Constructing the CKM and PMNS matrices from mixing data

TL;DR

This paper constructs the CKM and PMNS matrices using latest experimental data, exploring CP violation and unitarity constraints to improve understanding of quark and lepton mixing.

Contribution

It provides a novel, data-driven construction of the CKM and PMNS matrices, including analysis of CP violation and unitarity triangles with minimal theoretical assumptions.

Findings

Constructed CKM and PMNS matrices from experimental data.

Analyzed CP violation implications in quark and lepton sectors.

Addressed discrepancies in |V_{ub}| measurements.

Abstract

The CKM and PMNS matrices have been constructed based on the latest measurements, largely free from theoretical inputs as well as likely NP effects in the case of the former. To facilitate the construction of the CKM matrix in the PDG representation as well as in view of the comparatively large error in the measured value of the CP violating phase \delta, the possibility of its construction from the tree level measured CKM elements has also been explored using the unitarity triangle. In view of the persistent difference between the |V_{ub}| exclusive and inclusive values, we have carried out separate analyses corresponding to these. The PMNS matrix has been constructed by incorporating the constraints due to solar and atmospheric neutrinos as well as by giving full variation to the Dirac-like CP violating phase \delta and considering different values of s_{13} having implications for different models of lepton mass matrices. Taking clue from quark mixing phenomenology, an analogous analysis of the leptonic unitarity triangle allows an estimate of the likely presence of CP violation in the leptonic sector.