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) × 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.
Highlights
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
That can lead to large contributions to the T -parameter even when the custodial symmetry is preserved by the strong sector
No combination of C1, C2 and P is even an approximate symmetry. In this situation CP is violated at O(1) by the top-Higgs sector, and the custodial symmetry is broken at O(1) by the vacuum expectation value (VEV) structure
Summary
The basic structure of our composite-Higgs scenario is as follows. As depicted in figure 1, there exists a new sector, that we denote as “strong”, or “strongly-interacting” sector, which is endowed with a global group G of symmetry, spontaneously broken to H ⊂ G. At the leading two-derivatives order, the sigma-model interactions are dictated by the dimension-full coupling 1/f which, given our assumptions on the strong sector, has to be identified with gρ/mρ, leading to the relation mρ gρf Notice that it is only if the NGB form an irreducible representation of H that their two-derivative interactions are completely fixed, and predicted, in terms of a unique parameter f. We could write bilinear terms, involving one left- and one right-handed fermion coupled to a bosonic strong sector operator with the quantum numbers of the Higgs This is the standard mechanism for fermions mass generation in technicolor-like theories. The Higgs bosons Π, because of their NGB nature, only appear in combination with the decay constant f , through the dimensionless functions Fi n This notably occurs in the minimal SO(5)/SO(4) composite Higgs model (MCHM) [2]
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