Minimal Tree-Level Seesaws with a Heavy Intermediate Fermion

TL;DR

This paper classifies minimal tree-level seesaw models with a heavy fermion mediator that naturally generate small neutrino masses, extending known models and identifying a finite set of natural, non-tuned variants.

Contribution

It systematically enumerates all minimal, natural tree-level seesaw models with a heavy fermion, including new variants beyond Type-I and Type-III.

Findings

Finite set of minimal models identified

New models generalizing Type-I and Type-III seesaws presented

Exhaustive classification of non-tuned variants achieved

Abstract

There exists a generic minimal tree-level diagram, with two external scalars and a heavy intermediate fermion, that can generate naturally small neutrino masses via a seesaw. This diagram has a mass insertion on the internal fermion line, and the set of such diagrams can be partitioned according to whether the mass insertion is of the Majorana or Dirac type. We show that, once subjected to the demands of naturalness (i.e. precluding small scalar vacuum expectation values that require fine-tuning), this set is finite, and contains a relatively small number of elements. Some of the corresponding models have appeared in the literature. We present the remaining original models, thus generalizing the Type-I and Type-III seesaws, and apparently exhausting the list of their minimal non-tuned variants.