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We perform a Bayesian statistical analysis of the constraints on thenonlinear Effective Theory given by the Higgs electroweak chiral Lagrangian. Weobtain bounds on the effective coefficients entering in Higgs observables atthe leading order, using all available Higgs-boson signal strengths from theLHC runs 1 and 2. Using a prior dependence study of the solutions, we discussthe results within the context of natural-sized Wilson coefficients. We furtherstudy the expected sensitivities to the different Wilson coefficients atvarious possible future colliders. Finally, we interpret our results in termsof some minimal composite Higgs models.

Current and future constraints on Higgs couplings in the nonlinear Effective Theory