Abstract
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.
Highlights
Recent precision measurements[1,2,3,4] and latest global 3ν oscillation analysis[5] of neutrino mixing parameters, have confirmed non-vanishing value of θ13 as well as deviation of atmospheric mixing angle from maximal value, θ23 < π/4
We have studied two possible forms of the lepton mixing matrix Ul which can produce desired deviations from the bimaximal (BM) and tri-bimaximal(TB) mixings of neutrino sector under charged lepton corrections
After the introduction of Dirac CP phase we observe that tan2 θ12 is affected by the phase, but not tan2 θ23
Summary
Recent precision measurements[1,2,3,4] and latest global 3ν oscillation analysis[5] of neutrino mixing parameters, have confirmed non-vanishing value of θ13 as well as deviation of atmospheric mixing angle from maximal value, θ23 < π/4. Charged lepton corrections[7] to neutrino mixing matrix is an attractive tool which can impart non-zero value of θ13 as well as deviation of θ23 from maximal value. We address the issue of charged lepton correction to both bimaximal(BM) and tri-bimaximal(TB) neutrino mixings to produce desired results. In relation (1), Ul and Uν are the diagonalizing matrices for charged lepton and left-handed Majorana neutrino mass matrices respectively which are defined as : ml = UlLmdl iagVlR† and mν = Uν∗mdνiagUν†. In the standard Particle Data Group (PDG) parametrization[10], with three mixing angles and three CP phases- one Dirac CP phase (δ) and two Majorana CP phases (α, β), PMNS matrix has the form, c12c13. The paper is organized as follows: In section 2 we discuss charged lepton correction to BM neutrino mixing and present predictions of the mixing angles along with graphical representations.
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