The radiative corrections to the electroweak parameters in the dominant fermion-loop approximation

Abstract

A simple treatment of the dominant radiative corrections to theW ^± andZ ⁰ mass formulae due to fermion-loop corrections to the propagator is given, including the possibility of a very massive top quark,m _t >M _w . A thorough comparison with the results of the complete (SU(2) _L ×U(1) _Y ) one-loop calculations is presented. Using α,G _μ andM _z as input, we find excellent agreement with the complete one-loop calculations (withm _HIGGS≃100GeV) for all values ofm _t within an expected error ofΔM _W ≅(α/2πM _W ≅100MeV) inM _W andΔs ² _W ≅0.002 in the weak angle,s ² _w . Technically we differ from previous work in diagonalizing the γZ propagator for arbitrary values ofq ², thus allowing for extensive use of the notion of “running” coupling constants and masses. We also give a simple and closed formula for the radiative corrections to be applied tos ² _w (accurate within an expected error ofΔs ² _w ≅0.002), when extractings ² _W ≅0.002), when extractings ² _W from neutrino scattering experiments. As a strategy for future precision tests of the electroweak theory, we suggest attempting to isolate and to test directly the “new physics” of boson loops and other new phenomena by comparing with and looking for deviations (larger thanΔM _W ≅(α/2π)M _w ) from the predictions of the dominant fermion-loop calculation.