Jarlskog determinant and data on flavor matrices

The essences of the weak 𝒞𝒫 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 𝒞𝒫 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 Jq in the quark sector is found to be ∼ 3.11 × 10−5|sin α KS| while Jℓ in the leptonic sector is ∼ 2.96 × 10−2|sin α KSℓ| in the normal hierarchy parametrization.