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.
Highlights
The Mexican hat potential is reminiscent of the effective potential for conventional superconductivity proposed by Ginzburg and Landau in 1950 [7]
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
The most important observation for our purpose is that there are only 7 unknown ci’s in eq (2.46), which parameterize effects of the incalculable ultraviolet physics. These 6 coefficients enter into tables 1–3, which contain a total of 25 operators entering HVV, HHVV, HVVV and TGC couplings
Summary
The effective Lagrangian involving the self-interactions of the 125 GeV Higgs in composite Higgs models is universal, other light degrees of freedom, if there, could contribute to on-shell amplitudes of the Higgs boson as an intermediate propagator. H2 could contribute to S-matrix elements involving four external h1 bosons. The existence of such a contribution does not invalidate the universal relations, which. Relate couplings in the effective Lagrangian, not S-matrix elements. Their presence complicates the experimental effort to verify and test the universal relations, as additional observables and techniques might be necessary to disentangle the H1VV and H1H1VV couplings from the rest. This is not dissimilar to efforts to measure different tensor structures of HVV couplings using differential distributions of decay products and multivariate techniques. We include two appendices: appendix A on our convention of SO(4) group generators and appendix B on matching the universal nonlinear Lagrangian to linearized dimension-6 operators
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