---
abstract: 'We analyze the consistency of electroweak breaking within the simplest “dark matter completions” of the high-scale type-I seesaw mechanism. We derive the full two-loop RGEs of the relevant parameters, including the quartic Higgs self-coupling $\lambda$ of the Standard Model. For the simplest type-I seesaw with bare “right-handed” neutrino mass terms, we find that with sizeable Yukawa couplings, the Higgs quartic self-coupling $\lambda$ becomes negative much before reaching the seesaw scale. For “large” Yukawa couplings the type-I seesaw may be inconsistent even as an effective theory. We further show that simple extensions of the canonical type-I seesaw involving a viable dark matter candidate can indeed fix this problem rendering the Higgs vacuum stable up to Planck scale. We examine two such extensions, the type-I seesaw with spontaneous lepton number violation and the recently proposed scoto-seesaw mechanism. Both have better stability properties due to the new scalars required.'
author:
- Sanjoy Mandal
- Rahul Srivastava
- 'José W. F. Valle'
bibliography:
- 'bibliography.bib'
title: ' Consistency of minimal dark matter completions of type-I seesaw'
---

Introduction {#sec:introduction}
============

The discovery of a scalar particle with 125 GeV mass plays a central role within particle physics [@Aad:2012tfa; @Chatrchyan:2012xdj]. In particular, the 