Estimating the effect of NNLO contributions on global parton analyses

We use the recent estimates of NNLO splitting functions, made by van Neerven and Vogt, to perform exploratory fits to deep inelastic and related hard scattering data. We investigate the hierarchy of parton distributions obtained at LO, NLO and NNLO, and, more important, the stability of the resulting predictions for physical observables. We use the longitudinal structure function $F_L$ and the cross sections $\sigma_W, \sigma_Z$ for $W$ and $Z$ hadroproduction as examples. For $F_L$ we find relatively poor convergence, with increasing order, at small $x$; whereas $\sigma_{W,Z}$ are much more reliably predicted.