Consistency of the triplet seesaw model revisited

TL;DR

This paper reexamines the type-II seesaw model with a scalar triplet, correcting previous bounded-from-below conditions and analyzing the implications for neutrino mass generation and vacuum stability.

Contribution

It provides a revised analysis of the scalar potential's stability conditions in the triplet seesaw model, highlighting significant corrections to prior assumptions.

Findings

Corrected bounded-from-below conditions for the scalar potential

Identification of scenarios with significant impact from the correction

Sketch of the expected scalar boson profile under the revised conditions

Abstract

Adding a scalar triplet to the Standard Model is one of the simplest ways of giving mass to neutrinos, providing at the same time a mechanism to stabilize the theory's vacuum. In this paper, we revisit these aspects of the type-II seesaw model pointing out that the bounded-from-below conditions for the scalar potential in use in the literature are not correct. We discuss some scenarios where the correction can be significant and sketch the typical scalar boson profile expected by consistency.