Abstract: The particle spectrum of all Majorana neutrino mass models with spontaneous violation of global lepton number include a Goldstone boson, the so-called majoron. The presence of this massless pseudoscalar changes the phenomenology dramatically. In this work we derive general analytical expressions for the 1-loop coupling of the majoron to charged leptons. These can be applied to any model featuring a majoron that have a clear hierarchy of energy scales, required for an expansion in powers of the low-energy scale to be valid. We show how to use our general results by applying them to some example models, finding full agreement with previous results in several popular scenarios and deriving novel ones in other setups.

Abstract: In this paper we discuss SU(5)3 with cyclic symmetry as a possible grand unified theory (GUT). The basic idea of such a tri-unification is that there is a separate SU(5) for each fermion family, with the light Higgs doublet(s) arising from the third family SU(5), providing a basis for charged fermion mass hierarchies. SU(5)3 tri-unification reconciles the idea of gauge non-universality with the idea of gauge coupling unification, opening the possibility to build consistent non-universal descriptions of Nature that are valid all the way up to the scale of grand unification. As a concrete example, we propose a grand unified embedding of the tri-hypercharge model \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{U}}{\left(1\right)}_{Y}<^>{3}$$\end{document} based on an SU(5)3 framework with cyclic symmetry. We discuss a minimal tri-hypercharge example which can account for all the quark and lepton (including neutrino) masses and mixing parameters. We show that it is possible to unify the many gauge couplings into a single gauge coupling associated with the cyclic SU(5)3 gauge group, by assuming minimal multiplet splitting, together with a set of relatively light colour octet scalars. We also study proton decay in this example, and present the predictions for the proton lifetime in the dominant e+pi 0 channel.

Abstract: Scotogenic models constitute an appealing solution to the generation of neutrino masses and to the dark matter mystery. In this work we consider a version of the scotogenic model that breaks the lepton number spontaneously. At this scope, we extend the particle content of the scotogenic model with an additional singlet scalar which acquires a nonzero vacuum expectation value and breaks a global lepton number symmetry. As a consequence, a massless Goldstone boson, the majoron, appears in the particle spectrum. We discuss how the presence of the majoron modifies the phenomenology, both in flavor and dark matter observables. We focus on the fermionic dark matter candidate and analyze its relic abundance and prospects for both direct and indirect detection.