Local unitarity: cutting raised propagators and localising renormalisation
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2022
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Journal Article
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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 (MS) over bar and On-Shell scheme whose only analytic input is single-scale vacuum diagrams. We validate this novel technology by providing (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* -> jj and gamma*-> t (t) over bar.
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published
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2022 (10)
Pages / Article No.
120
Publisher
Springer
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Subject
Automation; Higher-Order Perturbative Calculations; Renormalization and Regularization; Scattering Amplitudes
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694712 - Automatization of perturbative QCD at very high orders (EC)
179016 - Singlular structure of two-loop amplitudes and their numerical evaluation (SNF)
179016 - Singlular structure of two-loop amplitudes and their numerical evaluation (SNF)