Local unitarity: cutting raised propagators and localising renormalisation
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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2022-10-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP10(2022)120 |
| _version_ | 1797985949160833024 |
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| author | Zeno Capatti Valentin Hirschi Ben Ruijl |
| author_facet | Zeno Capatti Valentin Hirschi Ben Ruijl |
| author_sort | Zeno Capatti |
| collection | DOAJ |
| description | 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 ¯ $$ \overline{\textrm{MS}} $$ 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 γ ∗ → jj and γ ∗ → t t ¯ $$ {\gamma}^{\ast}\to t\overline{t} $$ . |
| first_indexed | 2024-04-11T07:26:11Z |
| format | Article |
| id | doaj.art-27f5085bbad74cd29ea021a359ec1387 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-04-11T07:26:11Z |
| publishDate | 2022-10-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-27f5085bbad74cd29ea021a359ec13872022-12-22T04:37:04ZengSpringerOpenJournal of High Energy Physics1029-84792022-10-0120221018210.1007/JHEP10(2022)120Local unitarity: cutting raised propagators and localising renormalisationZeno Capatti0Valentin Hirschi1Ben Ruijl2Department of Physics, ETH ZürichDepartment of Theoretical Physics, CERNDepartment of Physics, ETH ZürichAbstract 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 ¯ $$ \overline{\textrm{MS}} $$ 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 γ ∗ → jj and γ ∗ → t t ¯ $$ {\gamma}^{\ast}\to t\overline{t} $$ .https://doi.org/10.1007/JHEP10(2022)120AutomationHigher-Order Perturbative CalculationsRenormalization and RegularizationScattering Amplitudes |
| spellingShingle | Zeno Capatti Valentin Hirschi Ben Ruijl Local unitarity: cutting raised propagators and localising renormalisation Journal of High Energy Physics Automation Higher-Order Perturbative Calculations Renormalization and Regularization Scattering Amplitudes |
| title | Local unitarity: cutting raised propagators and localising renormalisation |
| title_full | Local unitarity: cutting raised propagators and localising renormalisation |
| title_fullStr | Local unitarity: cutting raised propagators and localising renormalisation |
| title_full_unstemmed | Local unitarity: cutting raised propagators and localising renormalisation |
| title_short | Local unitarity: cutting raised propagators and localising renormalisation |
| title_sort | local unitarity cutting raised propagators and localising renormalisation |
| topic | Automation Higher-Order Perturbative Calculations Renormalization and Regularization Scattering Amplitudes |
| url | https://doi.org/10.1007/JHEP10(2022)120 |
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