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

We consider the general chiral effective action which parametrizes the nonlinear realization of the spontaneous breaking of the electroweak symmetry with a light Higgs boson 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 one-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.