Vanishing minors in the neutrino mass matrix from abelian gauge symmetries

Abstract

Augmenting the Standard Model by three right-handed neutrinos allows for an anomaly-free gauge group extension Gmax = U (1)B−L × U (1)L e −Lµ × U (1)L µ −Lτ . While simple U (1) subgroups of Gmax have already been discussed in the context of approximate flavor symmetries, we show how two-zero textures in the right-handed neutrino Majorana mass matrix can be enforced by the flavor symmetry, which is spontaneously broken very economically by singlet scalars. These zeros lead to two vanishing minors in the low-energy neutrino mass matrix after the seesaw mechanism. This study may provide a new testing ground for a zero-texture approach: the different classes of two-zero textures with almost identical neutrino oscillation phenomenology can in principle be distinguished by their different Z ′ interactions at colliders. * Electronic address: araki@ihep.ac.cn

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

“…In gauged U(1) L μ −L τ models, however, the neutrino-mass structure is tightly restricted since the second and third generation leptons are charged under the U(1) L μ −L τ gauge symmetry [40][41][42][43][44]. In fact, in the U(1) L μ −L τ preserving limit, the Dirac mass matrix is diagonal, while in the Majorana mass matrix only the (e, e), (μ, τ ), and (τ, μ) components can be non-zero.…”

“…In this case, the (μ, μ) and (τ, τ ) components of the Majorana mass matrix for the right-handed neutrinos remain zero even after the U(1) L μ −L τ symmetry is spontaneously broken. 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].…”

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.…”

“…It is to be noted that part of the list was already derived in [65,66]. Later in section 2.3, we shall examine the consistency of these symmetries with the flavour data.…”

“…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].…”