Local renormalisation from causal loop-tree duality
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913492638892032 |
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| author | Sborlini, German Rios-Sanchez, Jose |
| author_facet | Sborlini, German Rios-Sanchez, Jose |
| contents | We report recent progress on the development of a local renormalisation formalism based on causal loop-tree duality (cLTD). By performing an expansion around the UV-propagator in an Euclidean space, we manage to build counter-terms to cancel the non-integrable terms in the UV limit. This procedure is then combined with the so-called causal representation, and the UV expansion is performed at the level of on-shell energies. The resulting expressions are more compact, and they retain nice properties of the original causal representation. The proposed formalism is tested up to three-loops, with relevant families of topologies. In all the cases, we successfully cancel the UV divergences and achieve a smooth numerical implementation. These results constitute a first step towards a new renormalisation program in four space-time dimensions (by-passing DREG), perfectly suitable for fully numerical simulations. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2408_17319 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Local renormalisation from causal loop-tree duality Sborlini, German Rios-Sanchez, Jose High Energy Physics - Phenomenology High Energy Physics - Theory We report recent progress on the development of a local renormalisation formalism based on causal loop-tree duality (cLTD). By performing an expansion around the UV-propagator in an Euclidean space, we manage to build counter-terms to cancel the non-integrable terms in the UV limit. This procedure is then combined with the so-called causal representation, and the UV expansion is performed at the level of on-shell energies. The resulting expressions are more compact, and they retain nice properties of the original causal representation. The proposed formalism is tested up to three-loops, with relevant families of topologies. In all the cases, we successfully cancel the UV divergences and achieve a smooth numerical implementation. These results constitute a first step towards a new renormalisation program in four space-time dimensions (by-passing DREG), perfectly suitable for fully numerical simulations. |
| title | Local renormalisation from causal loop-tree duality |
| topic | High Energy Physics - Phenomenology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2408.17319 |