# Two-loop splitting amplitudes and the single-real contribution to inclusive Higgs production at N$^{3}$LO

Duhr, Claude; Gehrmann, Thomas; Jaquier, Matthieu (2015). Two-loop splitting amplitudes and the single-real contribution to inclusive Higgs production at N$^{3}$LO. Journal of High Energy Physics, 2015(2):77.

## 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 (N$^{3}$LO) in perturbative QCD.

## 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 (N$^{3}$LO) in perturbative QCD.

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