Almost exact diagonal reflection symmetries and three-zero texture

Abstract

In this paper, we consider the diagonal reflection symmetries and three-zero texture in the SM. The three-zero texture has two less assumptions ((Mu)11, (Mν)11 = 0) than the universal four-zero texture for mass matrices (M f )11 = (M f )13,31 = 0 for f = u, d, ν, e. The texture and symmetries reproduce the CKM and MNS matrices with accuracies of O(10 −4 ) and O(10 −3 ).By assuming a de unified relation (M d ∼ Me), this system predicts the normal hierarchy, the Dirac phase δCP ≃ 202 • , the Majorana phases α12 = 11.3 • , α13 = 6.90 • up to π, and the lightest neutrino mass m1 ≃ 2.97 − 4.72 [meV]. The effective mass of the double beta decay |mee| is found to be 1.24 ∼ 1.77 [meV].

A general formula by $LDL^{T}$ decomposition for the type-I seesaw mechanism

“…Since phases of a i or b i can be eliminated approximately by field redefinitions, this case indicates the existence of an approximate generalized CP symmetry [29][30][31][32] for neutrino mass m in some basis. One such example is diagonal reflection symmetries that imposed on X = m , Y , M and the mass matrix of electrons Y e [33][34][35][36];…”

Diagonal reflection symmetries and universal four-zero texture *

“…These errors can be improved to O(10 −3 ) by allowing (M ν ) 11 = 0 and making Eq. (1) a three-zero texture [83].…”