Abstract
We compute the 1-loop correction to the electroweak observables from spin-1 resonances in SO(5)/SO(4) composite Higgs models. The strong dynamics is modeled with an effective description comprising the Nambu-Goldstone bosons and the lowest-lying spin-1 resonances. A classification is performed of the relevant operators including custodially-breaking effects from the gauging of hypercharge. The 1-loop contribution of the resonances is extracted in a diagrammatic approach by matching to the low-energy theory of Nambu-Goldstone bosons. We find that the correction is numerically important in a significant fraction of the parameter space and tends to weaken the bounds providing a negative shift to the S parameter.
Highlights
The strong dynamics is modeled with an effective description comprising the Nambu-Goldstone bosons and the lowest-lying spin1 resonances
These latter are assumed to be lighter and more weakly interacting than the other composite states at the cutoff. This working assumption might not be realized by the underlying strong dynamics, we expect our calculation to give a quantitative approximate description of the contributions from spin-1 resonances arising in full models
In order to estimate the coefficients of the operators appearing in the effective Lagrangian, we adopt the criterion of Partial UV Completion (PUVC) [35]
Summary
We construct the low-energy effective Lagrangian describing the NG bosons and massive spin-1 resonances by using the formalism of Callan, Coleman, Wess and Zumino (CCWZ) [33, 34] for SO(5)/SO(4). In order to estimate the coefficients of the operators appearing in the effective Lagrangian, we adopt the criterion of Partial UV Completion (PUVC) [35] This premises that the coupling strengths of the resonances to the NG bosons and to themselves do not exceed, and preferably saturate, the σ-model coupling g∗ = Λ/f at the cutoff scale. Under this assumption, neglecting for simplicity CP -odd operators, the leading terms in the Lagrangian are. Among the operators involving χ, we have kept only those relevant for the present analysis
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