Research PapersNo Access

A systematic analysis of perturbations for hexagonal mixing matrix

Sumit K. Garg

Department of Physics, CMR University, Bengaluru 562149, India

https://doi.org/10.1142/S0217751X19500052Cited by:3 (Source: Crossref)

Abstract

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 $(R)$ $(R)$ with modified PMNS matrix of the forms $(R_{α β}^{l} \cdot V_{HG}, V_{HG} \cdot R_{α β}^{r}, V_{HG} \cdot R_{α β}^{r} \cdot R_{γ δ}^{r}, R_{α β}^{l} \cdot R_{γ δ}^{l} \cdot V_{HG}, R_{α β}^{l} \cdot V_{HG} \cdot R_{γ δ}^{r})$ $(R_{α β}^{l} \cdot V_{HG}, V_{HG} \cdot R_{α β}^{r}, V_{HG} \cdot R_{α β}^{r} \cdot R_{γ δ}^{r}, R_{α β}^{l} \cdot R_{γ δ}^{l} \cdot V_{HG}, R_{α β}^{l} \cdot V_{HG} \cdot R_{γ δ}^{r})$ . Here, $R_{α β}^{l, r}$ $R_{α β}^{l, r}$ is rotation in $i j$ $i j$ sector and $V_{HG}$ $V_{HG}$ is unperturbed Hexagonal mixing matrix. The detailed numerical investigation of all possible cases is performed with scanning of parameter space using $χ^{2}$ $χ^{2}$ approach. We found that the perturbative schemes governed by single rotation are unable to fit the mixing angle data even at $3 σ$ $3 σ$ level. The mixing schemes which involve two rotation matrices only $(R_{12}^{l} \cdot R_{13}^{l} \cdot V_{HG}, R_{13}^{l} \cdot R_{12}^{l} \cdot V_{HG}, R_{13}^{l} \cdot V_{HG} \cdot R_{12}^{r}, R_{12}^{l} \cdot V_{HG} \cdot R_{12}^{r}, R_{13}^{l} \cdot V_{HG} \cdot R_{13}^{r})$ $(R_{12}^{l} \cdot R_{13}^{l} \cdot V_{HG}, R_{13}^{l} \cdot R_{12}^{l} \cdot V_{HG}, R_{13}^{l} \cdot V_{HG} \cdot R_{12}^{r}, R_{12}^{l} \cdot V_{HG} \cdot R_{12}^{r}, R_{13}^{l} \cdot V_{HG} \cdot R_{13}^{r})$ are successful in fitting all neutrino mixing angles within $1 σ$ $1 σ$ range for normal hierarchy (NH). However for inverted hierarchy (IH), only $R_{13}^{l} \cdot V_{HG} \cdot R_{13}^{r}$ $R_{13}^{l} \cdot V_{HG} \cdot R_{13}^{r}$ is most preferable as it can fit all mixing angles at $1 σ$ $1 σ$ level. The remaining perturbative cases are either excluded at $3 σ$ $3 σ$ level or successful in producing mixing angles only at $2 – 3 σ$ $2 – 3 σ$ level. To study the impact of phase parameter, we also looked into CP violating effects for single rotation case. The predicted value of $δ_{CP}$ $δ_{CP}$ lies in the range $39 . 0^{\circ} (40 . 4^{\circ}) \leq | δ_{CP} | \leq 78 . 7^{\circ} (79 . 2^{\circ})$ $39 . 0^{\circ} (40 . 4^{\circ}) \leq | δ_{CP} | \leq 78 . 7^{\circ} (79 . 2^{\circ})$ for $U_{12}^{l} \cdot V_{HM}$ $U_{12}^{l} \cdot V_{HM}$ and $U_{13}^{l} \cdot V_{HM}$ $U_{13}^{l} \cdot V_{HM}$ case with normal (inverted) hierarchy.

Keywords:

PACS: 12.15.Ff, 14.60.Pq

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