epsilon

epsilon: A tool to find a canonical basis of master integrals. In 2013, Henn proposed a special basis for a certain class of master integrals, which are expressible in terms of iterated integrals. In this basis, the master integrals obey a differential equation, where the right hand side is proportional to ϵ in d=4−2ϵ space-time dimensions. An algorithmic approach to find such a basis was found by Lee. We present the tool epsilon, an efficient implementation of Lee’s algorithm based on the Fermat computer algebra system as computational backend.


References in zbMATH (referenced in 17 articles )

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  1. Chen, Jiaqi; Jiang, Xuhang; Xu, Xiaofeng; Yang, Li Lin: Constructing canonical Feynman integrals with intersection theory (2021)
  2. Di Vecchia, Paolo; Heissenberg, Carlo; Russo, Rodolfo; Veneziano, Gabriele: The eikonal approach to gravitational scattering and radiation at (\mathcalO(G^3)) (2021)
  3. Dlapa, Christoph; Li, Xiaodi; Zhang, Yang: Leading singularities in Baikov representation and Feynman integrals with uniform transcendental weight (2021)
  4. Heinrich, Gudrun: Collider physics at the precision frontier (2021)
  5. Pikelner, Andrey: Three-loop vertex integrals at symmetric point (2021)
  6. Parra-Martinez, Julio; Ruf, Michael S.; Zeng, Mao: Extremal black hole scattering at (\mathcalO(G^3)): graviton dominance, eikonal exponentiation, and differential equations (2020)
  7. Roman N. Lee: Libra: a package for transformation of differential systems for multiloop integrals (2020) arXiv
  8. Abreu, Samuel; Page, Ben; Zeng, Mao: Differential equations from unitarity cuts: nonplanar hexa-box integrals (2019)
  9. Hidding, Martijn; Moriello, Francesco: All orders structure and efficient computation of linearly reducible elliptic Feynman integrals (2019)
  10. Lee, Roman N.; Smirnov, Alexander V.; Smirnov, Vladimir A.: Evaluating `elliptic’ master integrals at special kinematic values: using differential equations and their solutions via expansions near singular points (2018)
  11. Lee, Roman N.; Smirnov, Alexander V.; Smirnov, Vladimir A.: Solving differential equations for Feynman integrals by expansions near singular points (2018)
  12. Bosma, Jorrit; Sogaard, Mads; Zhang, Yang: Maximal cuts in arbitrary dimension (2017)
  13. Gituliar, Oleksandr; Magerya, Vitaly: Fuchsia: a tool for reducing differential equations for Feynman master integrals to epsilon form (2017)
  14. Kasper J. Larsen, Robbert Rietkerk: MultivariateResidues - a Mathematica package for computing multivariate residues (2017) arXiv
  15. Mario Prausa: epsilon: A tool to find a canonical basis of master integrals (2017) arXiv
  16. Prausa, Mario: \textttepsilon: a tool to find a canonical basis of master integrals (2017)
  17. Zeng, Mao: Differential equations on unitarity cut surfaces (2017)