Leading logarithmic corrections to the weak leptonic and semi-leptonic low-energy hamiltonian

Abstract If one defines the parameters of the Weinberg-Salam theory at a momentum scale M = O( M W , M Z ), the weak effective hamiltonian at a momentum scale μ ⪡ M has logarithmically enhanced corrections, of order α ln( M 2 / μ 2 ). We present a computation of these corrections, for that part of the hamiltonian which leads to detectable weak-electromagnetic interference effects. The largest correction can be absorbed into a running sin 2 θ ( μ ). Other, smaller, corrections are estimated, taking into account the effect of strong interactions. An estimate of the non-logarithmically enhanced corrections is also given, by evaluating them in the limit sin 2 θ → 0. From the SLAC e - d asymmetry it was found sin 2 θ = 0.224 ± 0.020 at μ 2 ≅ 2 GeV 2 . In correspondence, we find sin 2 θ ( M ) = 0.217 ± 0.020. This value, however, is subject to uncertainties deriving from the effect of the strange and of the antiquark parton sea.