Minimal conformal extensions of the Higgs sector

TL;DR

The paper investigates how to solve the gauge hierarchy problem via conformal, radiative electroweak symmetry breaking and identifies the minimal RG-stable extension of the SM Higgs sector up to the Planck scale. Using the Gildener–Weinberg formalism and full one-loop RGEs, it shows that extensions with one extra scalar fail to remain perturbative up to $M_{ ext{Pl}}$, while the minimal viable model requires two real scalar singlets, one of which acquires a vev and mixes with the SM Higgs. In this minimal model, a light Higgs emerges as a pseudo-Goldstone boson, there is a heavier scalar that can serve as a dark matter candidate, and the Higgs-mixing is sizable and testable at colliders; neutrino masses can be accommodated and the model is constrained by LHC Higgs signal strength. The authors also discuss how a semi-classical gravity matching could realize the necessary trace-anomaly conditions and outline the phenomenological implications, including DM stability, exotic Higgs decays, and detectable Higgs-singlet mixing.

Abstract

In this work we find the minimal extension of the Standard Model's Higgs sector which can lead to a light Higgs boson via radiative symmetry breaking and is consistent with the phenomenological requirements for a low-energy realization of a conformal theory. The model which turns out to be stable under renormalization group translations is an extension of the Standard Model by two scalar fields, one of which acquires a finite vacuum expectation value and therefore mixes into the physical Higgs. We find that the minimal model predicts a sizable amount of mixing which makes it testable at a collider. In addition to the physical Higgs, the theory's scalar spectrum contains one light and one heavy boson. The heavy scalar's properties render it a potential dark matter candidate.

Figures (9)

• Figure 1: Largest possible UV scale in extensions of the conformal SM by one real SU(2)$_L$$N$-plet with vanishing vev. The color code indicates which set of beta functions and couplings are taken into account.
• Figure 2: Running of the relative contributions to the beta function of the Higgs self-coupling. The different contributions from the scalar, Yukawa and gauge sectors are displayed in blue, red and green, respectively. Note that the dashed red (dotted green) curve shows the absolute value of the negative contribution proportional to $- y^4$ ($-\lambda g^2$) for better comparison with the positive ones.
• Figure 3: Largest possible UV scale in extensions of the conformal SM by one real SU(2)$_L$$N$-plet with finite vev $v_\chi < \sqrt{2} v_\phi$. The color code indicates which set of beta functions and couplings are taken into account.
• Figure 4: Largest possible UV scale in extensions of the conformal SM by one complex SU(2)$_L$$N$-plet with hypercharge $Y$ and vanishing vev.
• Figure 5: Largest possible UV scale in extensions of the conformal SM by two real scalar SU(2)$_L$ multiplets with vanishing vevs. The results were obtained using RGEs including Left: scalar contributions only. Right: scalar and top-quark contributions.