Electroweak radiative corrections to neutrino and electron scattering and the value of sin 2θw

Abstract

We describe in detail the calculation of all first-order electroweak radiative corrections to total and differential neutrino cross sections and to the parity-violating asymmetry in ed scattering. We find that leading log approximations agree well with our exact result for the shape, but not necessarily the magnitude, of the corrections to dσ ν, ν / dγ except for γ → 1. Corrections to total neutrino cross sections have also been calculated by Marciano and Sirlin; our results agree with theirs. The corrections to sin 2 θ w are experiment dependent. If sin 2 θ w is defined in the MS scheme at a scale M w, they reduce the average value found from the ratio of charged to neutral current neutrino scattering by 0.012 to 0.215 ± 0.015. They reduce the value obatained from the Paschos Wolfenstein relation by 0.008 to 0.221 ± 0.014. In ed scattering they reduce the value by 0.008 to 0.215 ± 0.015. Using a corrected value of 0.215 ± 0.015 and the first-order corrections to the mass formulae, the SU(2) × U(1) predictions for the vector boson masses are M w = 83.1 −2.8 +3.1 rmGeV and M z = 93.8 −2.2 +2.5 GeV, about five GeV larger than obtained from the lowest order analysis.