Seesaw Models of Neutrino Masses on the Convex Cone of Positivity Bounds

TL;DR

This paper uses convex positivity bounds to analyze seesaw models of neutrino masses, providing a geometric framework to constrain UV states and distinguish between models based on their effective operators.

Contribution

It introduces a convex cone of positivity bounds tailored to seesaw models, enabling new constraints on the seesaw scale and UV states from a bottom-up geometric perspective.

Findings

Constrains UV states in seesaw models using positivity bounds.

Provides a method to differentiate seesaw models based on effective operators.

Derives lower bounds on the seesaw scale.

Abstract

The convex geometric framework of positivity bounds allows us to explore the ultraviolet (UV) states in new physics models from the bottom up. The UV states in three types of seesaw models for tiny Majorana neutrino masses, as irreducible representations of the ${\rm SU}(2)^{}_{\rm L}$ gauge group, naturally fit into this framework. Since neutrino masses arising from the dimension-five Weinberg operator imply that the UV states may couple to the left-handed lepton doublet $L$ and the Higgs doublet $H $, we construct a convex cone of positivity bounds to constrain the dimension-eight operators consisting of $L$ or $H$. Such a construction offers a novel way to distinguish between different seesaw models and derive lower bounds on the seesaw scale.