Universal relations in composite Higgs models

Abstract

We initiate a phenomenological study of "universal relations" in composite Higgs models, which are dictated by nonlinear shift symmetries acting on the 125 GeV Higgs boson. These are relations among one Higgs couplings with two electroweak gauge bosons (HVV), two Higgses couplings with two electroweak gauge bosons (HHVV), one Higgs couplings with three electroweak gauge bosons (HVVV), as well as triple gauge boson couplings (TGC), which are all controlled by a single input parameter: the decay constant f of the pseudo-Nambu-Goldstone Higgs boson. Assuming custodial invariance in strong sector, the relation is independent of the symmetry breaking pattern in the UV, for an arbitrary symmetric coset G/H. The complete list of corrections to HVV, HHVV, HVVV and TGC couplings in composite Higgs models is presented to all orders in 1/f , and up to four-derivative level, without referring to a particular G/H. We then present several examples of universal relations in ratios of coefficients which could be extracted experimentally. Measuring the universal relation requires a precision sensitive to effects of dimension-8 operators in the effective Lagrangian and highlights the importance of verifying the tensor structure of HHVV interactions in the standard model, which remains untested to date. arXiv:1809.09126v1 [hep-ph]

The infrared structure of exceptional scalar theories

“…Recent works [59,68,69] present interesting single trace results, while NGB interactions at four derivative level clearly contains double trace contributions. On the other hand, with the tools at hand we can study the soft limit of the NGB interactions beyond the two derivative Lagrangian, and the four derivative terms have important phenomenological applications for the study of the Higgs boson in new physics models [70,71]. Scalar EFTs also appear in a wide range of models of cosmology, and the shift symmetry in these models leads to important observable effects [72].…”

Composite Higgs revealed in Higgs pair photo-production at future colliders

“…The coset-independence of the relation between the W ± /Z masses and the compositeness scale leads to universal couplings of the Higgs boson to the electroweak gauge bosons, as observed in refs. [33,34]. These couplings can be elegantly expressed in terms of derivatives with respect to the misalignment angle, as follows:…”

Soft bootstrap and effective field theories

“…At O(p 4 ), the number of independent operators is enumerated in Refs. [47,48] for the SO(5)/SO(4) coset, although we checked that the counting is valid for all N. 8 Again, using the completeness relation in Eq. (87) all flavor indices are contracted by Kronecker deltas:…”