Study of the uncertainty of the gluon distribution

The uncertainty in the calculation of many important new processes at the Fermilab Tevatron and CERN LHC is dominated by that concerning the gluon distribution function. We investigate the uncertainty in the gluon distribution of the proton by systematically varying the gluon parameters in the global QCD analysis of parton distributions. The results depend critically on the parton momentum fraction $x$ and the QCD scale $Q^2.$ The uncertainties are presented for integrated gluon-gluon and gluon-quark luminosities for both the Tevatron and LHC as a function of $\sqrt{\tau }=\sqrt{x_1{x}_2}=\sqrt{ŝ/s},$ the most relevant quantity for new particle production. The uncertainties are reasonably small, except for large $x$.