Fuchsia: a tool for reducing differential equations for Feynman master integrals to epsilon form. Nature of problem: Feynman master integrals may be calculated from solutions of a linear system of differential equations with rational coefficients. Such a system can be easily solved as an e -series when its epsilon form is known. Hence, a tool which is able to find the epsilon form transformations can be used to evaluate Feynman master integrals. Solution method: The solution method is based on the Lee algorithm (Lee, 2015) which consists of three main steps: fuchsification, normalization, and factorization. During the fuchsification step a given system of differential equations is transformed into the Fuchsian form with the help of the Moser method (Moser, 1959). Next, during the normalization step the system is transformed to the form where eigenvalues of all residues are proportional to the dimensional regulator . Finally, the system is factorized to the epsilon form by finding an unknown transformation which satisfies a system of linear equations.

References in zbMATH (referenced in 20 articles , 1 standard article )

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  1. Chen, Jiaqi; Jiang, Xuhang; Xu, Xiaofeng; Yang, Li Lin: Constructing canonical Feynman integrals with intersection theory (2021)
  2. Dlapa, Christoph; Li, Xiaodi; Zhang, Yang: Leading singularities in Baikov representation and Feynman integrals with uniform transcendental weight (2021)
  3. Heinrich, Gudrun: Collider physics at the precision frontier (2021)
  4. Mizera, Sebastian; Pokraka, Andrzej: From infinity to four dimensions: higher residue pairings and Feynman integrals (2020)
  5. Parra-Martinez, Julio; Ruf, Michael S.; Zeng, Mao: Extremal black hole scattering at (\mathcalO(G^3)): graviton dominance, eikonal exponentiation, and differential equations (2020)
  6. Roman N. Lee: Libra: a package for transformation of differential systems for multiloop integrals (2020) arXiv
  7. Abreu, Samuel; Page, Ben; Zeng, Mao: Differential equations from unitarity cuts: nonplanar hexa-box integrals (2019)
  8. Broedel, Johannes; Duhr, Claude; Dulat, Falko; Penante, Brenda; Tancredi, Lorenzo: Elliptic Feynman integrals and pure functions (2019)
  9. Frellesvig, Hjalte; Gasparotto, Federico; Laporta, Stefano; Mandal, Manoj K.; Mastrolia, Pierpaolo; Mattiazzi, Luca; Mizera, Sebastian: Decomposition of Feynman integrals on the maximal cut by intersection numbers (2019)
  10. Hidding, Martijn; Moriello, Francesco: All orders structure and efficient computation of linearly reducible elliptic Feynman integrals (2019)
  11. Kniehl, Bernd A.; Pikelner, Andrey F.; Veretin, Oleg L.: Three-loop effective potential of general scalar theory via differential equations (2018)
  12. Lee, Roman N.; Smirnov, Alexander V.; Smirnov, Vladimir A.: Solving differential equations for Feynman integrals by expansions near singular points (2018)
  13. 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)
  14. Bosma, Jorrit; Sogaard, Mads; Zhang, Yang: Maximal cuts in arbitrary dimension (2017)
  15. Frellesvig, Hjalte; Papadopoulos, Costas G.: Cuts of Feynman integrals in Baikov representation (2017)
  16. Gituliar, Oleksandr; Magerya, Vitaly: Fuchsia: a tool for reducing differential equations for Feynman master integrals to epsilon form (2017)
  17. Kasper J. Larsen, Robbert Rietkerk: MultivariateResidues - a Mathematica package for computing multivariate residues (2017) arXiv
  18. Mario Prausa: epsilon: A tool to find a canonical basis of master integrals (2017) arXiv
  19. Prausa, Mario: \textttepsilon: a tool to find a canonical basis of master integrals (2017)
  20. Zeng, Mao: Differential equations on unitarity cut surfaces (2017)