Abstract
We propose a simple model of spontaneous lepton number violation with potentially large flavor violating decays, including the possibility that majoron emitting decays, such as μ → eJ, saturate the experimental bounds. In this model the majoron is a singlet-doublet admixture. It generates a type-I seesaw for neutrino masses and contains also a vector-like lepton. As a by-product, the model can explain the anomalous (g − 2)μ in parts of its parameter space, where one expects that the branching ratio of the Higgs to muons is changed with respect to Standard Model expectations. However, the explanation of the muon g − 2 anomaly would lead to tension with recent astrophysical bounds on the majoron coupling to muons.
Highlights
The interaction of the majoron with charged leptons can be described in a model independent way as [7], L
We propose a simple model of spontaneous lepton number violation with potentially large flavor violating decays, including the possibility that majoron emitting decays, such as μ → e J, saturate the experimental bounds
As a by-product, the model can explain the anomalous (g − 2)μ in parts of its parameter space, where one expects that the branching ratio of the Higgs to muons is changed with respect to Standard Model expectations
Summary
We consider a type-I seesaw with spontaneous lepton number violation. The quark sector remains as in the SM, whereas the lepton sector is extended with the addition of 3 generations of singlet right-handed neutrinos, a pair of singlet vector-like leptons, FL and FR, the scalars σ and S and a U(1)L global symmetry, where L refers to lepton number. The scalar potential of the model includes new terms involving the σ and S fields. The μ parameter breaks an accidental U(1) symmetry that would lead in its absence to the appearance of an additional massless Goldstone boson. We turn to the charged scalar mass matrix In this case, the scalar potential contains the term. Eq (2.50) imposes constraints on the U L,R matrices and reduces their numbers of independent parameters It requires U L,R to lead to two vanishing 3 × 1 and 1 × 3 submatrices. The block-diagonal masses for the light and heavy charged leptons are given by mlight me mρmS MF mρm†ρme 2 MF2. Mlight ≈ me and mheavy ≈ MF , with corrections to these zeroth order results entering at different orders in 1/MF
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