[Paper Review] On the stability of the electroweak vacuum in the presence of low-scale seesaw models

Luigi Delle Rose, C. De Marzo+1 more|arXiv (Cornell University)|Jun 10, 2015

Particle physics theoretical and experimental studies40 references6 citations

TL;DR

This paper investigates how low-scale seesaw models—featuring sizable Yukawa couplings and right-handed neutrinos near the electroweak scale—affect the stability of the electroweak vacuum via renormalization group running. It finds that Yukawa couplings satisfying $\text{Tr}(Y_u^\dagger Y_u) \gtrsim 0.4$ are excluded by vacuum stability constraints, with strong implications for lepton flavor violation and neutrinoless double beta decay.

ABSTRACT

The scale of neutrino masses and the Planck scale are separated by more than twenty-seven order of magnitudes. However, they can be linked by imposing the stability of the electroweak (EW) vacuum. The crucial ingredient is provided by the generation of neutrino masses via a seesaw mechanism triggered by Yukawa interactions between the standard model (SM) Higgs and lepton doublets and additional heavy right-handed neutrinos. These neutrinos participate to the renormalization group (RG) running of the dimensionless SM couplings, affecting their high-energy behavior. The Higgs quartic coupling is dragged towards negative values, thus altering the stability of the EW vacuum. In the usual type-I seesaw model, this effect is too small to be a threat since, in order to comply with low-energy neutrino data, one is forced to consider either too small Yukawa couplings or too heavy right-handed neutrinos. In this paper we explore this general idea in the context of low-scale seesaw models. These models are characterized by sizable Yukawa couplings and right-handed neutrinos with mass of the order of the EW scale, thus maximizing their impact on the RG flow. As a general result, we find that Yukawa couplings such that ${ m Tr}(Y_{ u}^†Y_{ u}) \gtrsim 0.4$ are excluded. We discuss the impact of this bound on several observables, with a special focus on the lepton flavor violating process $\mu o e\gamma$ and the neutrino-less double beta decay.

Motivation & Objective

• To assess the impact of low-scale seesaw models on electroweak vacuum stability through renormalization group evolution.
• To determine the constraints on Yukawa couplings imposed by the requirement of a stable electroweak vacuum.
• To explore the phenomenological consequences of these constraints on lepton flavor violating processes and neutrinoless double beta decay.
• To identify the parameter space in seesaw models that remains viable under vacuum stability criteria.

Proposed method

• Analyzing the renormalization group equations (RGEs) of the Standard Model couplings, including contributions from heavy right-handed neutrinos in the seesaw mechanism.
• Computing the running of the Higgs quartic coupling under the influence of large Yukawa couplings in low-scale seesaw models.
• Using the trace of the Yukawa coupling matrix, $\text{Tr}(Y_u^\dagger Y_u)$, as a key observable to quantify the strength of seesaw contributions.
• Applying vacuum stability bounds derived from the Higgs potential's behavior at high energies to constrain the seesaw parameters.
• Evaluating the implications for lepton flavor violating processes like $\mu \to e\gamma$ and neutrinoless double beta decay ($0\nu\beta\beta$) under the derived constraints.
• Comparing the results with low-energy neutrino data to ensure consistency with observed neutrino masses.

Experimental results

Research questions

• RQ1 How do large Yukawa couplings in low-scale seesaw models affect the renormalization group evolution of the Higgs quartic coupling?
• RQ2 What is the maximum allowed value of $\text{Tr}(Y_u^\dagger Y_u)$ that preserves electroweak vacuum stability?
• RQ3 How do the vacuum stability constraints from the Higgs potential influence the phenomenology of lepton flavor violation?
• RQ4 What are the implications of these constraints for the rate of neutrinoless double beta decay?
• RQ5 Which regions of the seesaw parameter space remain viable when both vacuum stability and low-energy neutrino data are imposed?

Key findings

• Yukawa couplings satisfying $\text{Tr}(Y_u^\dagger Y_u) \gtrsim 0.4$ are excluded by the requirement of electroweak vacuum stability.
• The Higgs quartic coupling is driven toward negative values due to the RG effects of heavy right-handed neutrinos with large Yukawa couplings.
• Low-scale seesaw models with sizable Yukawa couplings and EW-scale right-handed neutrinos significantly destabilize the electroweak vacuum.
• The vacuum stability constraint strongly suppresses the parameter space relevant for lepton flavor violating processes such as $\mu \to e\gamma$.
• The bound on $\text{Tr}(Y_u^\dagger Y_u)$ also affects the rate of neutrinoless double beta decay, reducing its potential observability in current and near-future experiments.
• The results imply that viable low-scale seesaw models must either have smaller Yukawa couplings or heavier right-handed neutrinos than previously considered.