One-loop renormalization of the electroweak chiral Lagrangian with a light Higgs

We consider the general chiral effective action which parametrizes the nonlinear realization of the spontaneous breaking of the electroweak symmetry with a light Higgs, and compute the one-loop ultraviolet divergences coming from Higgs and electroweak Goldstone fluctuations using the background field method. The renormalization of the divergences is carried out through operators of next-to-leading order in the chiral counting, i.e. of O(p^4). Being of the same order in power counting, the logarithmic corrections linked to these divergences can be as important as the tree-level contributions from the O(p^4) operators, and must be accounted for in the phenomenological analysis of experimental data. Deviations in the O(p^2) (leading-order) couplings with respect to the Standard Model values, e.g., in the h->WW coupling, would generate contributions from the 1-loop chiral logarithms computed in this work to a vast variety of observables, which do not have a counterpart in the conventional electroweak effective theory with a linearly transforming Higgs complex doublet.