Model independent Analysis of Dirac CP Violating Phase for some well known mixing scenarios

TL;DR

This paper conducts a model-independent analysis of leptonic CP violation across various well-known neutrino mixing scenarios, providing generic formulas and exploring parameter spaces to predict CP phases and invariants.

Contribution

It introduces a unified, model-independent correction framework for mixing matrices and derives generic formulas for CP parameters, enhancing understanding of CP violation in neutrino physics.

Findings

Predicted ranges for leptonic CP phase $\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,",

Ranges for the Jarlskog invariant $J_{CP}$ are also reported.

The analysis covers modifications of Bimaximal, Democratic, Hexagonal, and Tribimaximal mixing schemes.

Abstract

We present a model-independent analysis of Leptonic CP violation for some well known mixing scenarios. In particular, we considered modified schemes for Bimaximal(BM), Democratic(DC), Hexagonal(HG) and Tribimaixmal(TBM) mixing for our numerical investigation. These model-independent corrections to mixing matrices are parameterized in terms of complex rotation matrices ($U$) with related modified PMNS matrix of the forms \big($U_{ij}^l\cdot V_{M},~V_{M}\cdot U_{ij}^r$ \big ) where $U_{ij}^{l, r}$ is complex rotation in ij sector and $V_{M}$ is unperturbed mixing scheme. We present generic formulae for mixing angles, Dirac CP phase($\delta_{CP}$) and Jarkslog Invariant($J_{CP}$) in terms of correction parameters. The parameter space of each modified mixing case is scanned for fitting neutrino mixing angles using $\chi^2$ approach and the corresponding predictions for Leptonic CP Phase($\delta_{CP}$) and Jarkslog Invariant($J_{CP}$) has been evaluated from allowed parameter space. The obtained ranges are reported for all viable cases.