Leading logarithm calculation of the e^+ e^- -> e^+ ν_e \bar{u} d cross section

Abstract

We analytically evaluate in the leading logarithm approximation the differential cross section for e^+ e^- -> e^+ ν_e \bar{u} d. We compare our order α^4 α_s^0 leading-log result to the order α^4 α_s^0 exact result obtained from the GRC4F Monte Carlo program. Finally we use the Gluck, Reya, Schienbien distribution of partons in a virtual photon, which incorporates both evolution and nonperturbative strong interaction contributions, to obtain better estimates of the differential cross section.