Skip to content
DraconiticResearch
Search Sources API
203,234 studies31 sourcesUpdated 26 min ago
Peer-reviewedCC BY 4.0Journal of High Energy Physics

Chebyshev approximations of Feynman integrals for collider physics

  • Samuel Abreu1,2
  • Afonso Guerreiro3,4
  • Ben Page5
5 affiliations
  1. 1Theoretical Physics Department, CERN
  2. 2The University of Edinburgh
  3. 3Universidade de Lisboa
  4. 4LIP — Laboratório de Instrumentação e Física Experimental de Partículas
  5. 5Ghent University
Open at sourcePDFDOICite

Abstract

We present a novel approach for solving canonical differential equations for Feynman integrals based on an approximation of the integrals with Chebyshev polynomials. By exploiting the analyticity properties of Feynman integrals, the method constructs rapidly converging polynomial approximations along a path, enabling highly efficient numerical evaluation. Moreover, we introduce an adaptive approximation method that dynamically samples to optimise convergence. We implement this framework in double-precision arithmetic and demonstrate its stability across physical phase space using a series of two-loop, five-point examples. Our proof-of-principle implementation proves competitive with state-of-the-art one-fold integral methods, while requiring little to no case-by-case intervention to handle spurious singularities.

Related

  1. A portable implementation of one-loop Feynman integrals
    Reet Barik, John M. Campbell, J. Taylor Childers +2
    arXivPreprintCC BY 4.0Full textHigh-energy & particle physicsarXiv
  2. Feynman Integrals Meet Second-Order Partial Differential Equations
    Xiang Chen, Hantian Zhang
    arXivPreprintarXiv licenceFull textHigh-energy & particle physicsarXiv
  3. Magic Relations and Critical Varieties of Feynman Integrals
    Giulio Crisanti, Hjalte Frellesvig, Andrzej Pokraka +1
    arXivPreprintCC BY 4.0Full textMathematical physicsHigh-energy & particle physicsarXiv
  4. Analyticity Bootstrap of Feynman Integrals
    Xiang Li, Dao-Ming Mu, Yan-Qing Ma
    arXivPreprintarXiv licenceFull textHigh-energy & particle physicsarXiv
  5. How to choose a good rational basis for elliptic Feynman integrals?
    Ekta Chaubey, Vasily Sotnikov
    arXivPreprintCC BY 4.0Full textHigh-energy & particle physicsarXiv

Cite

BibTeXRIS
BibTeX
@article{abreu2026chebyshev,
  title = {{Chebyshev approximations of Feynman integrals for collider physics}},
  author = {Samuel Abreu and Afonso Guerreiro and Ben Page},
  journal = {Journal of High Energy Physics},
  year = {2026},
  month = nov,
  doi = {10.1007/jhep11(2026)038},
  url = {https://link.springer.com/article/10.1007/JHEP11(2026)038},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Chebyshev approximations of Feynman integrals for collider physics
AU  - Samuel Abreu
AU  - Afonso Guerreiro
AU  - Ben Page
PY  - 2026
DA  - 2026/11/05
JO  - Journal of High Energy Physics
DO  - 10.1007/jhep11(2026)038
UR  - https://link.springer.com/article/10.1007/JHEP11(2026)038
AB  - We present a novel approach for solving canonical differential equations for Feynman integrals based on an approximation of the integrals with Chebyshev polynomials. By exploiting the analyticity properties of Feynman integrals, the method constructs rapidly converging polynomial approximations along a path, enabling highly efficient numerical evaluation. Moreover, we introduce an adaptive approximation method that dynamically samples to optimise convergence. We implement this framework in double-precision arithmetic and demonstrate its stability across physical phase space using a series of two-loop, five-point examples. Our proof-of-principle implementation proves competitive with state-of-the-art one-fold integral methods, while requiring little to no case-by-case intervention to handle spurious singularities.
SN  - 1029-8479
ER  -