Chinese Acad Sci, Inst High Energy Phys, Beijing 100039, Peoples R China
We study the renormalization of the nonlinear effective SU(2) Lagrangian up to O(p(4)) with spontaneous symmetry breaking. The Stueckelberg transformation, the background field gauge, the Schwinger proper time and heat kernel method, and the covariant short distance expansion technology guarantee gauge covariance and incorporate the Ward (Slavnov-Taylor) identities in the calculations. A modified power counting rule is introduced to consistently estimate and control the contributions of higher loops and higher-dimension operators. The one-loop renormalization group equations of the effective couplings are provided and analyzed. We find that the difference between the results obtained from the direct method and the renormalization group equation method can be quite large when the Higgs scalar boson is far below its decoupling limit. The exact one-loop calculation of d(1) in the renormalizable SU(2) Higgs model is provided to understand such a difference. A better way of calculating at the one-loop level in the framework of the effective theory method is suggested.