MSTW PDFs and impact of PDFs on cross sections at Tevatron and LHC

We briefly summarise the "MSTW 2008" determination of parton distribution functions (PDFs), and subsequent follow-up studies, before reviewing some topical issues concerning the PDF dependence of cross sections at the Tevatron and LHC. We update a recently published study of benchmark Standard Model total cross sections (W, Z, gg->H and t-tbar production) at the 7 TeV LHC, where we account for all publicly available PDF sets and we compare to LHC data for W, Z, and t-tbar production. We show the sensitivity of the Higgs cross sections to the gluon distribution, then we demonstrate the ability of the Tevatron jet data, and also the LHC t-tbar data, to discriminate between PDF sets with different high-x gluon distributions. We discuss the related problem of attempts to extract the strong coupling alpha_S from only deep-inelastic scattering data, and we conclude that a direct data constraint on the high-x gluon distribution is required to obtain a meaningful result. We therefore discourage the use of PDF sets obtained from "non-global" fits where the high-x gluon distribution is not directly constrained by data.