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

Abstract

We consider charged lepton correction to Tri-bimaximal(TBM) neutrino mixing, defined by the relation $U_{PMNS}=U_l^{†}{U}_{TB}$ 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.

Comments: 8 pages, 4 figures