The swampland conjecture and the Higgs expectation value

TL;DR

The paper examines how the swampland conjecture challenges the Standard Model with a Higgs potential, revealing that coupling to a quintessence field leads to observable long-range forces and time-dependent effects, conflicting with experimental constraints.

Contribution

It demonstrates that coupling the Higgs potential to a quintessence field under the swampland conjecture induces problematic long-range forces and time variations, challenging the viability of such models.

Findings

Q-dependent Higgs VEV causes long-range forces

Time-dependent Higgs VEV conflicts with proton-electron mass ratio measurements

Fine-tuning and radiative corrections undermine the model's consistency

Abstract

The recently proposed de Sitter swampland conjecture excludes local extrema of a scalar potential with a positive energy density in a low energy effective theory. Under the conjecture, the observed dark energy cannot be explained by the cosmological constant. The local maximum of the Higgs potential at the symmetric point also contradicts with the conjecture. In order to make the Standard Model consistent with the conjecture, it has been proposed to introduce a quintessence field, $Q$, which couples to the cosmological constant and the local maximum of the Higgs potential. In this paper, we show that such a modified Higgs potential generically results in a $Q$-dependent Higgs vacuum expectation value (VEV). The $Q$-dependence of the Higgs VEV induces a long-range force, which is severely excluded by the tests of the equivalence principle. Besides, as the quintessence field is in motion, the Higgs VEV shows a time-dependence, which is also severely constrained by the measurements of the time-dependence of the proton-to-electron mass ratio. Those constraints require an additional fine-tuning which is justified neither by the swampland conjecture nor the anthropic principle. We further show that, even if such an unjustified fine-tuning condition is imposed at the tree level, radiative corrections upset it. Consequently, we argue that most of the habitable vacua in the string landscape are in tension with the phenomenological constraints.