21831 2304.08542 10.1007/JHEP09(2023)151 151 151 Gravity-improved metastability bounds for the Type-I seesaw mechanism Regular Article - Theoretical Physics 1 40 2023 9 22 2023 4 30 2023 8 8 2023 9 11 2023 9 22 The Author(s) 2023 Open Access. This article is distributed under the terms of the Creative Commons Attribution License ( CC-BY 4.0 ), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. 13130 2023 2023 9 9 Garv Chauhan gchauhan@vt.edu Thomas Steingasser tstngssr@mit.edu https://ror.org/02smfhw86 grid.438526.e 0000 0001 0694 4940 Center for Neutrino Physics, Department of Physics Virginia Tech Blacksburg VA 24061 USA https://ror.org/02495e989 grid.7942.8 0000 0001 2294 713X Centre for Cosmology, Particle Physics and Phenomenology (CP3) Université catholique de Louvain Chemin du Cyclotron 2 B-1348 Louvain-la-Neuve Belgium https://ror.org/042nb2s44 grid.116068.8 0000 0001 2341 2786 Department of Physics Massachusetts Institute of Technology Cambridge MA 02139 USA https://ror.org/03vek6s52 grid.38142.3c 0000 0004 1936 754X Black Hole Initiative at Harvard University 20 Garden Street Cambridge MA 02138 USA Abstract Right-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, μ ∗ SM $$ {\mu}_{\ast}^{\textrm{SM}} $$ ∼ 1017 GeV. For large neutrino Yukawa coupling Y ν , 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 M N > 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 ν † $$ {Y}_{\nu}^{\dagger } $$ Y ν ), 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 ν † $$ {Y}_{\nu}^{\dagger } $$ Y ν Y ν † $$ {Y}_{\nu}^{\dagger } $$ Y ν ). Lastly, we use this insight to develop a new technique for an easier RG analysis applicable to scenarios with degenerate RHN masses. Keywords Anomalous Higgs Couplings Sterile or Heavy Neutrinos Renormalization Group Solitons Monopoles and Instantons ArXiv ePrint: 2304.08542