On the renormalization of the electroweak chiral Lagrangian with a Higgs

We consider the scalar sector of the effective non-linear electroweak Lagrangian with a light "Higgs" particle. For a leading order Lagrangian, the complete one-loop off-shell renormalization procedure is performed, including the effects of a finite Higgs mass. This determines the complete set of independent chiral invariant scalar counterterms required for consistency; these include bosonic operators often disregarded. A novel general parametrization of the Goldstone boson matrix is proposed, which reduces to the various usual ones for specific values of its parameter. Furthermore, new counterterms involving the Higgs field which are apparently chiral non-invariant are identified in the perturbative analysis. A redefinition of the Goldstone boson fields which absorbs all chiral non-invariant counterterms is then explicitly determined. The physical results translate into renormalization group equations which may be useful when comparing future Higgs data at different energies.