Further investigation on the precise formulation of the equivalence theorem

Based on a systematic analysis of the renormalization schemes in the general R_ξ gauge, the precise formulation of the equivalence theorem for longitudinal weak boson scatterings is given both in the SU(2)L Higgs theory and in the realistic SU(2) ×{} U(1) electroweak theory to all orders in the perturbation for an arbitrary Higgs boson mass mH. It is shown that there is generally a renormalization-scheme- and ξ dependent modification factor Cmod and a simple formula for Cmod is obtained. Furthermore, a convenient particular renormalization scheme is proposed in which Cmod is exactly unity. Results of Cmod in other currently used schemes are also discussed especially on their ξ and mH dependence through explicit one-loop calculations. It is shown that in some currently used schemes the deviation of Cmod from unity and the ξ dependence of Cmod are significant even in the large-mH limit. Therefore care should be taken when applying the equivalence theorem.