# Consistency of the dynamical high-scale type-I seesaw mechanism

## TL;DR

This paper investigates the stability of the Standard Model with high-scale type-I seesaw mechanisms, highlighting issues with large Yukawa couplings and proposing a more stable dynamical model with spontaneous lepton number violation.

## Contribution

It derives full two-loop RGEs for the model and compares the stability of bare versus dynamical high-scale seesaw scenarios.

## Key findings

- Large Yukawa couplings can destabilize the Higgs potential below the seesaw scale.
- Bare right-handed neutrino mass terms lead to negative Higgs quartic coupling, risking inconsistency.
- Dynamical high-scale seesaw with spontaneous lepton number violation exhibits better stability.

## Abstract

We analyze the consistency of electroweak breaking within the simplest high-scale Standard Model type-I seesaw mechanism. We derive the full two-loop RGEs of the relevant parameters, including the quartic Higgs self-coupling of the Standard Model. For the simplest case of bare "right-handed" neutrino mass terms we find that, with large Yukawa couplings, the Higgs quartic self-coupling becomes negative much below the seesaw scale, so that the model may be inconsistent even as an effective theory. We show, however, that the "dynamical" type-I high-scale seesaw with spontaneous lepton number violation has better stability properties.