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arXiv · 2203.11038

Local Unitarity: cutting raised propagators and localising renormalisation

Zeno Capatti·Valentin Hirschi·Ben Ruijl
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Abstract

The Local Unitarity (LU) representation of differential cross-sections locally realises the cancellations of infrared singularities predicted by the Kinoshita-Lee-Nauenberg theorem. In this work we solve the two remaining challenges to enable practical higher-loop computations within the LU formalism. The first concerns the generalisation of the LU representation to graphs with raised propagators. The solution to this problem results in a generalisation of distributional Cutkosky rules. The second concerns the regularisation of ultraviolet and spurious soft singularities, solved using a fully automated and local renormalisation procedure based on Bogoliubov's R-operation. We detail an all-order construction for the hybrid $\overline{\text{MS}}$ and On-Shell scheme whose only analytic input is single-scale vacuum diagrams. Using this novel technology, we provide (semi-)inclusive results for two multi-leg processes at NLO, study limits of individual supergraphs up to N3LO and present the first physical NNLO cross-sections computed fully numerically in momentum-space, namely for the processes $\gamma^* \rightarrow j j$ and $\gamma^* \rightarrow t \bar{t}$.

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Zeno Capatti, Valentin Hirschi, Ben Ruijl. 2022-03-21. Local Unitarity: cutting raised propagators and localising renormalisation. https://arxiv.org/abs/2203.11038

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