The unequal-mass three-loop banana integral
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866917057655734272 |
|---|---|
| author | Pögel, Sebastian Teschke, Toni Wang, Xing Weinzierl, Stefan |
| author_facet | Pögel, Sebastian Teschke, Toni Wang, Xing Weinzierl, Stefan |
| contents | We compute the three-loop banana integral with four unequal masses in dimensional regularisation. This integral is associated to a family of K3 surfaces, thus representing an example for Feynman integrals with geometries beyond elliptic curves. We evaluate the integral by deriving an $\varepsilon$-factorised differential equation, for which we rely on the algorithm presented in a recent publication. Equipping the space of differential forms in Baikov representation by a set of filtrations inspired by Hodge theory, we first obtain a differential equation with entries as Laurent polynomials in $\varepsilon$. Via a sequence of basis rotations we then remove any non-$\varepsilon$-factorising terms. This procedure is algorithmic and at no point relies on prior knowledge of the underlying geometry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_23594 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The unequal-mass three-loop banana integral Pögel, Sebastian Teschke, Toni Wang, Xing Weinzierl, Stefan High Energy Physics - Theory We compute the three-loop banana integral with four unequal masses in dimensional regularisation. This integral is associated to a family of K3 surfaces, thus representing an example for Feynman integrals with geometries beyond elliptic curves. We evaluate the integral by deriving an $\varepsilon$-factorised differential equation, for which we rely on the algorithm presented in a recent publication. Equipping the space of differential forms in Baikov representation by a set of filtrations inspired by Hodge theory, we first obtain a differential equation with entries as Laurent polynomials in $\varepsilon$. Via a sequence of basis rotations we then remove any non-$\varepsilon$-factorising terms. This procedure is algorithmic and at no point relies on prior knowledge of the underlying geometry. |
| title | The unequal-mass three-loop banana integral |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2507.23594 |