Constraining the EW Hierarchy from the Weak Gravity Conjecture

Abstract

In this addendum we complement the remarks made in ref[1] constraining the value of the cosmological constant ${\Lambda }_4$ in terms of neutrino masses. Those were based on a sharpened version of the Weak Gravity Conjecture as applied to compactifications of the SM to lower dimensions. We argue that the same line of reasoning implies that for fixed values of ${\Lambda }_4$ and the Yukawa coupling of the lightest neutrino $Y_{{\nu }_1}$, the EW scale is bounded above. This is a trivial consequence of neutrino masses depending on the Higgs vev. In the case of massive Majorana neutrinos with a see-saw mechanism associated to a large scale $M\simeq 10^{10-14}$ GeV and $Y_{{\nu }_1}\simeq 10^{-3}$, one obtains that the EW scale cannot exceed $M_{EW}\lesssim 10^2-10^4$ GeV. From this point of view, the delicate fine-tuning required to get a small EW scale would be a mirage, since parameters yielding higher EW scales would be in the swampland and would not count as possible consistent theories. This would bring a new perspective into the issue of the EW hierarchy.

3 pages, 2 figures

References in corpus (3)

• On the Geometry of the String Landscape and the Swampland
• Non-supersymmetric AdS and the Swampland
• Standard Model Vacua for Two-dimensional Compactifications

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• The String Landscape, the Swampland, and the Missing Corner
• The FL bound and its phenomenological implications
• Fine Tuning, Sequestering, and the Swampland
• The Fundamental Need for a SM Higgs and the Weak Gravity Conjecture
• Swampland Constraints on Neutrino Masses
• A dS obstruction and its phenomenological consequences
• Why The Cosmological Constant is a Boundary Condition
• AdS Swampland Conjectures and Light Fermions