Consistency of perturbed Tribimaximal, Bimaximal and Democratic mixing with Neutrino mixing data

Abstract

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 \big($R_{ij}^l\cdot U,~U\cdot R_{ij}^r,~U \cdot R_{ij}^r \cdot R_{kl}^r,~R_{ij}^l \cdot R_{kl}^l \cdot U$\big ) where $R_{ij}^{l, r}$ 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 \big($ R_{12}^l\cdot U_{BM},~R_{13}^l\cdot U_{BM},~U_{TBM}\cdot R_{13}^r$ \big ) can fit the mixing data at $3σ$ level. However for $R_{ij}^l\cdot R_{kl}^l\cdot U$ type rotations, only \big ($R_{23}^l\cdot R_{13}^l \cdot U_{DC} $\big ) is successful to fit all neutrino mixing angles within $1σ$ range. For $U\cdot R_{ij}^r\cdot R_{kl}^r$ perturbative scheme, only \big($U_{BM} \cdot R_{12}^r\cdot R_{13}^r$,~$U_{DC} \cdot R_{12}^r\cdot R_{23}^r$,~$U_{TBM} \cdot R_{12}^r\cdot R_{13}^r$\big ) are consistent at $1σ$ level. The remaining double rotation cases are either excluded at 3$σ$ level or successful in producing mixing angles only at $2σ-3σ$ level. We also updated our previous analysis on PMNS matrices of the form \big($R_{ij}\cdot U \cdot R_{kl}$\big ) with recent mixing data. We showed that the results modifies substantially with fitting accuracy level decreases for all of the permitted cases except \big($R_{12}\cdot U_{BM}\cdot R_{13}$, $R_{23}\cdot U_{TBM}\cdot R_{13}$ and $R_{13}\cdot U_{TBM} \cdot R_{13}$\big ) in this rotation scheme.