Abstract
We consider an inverse seesaw mechanism of neutrino mass generation in which the Standard Model is extended by 3+3 (heavy) sterile states, and endowed with a flavour symmetry G_f, G_f=Delta (3 , n^2) or G_f=Delta (6 , n^2), and a CP symmetry. These symmetries are broken in a peculiar way, so that in the charged lepton sector a residual symmetry G_ell is preserved, while the neutral fermion sector remains invariant under the residual symmetry G_nu =Z_2 times CP. We study the concrete setup, where the Majorana mass term for three of the sterile states conserves G_nu , while the remaining mass terms (i.e. couplings of left-handed leptons and heavy sterile states, as well as the Dirac-type couplings among the latter) do not break the flavour or CP symmetry. We perform a comprehensive analysis of lepton mixing for different classes of residual symmetries, giving examples for each of these, and study in detail the impact of the additional sterile states on the predictions for lepton mixing. We further confront our results with those obtained in the model-independent scenario, in which the light neutrino mass matrix leaves the residual symmetry G_nu intact. We consider the phenomenological impact of the inverse seesaw mechanism endowed with flavour and CP symmetries, in particular concerning effects of non-unitarity of the lepton mixing matrix (which strongly constrain the parameter space of the scenario), prospects for neutrinoless double beta decay and for charged lepton flavour violating processes.
Highlights
The inverse seesaw (ISS) mechanism offers a direct connection between the smallness of neutrino masses and the breaking of lepton number (LN) conservation: when compared to the canonical type-I seesaw, a potentially tiny LN violating (LNV) dimensionful coupling μS provides an additional source of suppression for the light neutrino masses, while being technically natural in the sense of ’t Hooft [45]
We note that the realisation of option 2 and option 3 requires in general that the assignment of the three sterile states Si, i = 1, 2, 3, under the flavour symmetry G f be altered compared to option 1, in order to ensure that the matrix μS is non-vanishing in the limit of unbroken G f, Z3(aux) and CP
We have considered an inverse seesaw mechanism with 3 + 3 heavy sterile states, endowed with a flavour symmetry G f = (3 n2) or G f = (6 n2) and a CP symmetry
Summary
We choose a non-abelian discrete symmetry G f combined with a CP symmetry, both acting non-trivially on flavour space. 194 Page 2 of 32 logical impact: as a consequence of the sizeable mixing between active neutrinos and the comparatively light additional sterile states (possibly within collider reach), extensive contributions to numerous observables can occur Among the latter, one can mention several charged lepton flavour violation (cLFV) processes [46–52], CP violating observables such as the electric dipole moment (EDM) of the electron [53], or neutrinoless double beta (0νββ) decays [54,55]. We show analytically and numerically that the impact of these heavy sterile states on lepton mixing (i.e., results for lepton mixing angles, predictions for CP phases as well as (approximate) sum rules) is always small, with relative deviations below 1% from the results previously obtained in the model-independent scenario [33] This is a consequence of effects arising due to deviations from unitarity of the PMNS. Additional information and complementary discussions are collected in several appendices
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