A Systematic Analysis of Perturbations for Hexagonal Mixing Matrix

TL;DR

This paper systematically analyzes perturbations to the Hexagonal neutrino mixing matrix using small rotations, identifying which schemes best fit current neutrino oscillation data for both hierarchies.

Contribution

It introduces a comprehensive numerical study of various perturbative schemes applied to the Hexagonal mixing matrix, highlighting successful configurations for fitting experimental data.

Findings

Single rotation schemes fail to fit data within 3σ.

Certain two-rotation schemes fit all angles within 1σ for NH.

Only specific schemes fit all angles within 1σ for IH.

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 parameterized in terms of small orthogonal rotations (R) with modified PMNS matrix of the forms \big($R_{\alpha\beta}^l\cdot V_{HG},~V_{HG}\cdot R_{\alpha\beta}^r,~V_{HG}\cdot R_{\alpha\beta}^r \cdot R_{\gamma\delta}^r,~R_{\alpha\beta}^l \cdot R_{\gamma\delta}^l \cdot V_{HG}$,~$R_{\alpha\beta}^l\cdot V_{HG}\cdot R_{\gamma\delta}^r$\big ). Here $R_{\alpha\beta}^{l, r}$ 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 $\chi^2$ approach. We found that the perturbative schemes governed by single rotation are unable to fit the mixing angle data even at $3\sigma$ level. The mixing schemes which involves two rotation matrices, only \big($R_{12}^l \cdot R_{13}^l \cdot V_{HG}$, ~$R_{13}^l \cdot R_{12}^l \cdot V_{HG}$,~$R_{13}^l \cdot V_{HG} \cdot R_{12}^r$,~$R_{12}^l \cdot V_{HG} \cdot R_{12}^r$, ~$R_{13}^l \cdot V_{HG} \cdot R_{13}^r$\big ) are successful in fitting all neutrino mixing angles within $1\sigma$ range for normal hierarchy(NH). However for inverted hierarchy(IH), only $R_{13}^l \cdot V_{HG} \cdot R_{13}^r$ is most preferable as it can fit all mixing angles at $1\sigma$ level. The remaining perturbative cases are either excluded at 3$\sigma$ level or successful in producing mixing angles only at $2-3\sigma$ level. To study the impact of phase parameter, we also looked into CP violating effects for single rotation case. The predicted value of $\delta_{CP}$ lies in the range $39.0^\circ(40.4^\circ) \le |\delta_{CP}| \le 78.7^\circ(79.2^\circ)$ for $U_{12}^l\cdot V_{HM}$ and $U_{13}^l\cdot V_{HM}$ case with Normal(Inverted) Hierarchy.