Zero minors of the neutrino mass matrix

Abstract

We examine the possibility that a certain class of neutrino mass matrices, namely those with two independent vanishing minors in the flavor basis, regardless of being invertible or not, is sufficient to describe current data. We compute generic formulae for the ratios of the neutrino masses and for the Majorana phases. We find that seven textures with two vanishing minors can accommodate the experimental data. We present an estimate of the mass matrix for these patterns. All the possible textures can be dynamically generated through the seesaw mechanism augmented with a discrete Abelian symmetry.

Predictions for the neutrino parameters in the minimal gauged $$\hbox {U}(1)_{L_\mu -L_\tau }$$ U ( 1 ) L μ - L τ model

“…Because of this structure of the Majorana mass matrix together with the diagonal Dirac mass matrix, the inverse of the neutrino-mass matrix also has zeros in the (μ, μ) and (τ, τ ) components [42,45]. The minimal gauged U(1) L μ −L τ model thus gives a concrete realization of a two-zero-minor model [46,47]. Intriguingly, due to the condition that the (μ, μ) and (τ, τ ) components in the inverse of the neutrino-mass matrix vanish, all the CP phases in the neutrino mixing matrix -the Dirac CP phase δ and the Majorana CP phases α 2 and α 3 -as well as the mass eigenvalues of the light neutrinos are uniquely determined as functions of the neutrino mixing angles θ 12 , θ 23 , and θ 13 , and the squared mass differences m 2 21 and m 2 31 .…”

“…This structure is sometimes called twozero minor [46,47]. For other previous studies of the twozero minor structure, see Refs.…”

“…Such quantum corrections can be taken into account by using renormalization-group equations. Remarkably, it is found that the two-zero minor structure of M ν L is preserved throughout the renormalization-group flow [46,47]. To see this, we first note that below the right-handed neutrino-mass scale, which is around the U(1) L μ −L τ symmetry breaking scale in this model, right-handed neutrinos are integrated out to give the following dimensionfive effective operator:…”

Neutrino mixing and R K anomaly in U(1) X models: a bottom-up approach

“…Only some specific textures of M R are allowed. While no three-zero textures are consistent with data, specific two-zero textures are allowed [63][64][65][66]. In addition, most one-zero textures [67], and naturally, all no-zero textures, are also permitted.…”

“…and L e − L µ ± 3L τ have already been explored in this context and the allowed parameter values determined [23,[63][64][65]76].…”