We present a systematic study of uncertainties due to parton distributions and the strong coupling on the gluon-fusion production cross section of the Standard Model Higgs at the Tevatron and LHC colliders. We compare procedures and results when three recent sets of PDFs are used, CTEQ6.6, MSTW08 and NNPDF1.2, and we discuss specifically the way PDF and strong coupling uncertainties are combined. We find that results obtained from different PDF sets are in reasonable agreement if a common value of the strong coupling is adopted. We show that the addition in quadrature of PDF and alphas uncertainties provides an adequate approximation to the full result with exact error propagation. We discuss a simple recipe to determine a conservative PDF+alphas uncertainty from available global parton sets, and we use it to estimate this uncertainty on the given process to be about 10% at the Tevatron and 5% at the LHC for a light Higgs.
Bibliographical note29 pages, 13 figures