The Weak Scale as a Trigger

TL;DR

This paper investigates how the Higgs mass parameter can act as a trigger for certain local operators, proposing models where this trigger influences the weak scale and potentially relates to dark matter and the cosmological constant.

Contribution

It introduces a novel mechanism where Higgs mass parameters trigger specific operators, including a new two Higgs doublet model with testable predictions at colliders.

Findings

Higgs mass can trigger the operator Tr(G tilde G) in the Standard Model.

A new two Higgs doublet model with a Z4 symmetry is proposed, predicting light Higgs states.

The model remains viable under current collider constraints and will be tested by future experiments.

Abstract

Does the value of the Higgs mass parameter affect the expectation value of local operators in the Standard Model? For essentially all local operators the answer to this question is "no", and this is one of the avatars of the hierarchy problem: nothing is "triggered" when the Higgs mass parameter crosses zero. In this letter, we explore settings in which Higgs mass parameters $can$ act as a "trigger" for some local operators ${\cal O}_T$. In the Standard Model, this happens for ${\cal O}_T = {\rm Tr} (G \tilde G)$. We also introduce a "type-0" two Higgs doublet model, with a $Z_4$ symmetry, for which ${\cal O}_T = H_1 H_2$ is triggered by the Higgs masses, demanding the existence of new Higgs states necessarily comparable to or lighter than the weak scale, with no wiggle room to decouple them whatsoever. Surprisingly, this model is not yet entirely excluded by collider searches, and will be incisively probed by the high-luminosity run of the LHC, as well as future Higgs factories. We also discuss a possibility for using this trigger to explain the origin of the weak scale, invoking a landscape of extremely light, weakly interacting scalars $\phi_i$, with a coupling to ${\cal O}_T$ needed to make it possible to find vacua with small enough cosmological constant. The weak scale trigger links the tuning of the Higgs mass to that of the cosmological constant, while coherent oscillations of the $\phi_i$ can constitute dark matter.