Towards multiloop local renormalization within Causal Loop-Tree Duality
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910441278537728 |
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| author | Rios-Sanchez, Jose Sborlini, German |
| author_facet | Rios-Sanchez, Jose Sborlini, German |
| contents | Renormalization is a well-known technique to get rid of ultraviolet (UV) singularities. When relying on Dimensional Regularization (DREG), these become manifest as $ε$-poles, allowing to define counter-terms with useful recursive properties. However, this procedure requires to work at \emph{integral-level} and poses difficulties to achieve a smooth combination with semi-numerical approaches. This article is devoted to the development of an integrand-level renormalization formalism, better suited for semi or fully numerical calculations. Starting from the Loop-Tree Duality (LTD), we keep the causal representations of the integrands of multiloop Feynman diagrams and explore their UV behaviour. Then, we propose a strategy that allows to build local counter-terms, capable of rendering the expressions integrable in the high-energy limit and in four space-time dimensions. Our procedure was tested on diagrams up to three-loops, and we found a remarkably smooth cancellation of divergences. The results of this work constitute a powerful step towards a fully local renormalization framework in QFT. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_13995 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Towards multiloop local renormalization within Causal Loop-Tree Duality Rios-Sanchez, Jose Sborlini, German High Energy Physics - Theory High Energy Physics - Phenomenology Renormalization is a well-known technique to get rid of ultraviolet (UV) singularities. When relying on Dimensional Regularization (DREG), these become manifest as $ε$-poles, allowing to define counter-terms with useful recursive properties. However, this procedure requires to work at \emph{integral-level} and poses difficulties to achieve a smooth combination with semi-numerical approaches. This article is devoted to the development of an integrand-level renormalization formalism, better suited for semi or fully numerical calculations. Starting from the Loop-Tree Duality (LTD), we keep the causal representations of the integrands of multiloop Feynman diagrams and explore their UV behaviour. Then, we propose a strategy that allows to build local counter-terms, capable of rendering the expressions integrable in the high-energy limit and in four space-time dimensions. Our procedure was tested on diagrams up to three-loops, and we found a remarkably smooth cancellation of divergences. The results of this work constitute a powerful step towards a fully local renormalization framework in QFT. |
| title | Towards multiloop local renormalization within Causal Loop-Tree Duality |
| topic | High Energy Physics - Theory High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2402.13995 |