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Cepedello, R., Fonseca, R. M., & Hirsch, M. (2018). Systematic classification of three-loop realizations of the Weinberg operator. J. High Energy Phys., 10(10), 197–34pp.
Abstract: We study systematically the decomposition of the Weinberg operator at three-loop order. There are more than four thousand connected topologies. However, the vast majority of these are infinite corrections to lower order neutrino mass diagrams and only a very small percentage yields models for which the three-loop diagrams are the leading order contribution to the neutrino mass matrix. We identify 73 topologies that can lead to genuine three-loop models with fermions and scalars, i.e. models for which lower order diagrams are automatically absent without the need to invoke additional symmetries. The 73 genuine topologies can be divided into two sub-classes: normal genuine ones (44 cases) and special genuine topologies (29 cases). The latter are a special class of topologies, which can lead to genuine diagrams only for very specific choices of fields. The genuine topologies generate 374 diagrams in the weak basis, which can be reduced to only 30 distinct diagrams in the mass eigenstate basis. We also discuss how all the mass eigenstate diagrams can be described in terms of only five master integrals. We present some concrete models and for two of them we give numerical estimates for the typical size of neutrino masses they generate. Our results can be readily applied to construct other d = 5 neutrino mass models with three loops.
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Anamiati, G., Castillo-Felisola, O., Fonseca, R. M., Helo, J. C., & Hirsch, M. (2018). High-dimensional neutrino masses. J. High Energy Phys., 12(12), 066–26pp.
Abstract: For Majorana neutrino masses the lowest dimensional operator possible is the Weinberg operator at d = 5. Here we discuss the possibility that neutrino masses originate from higher dimensional operators. Specifically, we consider all tree-level decompositions of the d = 9, d = 11 and d = 13 neutrino mass operators. With renormalizable interactions only, we find 18 topologies and 66 diagrams for d = 9, and 92 topologies plus 504 diagrams at the d = 11 level. At d = 13 there are already 576 topologies and 4199 diagrams. However, among all these there are only very few genuine neutrino mass models: At d = (9, 11, 13) we find only (2,2,2) genuine diagrams and a total of (2,2,6) models. Here, a model is considered genuine at level d if it automatically forbids lower order neutrino masses without the use of additional symmetries. We also briefly discuss how neutrino masses and angles can be easily fitted in these high-dimensional models.
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Fonseca, R. M., & Hirsch, M. (2017). Gauge vectors and double beta decay. Phys. Rev. D, 95(3), 035033–14pp.
Abstract: We discuss contributions to neutrinoless double beta (0 nu beta beta) decay involving vector bosons. The starting point is a list of all possible vector representations that may contribute to 0 nu beta beta decay via d = 9 or d = 11 operators at tree level. We then identify gauge groups which contain these vectors in the adjoint representation. Even though the complete list of vector fields that can contribute to 0 nu beta beta up to d = 11 is large (a total of 46 vectors), only a few of them can be gauge bosons of phenomenologically realistic groups. These latter cases are discussed in some more detail, and lower (upper) limits on gauge boson masses (mixing angles) are derived from the absence of 0 nu beta beta decay.
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Arbelaez, C., Hirsch, M., & Restrepo, D. (2017). Fermionic triplet dark matter in an SO(10)-inspired left-right model. Phys. Rev. D, 95(9), 095034–9pp.
Abstract: We study a left right (LR) extension of the Standard Model (SM) where the Dark Matter(DM) candidate is composed of a set of fermionic Majorana triplets. The DM is stabilized by a remnant Z(2) symmetry from the breaking of the LR group to the SM. Two simple scenarios where the DM particles plus a certain set of extra fields lead to gauge coupling unification with a low LR scale are explored. The constraints from relic density and predictions for direct detection are discussed for both scenarios. The first scenario with a SUd(2)(R) vectorlike fermion triplet contains a DM candidate which is almost unconstrained by current direct detection experiments. The second scenario, with an additional SU(2)R triplet, opens up a scalar portal leading to direct detection constraints which are similar to collider limits for right gauge bosons. The DM parameter space consistent with phenomenological requirements can also lead to successful gauge coupling unification in a SO(10) setup.
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Arbelaez, C., Gonzalez, M., Kovalenko, S. G., & Hirsch, M. (2017). QCD-improved limits from neutrinoless double beta decay. Phys. Rev. D, 96(1), 015010–12pp.
Abstract: We analyze the impact of QCD corrections on limits derived from neutrinoless double beta decay (0 nu beta beta ). As demonstrated previously, the effect of the color mismatch arising from loops with gluons linking the quarks from different color-singlet currents participating in the effective operators has a dramatic impact on the predictions for some particular Wilson coefficients. Here, we consider all possible contributions from heavy particle exchange, i.e. the so-called short-range mechanism of 0 nu beta beta decay. All high-scale models (HSM) in this class match at some scale around a similar to few TeV with the corresponding effective theory, containing a certain set of effective dimension-9 operators. Many of these HSM receive contributions from more than one of the basic operators and we calculate limits on these models using the latest experimental data. We also show with one nontrivial example, how to derive limits on more complicated models, in which many different Feynman diagrams contribute to 0 nu beta beta decay, using our general method.
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