The Equivalence Theorem And Its Radiative-Correction-Free Formulation For All R_xi Gauges

Abstract

The electroweak equivalence theorem quantitatively connects the physical amplitudes of longitudinal massive gauge bosons to those of the corresponding ``unphysical'' would-be Goldstone bosons. Its precise form depends on both the gauge fixing condition and the renormalization scheme. Our previous modification-free schemes have applied to a broad class of $R_ξ$ gauges including 't Hooft-Feynman gauge but excluding Landau gauge. In this paper we construct a new renormalization scheme in which the radiative modification factor, $C_{mod}^a$, is equal to unity for all $R_ξ$-gauges, including both 't Hooft-Feynman and Landau gauges. This scheme makes $C_{mod}^a$ equal to unity by specifying a convenient subtraction condition for the would-be Goldstone boson wavefunction renormalization constant $Z_{ϕ^a}$. We build the new scheme for both the standard model and the effective Lagrangian formulated electroweak theories (with either linearly or non-linearly realized symmetry breaking sector). Based upon these, a new prescription, called ``divided equivalence theorem'', is further proposed for extending the high energy region applicable to the equivalence theorem.