Charged lepton contributions to bimaximal and tri-bimaximal mixing for generating sinθ13≠0 and tan2θ23<1

Bimaximal (BM) and tri-bimaximal (TB) mixings of neutrinos are two special cases of lepton mixing matrix, which predict the reactor angle θ13=0 and the atmospheric angle tan2θ23=1. Recent precision measurements and global analysis of oscillation parameters, have confirmed a non-vanishing value of θ13 as well as deviations of θ12 and θ23 from their maximal values predicted by BM or TB mixing. In this work we mainly concentrate on θ13 and θ23 to assign θ13≠0 and tan2θ23<1 with the help of charged lepton corrections defined by UPMNS=Ul†Uν. We first consider Uν to be given separately by BM and TB mixing matrices and then find the possible forms of Ul such that the elements of PMNS matrix, finally yield θ13≠0 and tan2θ23<1 in agreement with latest observational data. To compute the values of mixing angles we assume the charged lepton correction to be of Cabibbo-Kobayashi-Maskawa (CKM) like. All the mixing matrices involved in the calculation satisfy the unitarity condition to leading order of expansion parameter. We also analyze both the mixing schemes in presence of Dirac CP phase and find expressions for the rephasing invariant quantity JCP which have been discussed in recent literature.