Naturalness of CP Violation in the Standard Model

TL;DR

This paper introduces a natural measure on the space of CKM matrices based on quark mass distributions, showing that the observed CP violation parameter is typical given the quark mass hierarchy.

Contribution

It constructs a measure on CKM matrices considering quark mass distributions, providing a statistical assessment of the CP violation parameter's naturalness.

Findings

The observed CP violation value is typical under the proposed measure.

The measure aligns with the observed quark mass hierarchy.

CP violation is statistically natural in the standard model context.

Abstract

We construct a natural measure on the space of CKM matrices in the standard model, assuming the fermion mass matrices are randomly selected from a distribution which fits the observed quark mass hierarchy. This measure allows us to assess the likelihood of Jarlskog's CP violation parameter J taking its observed value J $\approx$ 3 x 10^{-5}. While well below the mathematically allowed maximum, we find that this value is in fact typical, once the observed quark masses are assumed.