Canonical differential equations for the elliptic two-loop five-point integral family relevant to $t\bar t +$jet production at leading colour
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866916911279767552 |
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| author | Becchetti, Matteo Dlapa, Christoph Zoia, Simone |
| author_facet | Becchetti, Matteo Dlapa, Christoph Zoia, Simone |
| contents | We present differential equations (DEs) in canonical form for a family of two-loop five-point Feynman integrals containing elliptic functions and nested square roots. This is the only family for which canonical DEs were not yet available among those required to compute the two-loop leading-colour amplitude for top-pair production in association with a jet at hadron colliders. We write the DEs in terms of one-forms having (locally) simple poles at all singular points, and highlight the `duplet' structure that generalises the even/odd charge of square roots to nested roots. All transcendental functions in the DEs are expressed in closed form using complete elliptic integrals, while one-forms free of elliptic functions are given in terms of logarithms, including those with the nested roots. In addition to marking a significant step towards next-to-next-to-leading order QCD predictions for an important LHC process, this work represents the first time that a canonical basis of integrals involving elliptic functions has been obtained for a five-particle process. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_03603 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Canonical differential equations for the elliptic two-loop five-point integral family relevant to $t\bar t +$jet production at leading colour Becchetti, Matteo Dlapa, Christoph Zoia, Simone High Energy Physics - Theory High Energy Physics - Phenomenology We present differential equations (DEs) in canonical form for a family of two-loop five-point Feynman integrals containing elliptic functions and nested square roots. This is the only family for which canonical DEs were not yet available among those required to compute the two-loop leading-colour amplitude for top-pair production in association with a jet at hadron colliders. We write the DEs in terms of one-forms having (locally) simple poles at all singular points, and highlight the `duplet' structure that generalises the even/odd charge of square roots to nested roots. All transcendental functions in the DEs are expressed in closed form using complete elliptic integrals, while one-forms free of elliptic functions are given in terms of logarithms, including those with the nested roots. In addition to marking a significant step towards next-to-next-to-leading order QCD predictions for an important LHC process, this work represents the first time that a canonical basis of integrals involving elliptic functions has been obtained for a five-particle process. |
| title | Canonical differential equations for the elliptic two-loop five-point integral family relevant to $t\bar t +$jet production at leading colour |
| topic | High Energy Physics - Theory High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2503.03603 |