Integrand analysis, leading singularities and canonical bases beyond polylogarithms
- 1Technical University of Munich
- 2University of Oxford
- 3Max Planck Institute for Gravitational Physics (Albert Einstein Institute)
Abstract
A bstract : In this paper, we elaborate on the connection between leading singularities and canonical bases of Feynman integrals beyond polylogarithms. We start by discussing a notion of leading singularities in dimensional regularization, which can be generalized from the Riemann sphere to more complex geometries, and use it to demonstrate how selecting Feynman integrals with unit leading singularities necessitates introducing new transcendental functions related to the periods of the underlying geometries. Integrals with unit leading singularities in this generalized sense satisfy ϵ -factorized differential equations, and the new transcendental functions are in direct correspondence to the new differential forms appearing in their Gauss-Manin connection. We argue that this construction is mathematically equivalent to the splitting of the period matrix into semi-simple and unipotent parts plus a clean-up step, and demonstrate its use with examples of increasing complexity that require the interplay of multiple geometries.
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BibTeX
@article{forner2026integrand,
title = {{Integrand analysis, leading singularities and canonical bases beyond polylogarithms}},
author = {Felix Forner and Cesare Carlo Mella and Christoph Nega and Lorenzo Tancredi and Fabian J. Wagner},
journal = {Journal of High Energy Physics},
year = {2026},
month = oct,
doi = {10.1007/jhep10(2026)213},
url = {https://link.springer.com/article/10.1007/JHEP10(2026)213},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Integrand analysis, leading singularities and canonical bases beyond polylogarithms
AU - Felix Forner
AU - Cesare Carlo Mella
AU - Christoph Nega
AU - Lorenzo Tancredi
AU - Fabian J. Wagner
PY - 2026
DA - 2026/10/21
JO - Journal of High Energy Physics
DO - 10.1007/jhep10(2026)213
UR - https://link.springer.com/article/10.1007/JHEP10(2026)213
AB - A bstract : In this paper, we elaborate on the connection between leading singularities and canonical bases of Feynman integrals beyond polylogarithms. We start by discussing a notion of leading singularities in dimensional regularization, which can be generalized from the Riemann sphere to more complex geometries, and use it to demonstrate how selecting Feynman integrals with unit leading singularities necessitates introducing new transcendental functions related to the periods of the underlying geometries. Integrals with unit leading singularities in this generalized sense satisfy ϵ -factorized differential equations, and the new transcendental functions are in direct correspondence to the new differential forms appearing in their Gauss-Manin connection. We argue that this construction is mathematically equivalent to the splitting of the period matrix into semi-simple and unipotent parts plus a clean-up step, and demonstrate its use with examples of increasing complexity that require the interplay of multiple geometries.
SN - 1029-8479
ER -