Tribimaximal Mixing Matrices Research Articles

Consistency of perturbed tribimaximal, bimaximal and democratic mixing with neutrino mixing data

We scrutinize corrections to tribimaximal (TBM), bimaximal (BM) and democratic (DC) mixing matrices for explaining recent global fit neutrino mixing data. These corrections are parameterized in terms of small orthogonal rotations (R) with corresponding modified PMNS matrices of the forms (Rijl⋅U,U⋅Rijr,U⋅Rijr⋅Rklr,Rijl⋅Rkll⋅U) where Rijl,r is rotation in ij sector and U is any one of these special matrices. We showed that for perturbative schemes dictated by single rotation, only (R12l⋅UBM,R13l⋅UBM,UTBM⋅R13r) can fit the mixing data at 3σ level. However for Rijl⋅Rkll⋅U type rotations, only (R23l⋅R13l⋅UDC) is successful to fit all neutrino mixing angles within 1σ range. For U⋅Rijr⋅Rklr perturbative scheme, only (UBM⋅R12r⋅R13r,UDC⋅R12r⋅R23r,UTBM⋅R12r⋅R13r) are consistent at 1σ level. The remaining double rotation cases are either excluded at 3σ level or successful in producing mixing angles only at 2σ−3σ level. We also updated our previous analysis on PMNS matrices of the form (Rij⋅U⋅Rkl) with recent mixing data. We showed that the results modifies substantially with fitting accuracy level decreases for all of the permitted cases except (R12⋅UBM⋅R13,R23⋅UTBM⋅R13 and R13⋅UTBM⋅R13) in this rotation scheme.

Prediction of leptonicCPphase from perturbatively modified tribimaximal (or bimaximal) mixing

We consider the perturbatively modified tribimaximal (or bimaximal) mixing to estimate the (Dirac-type) CP phase in neutrino mixing matrix. The expressions for the CP phase are derived from the equivalence between the standard parametrization of the neutrino mixing matrix for the Majorana neutrino and modified tribimaximal or bimaximal mixing matrices with appropriate CP phases. Carrying out numerical analysis based on the current experimental results for neutrino mixing angles, we can predict the values of the CP phase for several possible cases.

Search for possible forms of neutrino mixing matrix [formula omitted

Two popular forms of neutrino mixing matrix UPMNS, are the Bi-maximal (BM) mixing and Tri-bimaximal (TBM) mixing matrices which are derived from well known underlying symmetry principles. In the present work, we examine their validity after taking appropriate charged lepton corrections. Tri-bimaximal mixing matrix with charged lepton correction, agrees with the present observational data at 1σ level, but the Bi-maximal mixing with charged lepton correction, fails to accommodate the present observational data at 1σ level on neutrino oscillations. This shortcoming is removed in Bi-large (BL) mixing ansatz with appropriate charged lepton correction. We also discuss the Quark–Lepton Complementarity(QLC) relations and other related issues in neutrino physics.

Corrections for tribimaximal, bimaximal and democratic neutrino mixing matrices

In this work we analyze the corrections to tribimaximal (TBM), bimaximal (BM) and democratic (DC) mixing matrices for explaining large reactor mixing angle $\theta_{13}$ and checking the consistency with other neutrino mixing angles. The corrections are parameterized in terms of small orthogonal rotations (R) with corresponding modified PMNS matrix of the form $R_{ij}\cdot U \cdot R_{kl}$ where $R_{ij}$ is rotation in ij sector and U is any one of these special matrices. We showed the rotations $R_{13}\cdot U \cdot R_{23}$, $R_{12}\cdot U \cdot R_{13}$ for BM and $R_{13}\cdot U \cdot R_{13}$ for TBM perturbative case successfully fit all neutrino mixing angles within $1\sigma$ range. The perturbed PMNS matrix $R_{12}\cdot U \cdot R_{13}$ for DC, TBM and $R_{23}\cdot U \cdot R_{23}$ for TBM case is successful in producing mixing angles at 2$\sigma$ level. The other rotation schemes are either excluded or successful in producing mixing angles at $3\sigma$ level.

Relatively large Theta13 from modification to the tri-bimaximal, bimaximal and democratic neutrino mixing matrices

Inspired by the indication of a relatively large θ 13 from accelerator and reactor neutrino oscillation experiments, we provide a systematic study of general modifications to the three well-studied neutrino mixing patterns, i.e., tri-bimaximal, bimaximal and democratic lepton mixing matrices. The correlation between θ 13 and the other two neutrino mixing angles are derived for each types of additional rotations. Predictions on θ 12 and θ 23 are also studied. Our study shows that, although some types of additional rotations are already excluded by the current global fit data of neutrino mixing angles, several types of additional rotations still survive. Our results may provide a guideline for the model building in neutrino physics.

Charged lepton contributions to bimaximal and tri-bimaximal mixing for generating [formula omitted] and [formula omitted

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.

NONZERO θ13 AND NEUTRINO MASSES FROM MODIFIED NEUTRINO MIXING MATRIX

The nonzero and relatively large θ13 have been reported by Daya Bay, T2K, MINOS and Double Chooz Collaborations. In order to accommodate the nonzero θ13, we modified the tribimaximal (TB), bimaxima (BM) and democratic (DC) neutrino mixing matrices. From three modified neutrino mixing matrices, two of them (the modified BM and DC mixing matrices) can give nonzero θ13 which is compatible with the result of the Daya Bay and T2K experiments. The modified TB neutrino mixing matrix predicts the value of θ13 which is greater than the upper bound value of the latest experimental results. By using the modified neutrino mixing matrices and imposing an additional assumption that neutrino mass matrices have two zeros texture, we then obtain the neutrino mass in normal hierarchy when (Mν)22 = (Mν)33 = 0 for the neutrino mass matrix from the modified TB neutrino mixing matrix and (Mν)11 = (Mν)13 = 0 for the neutrino mass matrix from the modified DC neutrino mixing matrix. For these two patterns of neutrino mass matrices, either the atmospheric mass squared difference or the solar mass squared difference can be obtained, but not both of them simultaneously. From four patterns of two zeros texture to be considered on the obtained neutrino mass matrix from the modified BM neutrino mixing matrix, none of them can correctly predict the neutrino mass spectrum (normal or inverted hierarchy).