Abstract
The recently suggested Festina-Lente (FL) bound provides a lower bound on the masses of U(1) charged particles in terms of the positive vacuum energy. Since the charged particle masses in the Standard Model (SM) are generated by the Higgs mechanism, the FL bound provides a testbed of consistent Higgs potentials in the current dark energy-dominated universe as well as during inflation. We study the implications of the FL bound on the UV behavior of the Higgs potential for a miniscule vacuum energy, as in the current universe. We also present values of the Hubble parameter and the Higgs vacuum expectation value allowed by the FL bound during inflation, which implies that the Higgs cannot stay at the electroweak scale during this epoch.
Highlights
One obtains the Festina Lente (FL) bound [18, 19]: the mass m for every state of charge q under U(1) gauge invariance with coupling g satisfies m4 8παq2 ≥ V ≥ 0
We study the implications of the FL bound on the UV behavior of the Higgs potential for a miniscule vacuum energy, as in the current universe
We present values of the Hubble parameter and the Higgs vacuum expectation value allowed by the FL bound during inflation, which implies that the Higgs cannot stay at the electroweak scale during this epoch
Summary
The shape of the Higgs potential at UV (h vEW) that is consistent with low energy SM parameter values is not precisely determined, yet. Non-renormalizable operators that are irrelevant at the EW scale may become important at the UV scale as well. They allow various possible UV behaviors of the Higgs potential [21, 30]. The FL bound comes from a gravitational argument, it is reasonable to assume that the FL bound can be applied to cases where the Higgs dominates the vacuum energy and the Higgs remains at some UV value for a sufficient amount of time. We discuss the applicability of the FL bound in these cases for each possible UV structure of the Higgs potential
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