings

New bound: mbda 1 heta g^3 M_P

CP-conserving theories may be inconsistent with quantum gravity

Small CP violation (10^{-15}) can explain the mass hierarchy

Abstract

We argue that CP violation has rather dramatic impact on the "gravity as the weakest force" conjecture. Namely we find that new ultraviolet scale must be $\Lambda \lesssim \theta g^3 M_P$, where $\theta$ is an effective parameter describing CP violation and $g$ is the gauge coupling constant. The bound implies that CP-conserving limit is discontinuous, and possibly indicates that the class of effective theories with strict CP conservation is inconsistent with a fundamental theory incorporating quantum gravity. At the same time, the mass hierarchy problem can be explained due to the smallness of the CP violation, $\theta \sim 10^{-15}$ or so.