On the precise formulation of the equivalence theorem

A systematic analysis of renormalization schemes and a general proof of the precise formulation of the equivalence theorem are given in the ${\mathit{R}}_{\xi }$ gauge for both the SU(2${)}_{\mathit{L}}$ and the SU(2)×U(1) theories. The precise formula for the modification factor ${\mathit{C}}_{\mathrm{mod}}$ is obtained, and a convenient particular scheme in which ${\mathit{C}}_{\mathrm{mod}}$ is exactly unity is proposed. ${\mathit{C}}_{\mathrm{mod}}$ in other schemes are discussed up to one loop in the heavy Higgs boson limit.