Radiative corrections to e⁺e⁻ to mu⁺mu⁻ in the Glashow-Salam-Weinberg model
A complete renormalization scheme for the Glashow-Salam-Weinberg model is presented. As input parameters the scheme uses the fine structure constant, α, the muon decay constant, Gμ and the Z° mass, MZ which are known or will be measured to high accuracy in the near future. These are used along with the Higgs and fermion masses to obtain the W mass, MW. The full one-loop weak radiative corrections to the longitudinal polarization asymmetry, Apol, and the forward-backward asymmetry, Afb, in e+e- → μ+μ- are then calculated both on and off resonance. On resonance the results depend extremely sensitively on the Z mass, MZ, and to a lesser extent on the top quark mass, mt, and the Higgs mass, MH, showing that this is a good place to test the standard model at the one loop level. The results are displayed over the full range of the parameters allowed by experimental and theoretical constraints. It is suggested that sufficiently accurate experiments may be able to set an upper bound on one of mt or MH if the other is known. It is noted that on resonance Apol is only weakly dependent on the beam pipe and on the nature of the outgoing fermions. Comparison is made with other calculations of Afb and the agreement is found to be good. The predictions are also compared with measurements of Afb off resonance and are found in all cases to lie within the experimental errors. Previous analyses that indicated a possible discrepancy are shown to be incorrect.