The Other Natural Two Higgs Doublet Model

TL;DR

The paper develops a framework for natural two-Higgs-doublet models in which both Higgses are PNGBs from a strong sector, analyzed via CCWZ with spurions controlling explicit G-breaking from SM couplings. Discrete symmetries, notably a $C_2$ parity or a CP-like $C_1P$, and potential extended custodial symmetry, are shown to be sufficient to tame the $\hat{T}$ parameter and Higgs-mediated FCNC, enabling calculable potentials dominated by top-sector effects. Explicit realizations based on the $SO(6)/SO(4)\times SO(2)$ coset (and notes on extended custodial cases) yield a spectrum where a SM-like light Higgs coexists with a richer set of heavier scalars, which can be inert or almost inert depending on the symmetry choices. The phenomenology predicts small corrections to Higgs couplings proportional to $\xi=v^2/f^2$, custodial-symmetry–protected relations among scalar masses, and characteristic production/decay patterns (e.g., suppressed $H^\pm W^\mp Z$ couplings and potential dark-matter–like inert states), with clear signatures accessible at the LHC and future colliders.

Abstract

We characterize models where electroweak symmetry breaking is driven by two light Higgs doublets arising as pseudo-Nambu-Goldstone bosons of new dynamics above the weak scale. They represent the simplest natural two Higgs doublet alternative to supersymmetry. We construct their low-energy effective Lagrangian making only few specific assumptions about the strong sector. These concern their global symmetries, their patterns of spontaneous breaking and the sources of explicit breaking. In particular we assume that all the explicit breaking is associated with the couplings of the strong sector to the Standard Model fields, that is gauge and (proto)-Yukawa interactions. Under those assumptions the scalar potential is determined at lowest order by very few free parameters associated to the top sector. Another crucial property of our scenarios is the presence of a discrete symmetry, in addition to custodial SO(4), that controls the $T$-parameter. That can either be simple CP or a $Z_2$ that distinguishes the two Higgs doublets. Among various possibilities we study in detail models based on SO(6)/SO(4)$\times$ SO(2), focussing on their predictions for the structure of the scalar spectrum and the deviations of their couplings from those of a generic renormalizable two Higgs doublet model.

Figures (5)

• Figure 1: Pictorial representation of our scenario.
• Figure 2: Power counting for the Higgs potential.
• Figure 3: The contribution from the exchange of heavy modes to the Yukawas and to the FCNC operators.
• Figure 4: Branching ratios for $H^0$ in the almost inert Higgs model.
• Figure 5: Branching ratios for $H^+$ and $A^0$ in the almost inert Higgs model.