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Infrared Structure at NNLO Using Antenna Subtraction

We consider the infrared structure of hadron-hadron collisions at next-to-next-to leading order using the antenna subtraction method. The general form of the subtraction terms is presented for double real, real-virtual and double virtual contributions. At NLO and NNLO it is shown that the virtual and double virtual subtraction terms can be written in terms of integrated dipoles, formed by systematically combining the mass factorisation contributions and integrated antenna functions. The integrated dipoles describing $\ell$ unresolved partons, denoted $\bs{J}_{2}^{(\ell)}$, are related to Catani's IR singularity operators, $\bs{I}_{ij}^{(\ell)}(\eps)$. It is shown that the IR pole structure of the virtual and double virtual contributions can be written as a sum over integrated dipoles within the antenna subtraction formalism and the master expressions analogous to Catani's one- and two-loop factorisation formulae are derived. To demonstrate the techniques described in this paper, we apply antenna subtraction to the production of two gluon jets via quark-antiquark scattering at NLO and NNLO. Double real, real-virtual and double virtual subtraction terms are explicitly derived for the leading colour NNLO contribution.