Systematic classification of three-loop realizations of the Weinberg operator

Understand

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.