Structure-function analysis andψ, jet,W, andZproduction: Determining the gluon distribution

We perform a next-to-leading-order structure-function analysis of deep-inelastic {μ}N and {ν}N scattering data and find acceptable fits for a range of input gluon distributions. We show three equally acceptable sets of parton distributions which correspond to gluon distributions which are (1) ``soft,'' (2) ``hard,'' and (3) which behave as xG(x){~}1/ {}x at small x. J/{ψ} and prompt photon hadroproduction data are used to discriminate between the three sets. Set 1, with the ``soft''-gluon distribution, is favored. W, Z, and jet production data from the CERN collider are well described but do not distinguish between the sets of structure functions. The precision of the predictions for σW and σZ allow the collider measurements to yield information on the number of light neutrinos and the mass of the top quark. Finally we discuss how the gluon distribution at very small x may be directly measured at DESY HERA.