Naturalness of CP Violation in the Standard Model

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.

Comments: 4 pages; corrected minor errors, added discussion of the work of Donoghue et al