A systematic analysis of perturbations for hexagonal mixing matrix

We present a systematic analysis of perturbative Hexagonal (HG) mixing for describing recent global fit neutrino mixing data with normal and inverted hierarchy. The corrections to unperturbed mixing are parametrized in terms of small orthogonal rotations (R) with modified PMNS matrix of the forms R^l _αβ V_HG,V_HG R^r _αβ,V_HG R^r _αβ R^r _γδ,R^l _αβ R^l _γδ V_HG,R^l _αβ V_HG R^r _γδ. Here, R^l _αβ,r is rotation in ij sector and V_HG is unperturbed Hexagonal mixing matrix. The detailed numerical investigation of all possible cases is performed with scanning of parameter space using χ2 approach. We found that the perturbative schemes governed by single rotation are unable to fit the mixing angle data even at 3σ level. The mixing schemes which involve two rotation matrices only R^l ₁₂ R^l ₁₃ V_HG,R^l ₁₃ R^l ₁₂ V_HG,R^l ₁₃ V_HG R^r ₁₂,R^l ₁₂ V_HG R^r ₁₂,R^l ₁₃ V_HG R^r ₁₃ are successful in fitting all neutrino mixing angles within 1σ range for normal hierarchy (NH). However for inverted hierarchy (IH), only R^l ₁₃ V_HG R^r ₁₃ is most preferable as it can fit all mixing angles at 1σ level. The remaining perturbative cases are either excluded at 3σ level or successful in producing mixing angles only at 2-3σ level. To study the impact of phase parameter, we also looked into CP violating effects for single rotation case. The predicted value of δCP lies in the range 39.0°(40.4°) ≤|δ CP|≤ 78.7(79.2) for U12l V HM and U13l V HM case with normal (inverted) hierarchy.