Naturalness of CP violation in the standard model

We construct a natural measure on the space of Cabibbo-Kobayashi-Maskawa matrices in the standard model, assuming the fermion mass matrices are randomly selected from a distribution which incorporates 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 ≈ 3×10−5. We find that the observed value, while well below the mathematically allowed maximum, is in fact typical once the observed quark masses are assumed.