Altarelli-Parisi (DGLAP) equation from one to three loops

We consider higher-order QCD corrections to the production of colourless highmass systems (lepton pairs, vector bosons, Higgs bosons, . . . ) in hadron collisions. We propose a new formulation of the subtraction method to numerically compute arbitrary infrared-safe observables for this class of processes. To cancel the infrared divergences, we exploit the universal behaviour of the associated transverse-momentum (qT ) distributions in the small-qT region. The method is illustrated in general terms up to the next-to-next-to-leading order (NNLO) in QCD perturbation theory. As a first explicit application, we study Higgs boson production through gluon fusion. Our calculation is implemented in a parton level Monte Carlo program that includes the decay of the Higgs boson in two photons. We present selected numerical results at the LHC. March 2007 ar X iv :h ep -p h/ 07 03 01 2v 2 6 Ju n 20 07 hep-ph/0703012 An NNLO subtraction formalism in hadron collisions and its a plication to Higgs boson production at the LHC Stefano Catani and Massimiliano Grazzini INFN, Sezione di Firenze and Dipartimento di Fisica, Università di Firenze, I-50019 Sesto Fiorentino, Florence, Italy