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Fonseca, R. M., Malinsky, M., Porod, W., & Staub, F. (2012). Running soft parameters in SUSY models with multiple U(1) gauge factors. Nucl. Phys. B, 854(1), 28–53.
Abstract: We generalize the two-loop renormalization group equations for the parameters of the softly broken SUSY gauge theories given in the literature to the most general case when the gauge group contains more than a single Abelian gauge factor. The complete method is illustrated at two-loop within a specific example and compared to some of the previously proposed partial treatments.
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Arbelaez, C., Fonseca, R. M., Romao, J. C., & Hirsch, M. (2013). Supersymmetric SO(10)-inspired GUTs with sliding scales. Phys. Rev. D, 87(7), 075010–19pp.
Abstract: We construct lists of supersymmetric models with extended gauge groups at intermediate steps, all of which are inspired by SO(10) unification. We consider three different kinds of setups: (i) the model has exactly one additional intermediate scale with a left-right (LR) symmetric group; (ii) SO(10) is broken to the LR group via an intermediate Pati-Salam scale; and (iii) the LR group is broken into SU(3)(c) X SU(2)(L) X U(1)(R) X U(1)(B-L), before breaking to the standard model (SM) group. We use sets of conditions, which we call the “sliding mechanism,” which yield unification with the extended gauge group(s) allowed at arbitrary intermediate energy scales. All models thus can have new gauge bosons within the reach of the LHC, in principle. We apply additional conditions, such as perturbative unification, renormalizability and anomaly cancellation and find that, despite these requirements, for the ansatz (i) with only one additional scale still around 50 different variants exist that can have a LR symmetry below 10 TeV. For the more complicated schemes (ii) and (iii) literally thousands of possible variants exist, and for scheme (ii) we have also found variants with very low Pati-Salam scales. We also discuss possible experimental tests of the models from measurements of supersymmetry masses. Assuming mSugra boundary conditions we calculate certain combinations of soft terms, called “invariants,” for the different classes of models. Values for all the invariants can be classified into a small number of sets, which contain information about the class of models and, in principle, the scale of beyond-minimal supersymmetric extension of the Standard Model physics, even in case the extended gauge group is broken at an energy beyond the reach of the LHC.
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Fonseca, R. M., & Grimus, W. (2014). Classification of lepton mixing matrices from finite residual symmetries. J. High Energy Phys., 09(9), 033–54pp.
Abstract: Assuming that neutrinos are Majorana particles, we perform a complete classification of all possible mixing matrices which are fully determined by residual symmetries in the charged-lepton and neutrino mass matrices. The classification is based on the assumption that the residual symmetries originate from a finite flavour symmetry group. The mathematical tools which allow us to accomplish this classification are theorems on sums of roots of unity. We find 17 sporadic cases plus one infinite series of mixing matrices associated with three-flavour mixing, all of which have already been discussed in the literature. Only the infinite series contains mixing matrices which are compatible with the data at the 3 sigma level.
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Boucenna, S. M., Fonseca, R. M., Gonzalez-Canales, F., & Valle, J. W. F. (2015). Small neutrino masses and gauge coupling unification. Phys. Rev. D, 91(3), 031702–5pp.
Abstract: The physics responsible for gauge coupling unification may also induce small neutrino masses. We propose a novel gauge-mediated radiative seesaw mechanism for calculable neutrino masses. These arise from quantum corrections mediated by new SU(3)(C) circle times SU(3)(L) circle times U(1)(X) (3-3-1) gauge bosons and the physics driving gauge coupling unification. Gauge couplings unify for a 3-3-1 scale in the TeV range, making the model directly testable at the LHC.
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Fonseca, R. M., & Hirsch, M. (2015). SU(5)-inspired double beta decay. Phys. Rev. D, 92(1), 015014–14pp.
Abstract: The short-range part of the neutrinoless double beta amplitude is generated via the exchange of exotic particles, such as charged scalars, leptoquarks and/or diquarks. In order to give a sizable contribution to the total decay rate, the masses of these exotics should be of the order of (at most) a few TeV. Here, we argue that these exotics could be the “light” (i.e., weak-scale) remnants of some B – L violating variants of SU(5). We show that unification of the standard model gauge couplings, consistent with proton decay limits, can be achieved in such a setup without the need to introduce supersymmetry. Since these nonminimal SU(5)-inspired models violate B – L, they generate Majorana neutrino masses and therefore make it possible to explain neutrino oscillation data. The light colored particles of these models can potentially be observed at the LHC, and it might be possible to probe the origin of the neutrino masses with Delta L = 2 violating signals. As particular realizations of this idea, we present two models, one for each of the two possible tree-level topologies of neutrinoless double beta decay.
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