Systematic classification of three-loop realizations of the Weinberg operator

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.Comment: Erratum added, published version in JHE

Proton decay and light sterile neutrinos

Within the standard model, non-renormalizable operators at dimension six ($d=6$) violate baryon and lepton number by one unit and thus lead to proton decay. Here, we point out that the proton decay mode with a charged pion and missing energy can be a characteristic signature of $d=6$ operators containing a light sterile neutrino, if it is not accompanied by the standard $\pi^0e^+$ final state. We discuss this effect first at the level of effective operators and then provide a concrete model with new physics at the TeV scale, in which the lightness of the active neutrinos and the stability of the proton are related.Comment: 7 pages, 2 figures, published versio

Proton decay at 1-loop

Proton decay is usually discussed in the context of grand unified theories. However, as is well-known, in the standard model effective theory proton decay appears in the form of higher dimensional non-renormalizable operators. Here, we study systematically the 1-loop decomposition of the $d=6$ $B+L$ violating operators. We exhaustively list the possible 1-loop ultra-violet completions of these operators and discuss that, in general, two distinct classes of models appear. Models in the first class need an additional symmetry in order to avoid tree-level proton decay. These models necessarily contain a neutral particle, which could act as a dark matter candidate. For models in the second class the loop contribution dominates automatically over the tree-level proton decay, without the need for additional symmetries. We also discuss possible phenomenology of two example models, one from each class, and their possible connections to neutrino masses, LHC searches and dark matter.Comment: 13 pages, 7 figure