# Jarlskog determinant and data on flavor matrices

## TL;DR

This paper analyzes the Jarlskog invariants related to CP violation in quark and lepton sectors, deriving bounds on CP phases and presenting updated flavor matrices based on experimental data.

## Contribution

It provides a detailed calculation of Jarlskog invariants and their bounds, offering new insights into CP violation parameters beyond the Standard Model.

## Key findings

- Jarlskog determinant in quark sector: ~3.11×10^{-5} |sin(δ_K)|
- Jarlskog determinant in leptonic sector: ~2.96×10^{-2} |sin(δ_{Kℓ})|
- Derived bounds on CP phases from unitarity and experimental data

## Abstract

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 MNS matrices from the experimental data, and present the results in matrix forms. The Jarlskog determinant $J^q$ in the quark sector is found to be $\sim 3.11\times 10^{-5}|\sin\delks|$ while $J^\ell$ in the leptonic sector is $\sim 2.96\times 10^{-2}|\sin\delksl|$ in the normal hierarchy parametrization.