Intersection numbers, polynomial division and relative cohomology
A bstract We present a simplification of the recursive algorithm for the evaluation of intersection numbers for differential n -forms, by combining the advantages emerging from the choice of delta-forms as generators of relative twisted cohomology groups and the polynomial division technique, recently proposed in the literature. We show that delta-forms capture the leading behaviour of the intersection numbers in presence of evanescent analytic regulators, whose use is, therefore, bypassed. This simplified algorithm is applied to derive the complete decomposition of two-loop planar and non-planar Feynman integrals in terms of a master integral basis. More generally, it can be applied to derive relations among twisted period integrals, relevant for physics and mathematical studies.
Authors
- Manoj K. Mandal (ORCID: https://orcid.org/0000-0003-0850-7685)
- Hjalte Frellesvig (ORCID: https://orcid.org/0000-0002-7367-4861)
- Giacomo Brunello (ORCID: https://orcid.org/0009-0004-4788-738X)
- Vsevolod Chestnov (ORCID: https://orcid.org/0000-0001-7067-0315)
- Pierpaolo Mastrolia (ORCID: https://orcid.org/0000-0001-9711-7798)
- Giulio Crisanti (ORCID: https://orcid.org/0009-0009-3053-2394)
Institutions
- University of Copenhagen (DK)
- Centre National de la Recherche Scientifique (FR)
- University of Padua (IT)
- Commissariat à l'Énergie Atomique et aux Énergies Alternatives (FR)
- Université Paris-Saclay (FR)
- Istituto Nazionale di Fisica Nucleare, Sezione di Padova (IT)
- CEA Paris-Saclay (FR)
- Institute of High Energy Physics (CN)
- Istituto Nazionale di Fisica Nucleare, Sezione di Bologna (IT)
- Institut de Physique Théorique (FR)
Publication Details
- Journal
- Journal of High Energy Physics
- Published
- 2024-09-05
- DOI
- https://doi.org/10.1007/jhep09(2024)015
- Citations
- 22
- Primary Topic
- Advanced Combinatorial Mathematics
- Type
- article
- Field-Weighted Citation Impact
- 27.77
Funders
- European Commission
- Università degli Studi di Padova