Dependence of $\tan^2 \theta_{12}$ on Dirac CP phase $\delta$ in tri-bimaximal neutrino mixing under charged lepton correction

TL;DR

This paper explores how charged lepton corrections to tri-bimaximal neutrino mixing influence the dependence of the solar mixing angle on the Dirac CP phase, providing constraints on the phase based on experimental data.

Contribution

It introduces a new parametrization for the Dirac CP phase and analyzes its effect on neutrino mixing angles under charged lepton corrections similar to CKM.

Findings

Dependence of $ an^2 \theta_{12}$ on the CP phase $\\delta$ is established.

Constraints on the CP phase $\\delta$ are derived from experimental mixing angles.

Charged lepton correction matrices are shown to be unitary and CKM-like.

Abstract

We consider charged lepton correction to Tri-bimaximal(TBM) neutrino mixing, defined by the relation $U_{PMNS}=U^{\dagger}_l U_{TB}$ and find possible form of $U_l$ which can impart non-zero value of $\sin \theta_{13}$ as well as $\tan^2 \theta_{23}<1$, consistent with latest global analysis data. We adopt a new parametrization, other than the standard PDG parametrization, to introduce Dirac CP violating phase $\delta$ in the PMNS matrix which is discussed by Fritzsch. Under such charged lepton correction pattern we note that $\tan^2 \theta_{12}$ becomes dependent on the CP phase $\delta$ from where constraints on $\delta$ phase can be obtained after employing experimental range of mixing angles. To compute the values of mixing angles we assume the charged lepton correction to be of Cabibbo-Kobayashi-Maskawa(CKM) like. Since all the mixing matrices involved in the calculation, are derived from three dimensional rotation matrices they satisfy unitarity condition.