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, \( {\mu}_{\ast}^{\textrm{SM}} \) ∼ 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(\( {Y}_{\nu}^{\dagger } \)Yν), 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(\( {Y}_{\nu}^{\dagger } \)Yν\( {Y}_{\nu}^{\dagger } \)Yν). Lastly, we use this insight to develop a new technique for an easier RG analysis applicable to scenarios with degenerate RHN masses.
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Acknowledgments
We thank David Kaiser, Juraj Klaric, Yannis Georis and Sudip Jana for many useful discussions and comments on the manuscript. The work of GC is supported by the U.S. Department of Energy under the award number DE-SC0020250. TS’s contributions to this work were made possible by the Walter Benjamin Programme of the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) — 512630918. Portions of this work were conducted in MIT’s Center for Theoretical Physics and partially supported by the U.S. Department of Energy under Contract No. DE-SC0012567. This project/publication is funded in part by the Gordon and Betty Moore Foundation. It was also made possible through the support of a grant from the John Templeton Foundation. The opinions expressed in this publication are those of the author(s) and do not necessarily reflect the views of these Foundations.
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Chauhan, G., Steingasser, T. Gravity-improved metastability bounds for the Type-I seesaw mechanism. J. High Energ. Phys. 2023, 151 (2023). https://doi.org/10.1007/JHEP09(2023)151
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DOI: https://doi.org/10.1007/JHEP09(2023)151