Antenna Subtraction for NNLO Calculations at the LHC

Abstract

In this thesis the task of computing higher order corrections to QCD scattering processes for the LHC is considered, specifically Next-to Leading Order (NLO) and Next-toNext-to Leading Order (NNLO) perturbative QCD corrections. The infrared (IR) divergent behaviour of the cross section is isolated using the antenna subtrac- tion formalism. This method has previously been used at NNLO in the calculation of jet production in the context of e+e− annihilation and for the leading colour contribution to dijet production via pure gluon scattering. The research presented in this thesis extends the formalism to include scattering processes involving quarks with initial-state partons. General formulae, including sub-leading colour contributions, are presented for the isolation and cancellation of IR and singularities when calculating the production of colourless final-states at the LHC at NLO and NNLO accuracy. The leading colour NNLO correction to the sub-process qq ̄ → gg is calculated and numerical results are presented to demonstrate the convergence of the physical cross section and the subtraction terms in the various unresolved limits. The calculations are organised with the aid of convenient quantities, referred to as integrated antenna strings. Using these quantities, the full calculation displays a clear and predictive structure, in particular at the double virtual level where the structures presented are new.