Radiative corrections to νμ + N → μ− + X and their effect on the determination of ϱ2 and sin 2θW

Abstract

We study the O(α) corrections to σ T( ν μ + N → μ − + X). The coefficient of the leading O( αln m Z) contribution is given by a general theorem as in the case of β decay, while the energy scale accompanying m Z in the argument of the logarithm as well as mass singularities and non-logarithmic terms are obtained by a detailed quark-parton model calculation. The effect of muon mass singularities, when there is an experimental vut in the low range of the y distribution, is also investigated. Combining these new results with our previous analysis of σ T( ν μ + N → ν μ + X), we calculate theSU(2) L × U(1) parameter ϱ ( ν μ ;h) 2 and evaluate the effect of the O(α) corrections on the determination of sin 2 θ W exp from deep inelastic ν μ scattering. Applying these corrections to existing data, we obtain the weigthed average sin 2 θ W exp = 0.216 ± 0.010 ± 0.004. This value when used in conjuction with our previous analysis of the W ± and Z 0 masses provides the predictions m W = 83.0 −2.8 +3.0 GeV and m Z = 93.8 −2.4 +2.5 GeV. For the weak interaction angle defined by modified minimal subtraction we find sin 2 θ W( m W) = 0.215 ± 0.010 ± 0.004, which is in very good agreement with the SU(5) prediction we have recently given.