Two-loop QCD corrections to gluon-gluon scattering∗

We present the O (α s) virtual QCD corrections to gluon-gluon scattering due to the interference of tree and two-loop amplitudes. We work in conventional dimensional regularisation and give analytic expressions renormalised in the MS scheme. The structure of the infrared divergences agrees with that predicted by Catani while formulae for the finite remainder are given in terms of logarithms and polylogarithms that are real in the physical region. These results, together with those previously obtained for quark-quark and quark-gluon scattering, complete the two-loop matrix elements needed for the next-to-next-to-leading order contribution to inclusive jet production at hadron colliders.