Neutrino Mass, Vacuum Stability and Higgs Inflation with Vector-Like Quarks and a Single Right-Handed Neutrino

TL;DR

We propose a minimal SM extension by adding $n$ down-type vector-like quarks and a single right-handed neutrino to address neutrino masses, electroweak vacuum stability, and Higgs inflation. The VLQs primarily stabilize the Higgs potential through renormalization-group effects, while the RHN generates light neutrino masses via a Type-I seesaw and smooths the inflationary running of the Higgs quartic coupling. By solving the RGEs at two loops for the SM and one loop for the new fermions with threshold matching, we map viable regions in $(n, M_{\mathcal{D}}, y_{\mathcal{D}})$ and compute inflationary observables $(n_s, r)$ that are consistent with Planck, WMAP, and Keck data. Compared with the VLQ-only scenario, the RHN reduces model dependence of the inflationary predictions and yields a smoother high-scale potential, making SM+(n)VLQ+RHN a predictive framework for neutrino masses, vacuum stability, and Higgs inflation.

Abstract

We investigate a Standard Model extension containing $n$ degenerate down-type isosinglet vector-like quarks (VLQs) with masses $M_{\mathcal D}$ and Yukawa couplings $y_{\mathcal D}$, supplemented by a single right-handed neutrino (RHN), aiming to simultaneously address neutrino mass generation, electroweak vacuum stability, and Higgs inflation. The VLQs play the dominant role in stabilizing the Higgs potential through their impact on the renormalization-group evolution, while the RHN generates light neutrino masses via a Type-I seesaw mechanism and smooths the high-scale running of the Higgs quartic coupling in the inflationary regime. We perform a two-loop Standard Model renormalization-group equation analysis supplemented by the one-loop contributions of the VLQs and the RHN, with proper matching across their mass thresholds. Using these RG trajectories, we identify the regions in $(n,\, y_{\mathcal D},\, M_{\mathcal D})$ that stabilize the Higgs potential up to the Planck scale while satisfying experimental constraints. Employing the RG-improved Higgs potential in the metric formulation of non-minimal Higgs inflation, we compute the inflationary observables $n_s$ and $r$. The SM+$(n)$VLQ+RHN framework yields predictions consistent with the combined Planck, WMAP, and BICEP/Keck data, while simultaneously ensuring electroweak vacuum stability and phenomenologically viable neutrino masses within well-defined regions of parameter space. For comparison, we also investigate the SM+$(n)$VLQ limit and present its vacuum stability and Higgs inflation predictions as a reference to quantify the stabilizing role of the VLQ sector.

Figures (6)

• Figure 1: Vacuum stability in the SM+$(n)$ VLQ+RHN framework. Panels (a)–(c) show the minimum value $\lambda_{\min}$ as a function of the VLQ Yukawa coupling $y_D$ for benchmark masses $M_{\mathcal{D}} = 1.5,\,3.0,\,5.0$ TeV, respectively. In each panel, curves correspond to $n=1\text{--}10$.
• Figure 2: Running of the Higgs quartic coupling $\lambda(\mu)$ in the SM+$(n)$VLQ+RHN model for the benchmark VLQ masses $M_{\mathcal{D}} = 1.5,;3.0,;5.0~\mathrm{TeV}$. The curves correspond to $n=1$--$10$ for fixed $y_{\mathcal{D}} = 0.15$ and $y_N = 0.42$, while the dashed black curve shows the SM result. The vertical dashed and dotted lines indicate the VLQ and RHN mass thresholds, respectively.
• Figure 3: Vacuum stability in the SM+$(n)$ VLQ framework. Panels (a)–(c) show the minimum value $\lambda_{\min}$ as a function of the VLQ Yukawa coupling $y_D$ for benchmark masses $M_{\mathcal{D}} = 1.5,\,3.0,\,5.0$ TeV, respectively. In each panel, curves correspond to $n=1\text{--}10$.
• Figure 4: Running of the Higgs quartic coupling $\lambda(\mu)$ in the SM+$(n)$VLQ framework for the benchmark VLQ masses $M_{\mathcal{D}} = 1.5,;3.0,;5.0~\mathrm{TeV}$. The curves correspond to $n=1$--$10$ for fixed $y_{\mathcal{D}} = 0.15$, while the dashed black curve shows the SM result. The vertical dashed line indicates the VLQ mass threshold.
• Figure 5: Predictions for the spectral index $n_s$ and tensor-to-scalar ratio $r$ in the SM+($n$)VLQ+RHN framework for benchmark VLQ masses $M_\mathcal{D} = 1.5$, $3.0$, and $5.0~\text{TeV}$. Each coloured point corresponds to a different value of $n$, with the associated non-minimal coupling $\xi$ determined by the CMB amplitude. The dark and light grey regions correspond to the 68% and 95% confidence contours from the combined Planck, WMAP, and BICEP/Keck analysis Ade:2021.