Diagonal reflection symmetries and universal four-zero texture

Abstract

In this talk, we consider a set of new symmetries in the SM: {¥it diagonal reflection} symmetries $R ¥, m_{u,¥nu}^{*} ¥, R = m_{u,¥nu}, ~ m_{d,e}^{*} = m_{d,e}$ with $R =$ diag $(-1,1,1)$. % By combining the symmetries with the four-zero texture, the mass eigenvalues and mixing matrices of quarks and leptons are reproduced with precisions of $10^{-3}$. % Since this scheme have only eight parameters in the lepton sector, it has four predictions; the Dirac phase $¥delta_{CP} ¥simeq 203^{¥circ},$ the Majorana phases $(¥alpha_{2}, ¥alpha_{3}) ¥simeq (11.3^{¥circ}, 7.54^{¥circ})$ up to $180^{¥circ}$, and $|m_{1}| ¥simeq 2.5$ or $6.2 ¥, $[meV] with the normal hierarchy. ¥¥ In this scheme, the type-I seesaw mechanism and a given neutrino Yukawa matrix $Y_{¥nu}$ completely determine the structure of the right-handed neutrino mass $M_{R}$. A $u-¥nu$ unification predicts the mass eigenvalues to be $ (M_{R1} ¥, , M_{R2} ¥, , M_{R3}) = (O (10^{5}) ¥, , O (10^{9}) ¥, , O (10^{14})) ¥, $[GeV] with a strong hierarchy $M_{R} ¥sim Y_{u}^{T} Y_{u}$. ¥¥ The symmetries are approximately stable under the renormalization of SM. This statement holds without the four-zero texture as long as couplings in the first row and column of the Yukawa matrices are sufficiently small. % Then, they can possess information on a high energy scale.