Abstract
We provide a complete systematic classification of all two-loop realizations of the dimension four operator for Dirac neutrino masses. Our classification is multi-layered, starting first with a classification in terms of all possible distinct two loop topologies. Then we discuss the possible diagrams for each topology. Model-diagrams originating from each diagram are then considered. The criterion for genuineness is also defined and discussed at length. Finally, as examples, we construct two explicit models which also serve to highlight the intimate connection between the Dirac nature of neutrinos and the stability of dark matter.
Highlights
We have identified all the 1 Particle Irreducible (1PI) topologies and diagrams with 3 external legs, two-loops and 3, 4-point vertices which gives the dominant contribution to the neutrino mass
A set of 18 renormalizable diagrams are generated straightforward from the 5 genuine topologies
The three diagrams generated from topologies T1 and T2 given in figure 3 are genuine in general
Summary
We start our discussion by first introducing certain key concepts and setting up the notation in generic terms. In principle the choice of the symmetries used to forbid tree-level masses and ensuring the Dirac nature of neutrinos is model-dependent, some general conclusions can be given in order to establish a useful classification for model builders. It is important to clarify that if one imposes a symmetry that forbids the tree-level Dirac mass term, all the realizations of the operator LφcνR(φ†φ)n with n ∈ N will automatically vanish For this reason, one must break such a symmetry, either softly or spontaneously, in order to allow radiative or higher-dimensional Dirac neutrino mass models such that the tree-level term is still absent [28, 32, 53]. Since this would increase the dimensionality of the UV complete Dirac mass operator, we will not study it further
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