Jarlskog determinant and data on flavor matrices

Abstract

The essences of the weak [Formula: see text] violation, the quark and lepton Jarlskog invariants, are determined toward future model buildings beyond the Standard Model (SM). The equivalence of two calculations of Jarlskog invariants gives a bound on the [Formula: see text] phase in some parametrization. Satisfying the unitarity condition, we obtain the CKM and PMNS matrices from the experimental data, and present the results in matrix forms. The Jarlskog determinant [Formula: see text] in the quark sector is found to be [Formula: see text] while [Formula: see text] in the leptonic sector is [Formula: see text] in the normal hierarchy parametrization.