On-shelļ methods for perturbative QCD

Abstract

We present new on-shell techniques for the calculation of colour ordered helicity amplitudes in QCD. We review the methods of on-shell recursion and the MHV rules before applying them to tree-level processes within the Standard Model. The MHV rules are applied to QCD corrections to Higgs amplitudes in the heavy top quark limit at tree- level, generating simple n֊point expressions for specific helicity configurations as well as developing more generally applicable recursion relations. We then generalise the on-shell recursion relations for massless QCD to include massive propagating particles and apply them to amplitudes with massive scalar particles, vector bosons and fermions. We then apply on-shell methods to compute the cut-constructible parts of 1-loop Higgs plus multi-gluon amplitudes fixing the remaining rational terms through Feynman diagrams. In all cases we find that the on-shell methods generate simpler analytic expressions than the traditional off-shell methods