Chauhan, GarvSteingasser, Thomas2023-09-252023-09-252023-09-22Journal of High Energy Physics. 2023 Sep 22;2023(9):151http://hdl.handle.net/10919/116323Right-handed neutrinos (RHN) destabilize the electroweak vacuum by increasing its decay rate. In the SM, the latter is dominated by physics at the RG scale at which λ reaches its minimum, 𝜇SM∗ ∼ 1017 GeV. For large neutrino Yukawa coupling Yν, RHNs can push μ* beyond the Planck scale, implying that gravitational effects need to be taken into account. In this work, we perform the first comprehensive study of electroweak vacuum metastability in the type-I seesaw mechanism including these effects. Our analysis covers both low- and high-scale seesaw models, with two as well as three RHNs and for multiple values of the Higgs’ non-minimal coupling to gravity. We find that gravitational effects can significantly stabilize the vacuum, leading to weaker metastability bounds. We show that metastability sets the strongest bounds for low-scale seesaws with MN > 1 TeV. For high-scale seesaws, we find upper bounds on the allowed masses for the RHNs, which are relevant for high-scale leptogenesis. We also point out that Tr(𝑌†𝜈Yν), which is commonly used to express these metastability bounds, cannot be used for all of parameter space. Instead, we argue that bounds can always be expressed reliably through Tr(𝑌†𝜈Yν𝑌†𝜈Yν). Lastly, we use this insight to develop a new technique for an easier RG analysis applicable to scenarios with degenerate RHN masses.application/pdfenCreative Commons Attribution 4.0 InternationalArticle - Refereed2023-09-24The Author(s)https://doi.org/10.1007/JHEP09(2023)151