Abstract
The factorisation of QCD matrix elements in the limit of two external partons becoming collinear is described by process-independent splitting amplitudes, which can be expanded systematically in perturbation theory. Working in conventional dimensional regularisation, we compute the two-loop splitting amplitudes for all simple collinear splitting processes, including subleading terms in the regularisation parameter. Our results are then applied to derive an analytical expression for the two-loop single-real contribution to inclusive Higgs boson production in gluon fusion to fourth order (N3LO) in perturbative QCD.
Highlights
At next-to-next-to-leading order (NNLO), tree-level contributions with up to two unresolved particles contribute, again displaying universal factorization properties in collinear and soft limits [12, 13]
Our results are applied to derive an analytical expression for the two-loop single-real contribution to inclusive Higgs boson production in gluon fusion to fourth order (N3LO) in perturbative QCD
With the two-loop soft gluon current recently derived to all orders in the regulator [25, 26], N3LO calculations at the two-loop single real level are missing only the two-loop corrections to simple collinear limits, described by the two-loop splitting amplitudes
Summary
We consider an l-loop QCD amplitude with a certain number of coloured partons in the final state. The splitting amplitude Pg(ql)(z) only develops a soft singularity if the gluon becomes soft, i.e., z → 0, and the residue at the pole is given by the QCD soft current, known up to two loops in perturbative QCD [2, 3, 14, 22, 25, 26], Pg(ql)(z) =. Our goal is to compute the two-loop splitting amplitudes to O(ǫ) in conventional dimensional regularisation (CDR). This result is needed in order to construct the collinear counterterms for the double-virtual-real contributions to the inclusive N3LO cross section for the production of a heavy colourless state
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