@article{TMF_2024_219_3_a6,
author = {V. A. Smirnov},
title = {Simplifying the~large-mass expansion of {Feynman} integrals},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {523--530},
year = {2024},
volume = {219},
number = {3},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2024_219_3_a6/}
}
V. A. Smirnov. Simplifying the large-mass expansion of Feynman integrals. Teoretičeskaâ i matematičeskaâ fizika, Tome 219 (2024) no. 3, pp. 523-530. http://geodesic.mathdoc.fr/item/TMF_2024_219_3_a6/
[1] K. G. Chetyrkin, “Operatornye razlozheniya v skheme minimalnykh vychitanii. I. Metod skleivaniya”, TMF, 75:1 (1988), 26–40 | DOI | MR
[2] S. G. Gorishny, “Construction of operator expansions and effective theories in the MS scheme”, Nucl. Phys. B, 319:3 (1989), 633–666 | DOI | MR
[3] V. A. Smirnov, “Asymptotic expansions in limits of large momenta and masses”, Commun. Math. Phys., 134:1 (1990), 109–137 | DOI | MR
[4] V. A. Smirnov, “Asymptotic expansions in momenta and masses and calculation of Feynman diagrams”, Modern Phys. Lett. A, 10:21 (1995), 1485–1499, arXiv: hep-th/9412063 | DOI
[5] V. A. Smirnov, Analytic Tools for Feynman Integrals, Springer Tracts in Modern Physics, 250, Springer, Heidelberg, 2012 | DOI | MR
[6] M. Beneke, V. A. Smirnov, “Asymptotic expansion of Feynman integrals near threshold”, Nucl. Phys. B, 522:1–2 (1998), 321–344, arXiv: hep-ph/9711391 | DOI
[7] V. A. Smirnov, “Problems of the strategy of regions”, Phys. Lett. B, 465:1–4 (1999), 226–234, arXiv: hep-ph/9907471 | DOI
[8] V. A. Smirnov, Applied Asymptotic Expansions in Momenta and Masses, Springer Tracts in Modern Physics, 177, Springer, Berlin, 2002 | DOI | MR
[9] V. A. Smirnov, “Expansion by regions: An overview”, Anti-Differentiation and the Calculation of Feynman Amplitudes, eds. J. Blümlein, C. Schneider, Springer, Cham, 2021, 487–499 | DOI | MR
[10] A. Pak, A. Smirnov, “Geometric approach to asymptotic expansion of Feynman integrals”, Eur. Phys. J. C, 71 (2011), 1626, 6 pp., arXiv: 1011.4863 | DOI | MR
[11] B. Jantzen, A. V. Smirnov, V. A. Smirnov, “Expansion by regions: revealing potential and Glauber regions automatically”, Eur. Phys. J. C, 72 (2012), 2139, 14 pp., arXiv: 1206.0546 | DOI
[12] A. V. Smirnov, N. D. Shapurov, L. I. Vysotsky, “FIESTA5: Numerical high-performance Feynman integral evaluation”, Comput. Phys. Commun., 277 (2022), 108386, 16 pp., arXiv: 2110.11660 | DOI | MR
[13] M. Bonetti, Private communication, 2023
[14] K. G. Chetyrkin, F. V. Tkachov, “Integration by parts: The algorithm to calculate beta functions in 4 loops”, Nucl. Phys. B, 192:1 (1981), 159–204 | DOI
[15] R. N. Lee, Presenting LiteRed: a tool for the Loop InTEgrals REDuction, arXiv: 1212.2685
[16] R. N. Lee, “LiteRed 1.4: a powerful tool for reduction of multiloop integrals”, J. Phys.: Conf. Ser., 523 (2014), 012059, 8 pp., arXiv: 1310.1145 | DOI
[17] A. V. Smirnov, “FIRE5: A C++ implementation of Feynman integral reduction”, Comput. Phys. Commun., 189 (2015), 182–191, arXiv: 1408.2372 | DOI
[18] A. V. Smirnov, F. S. Chukharev, “FIRE6: Feynman integral reduction with modular arithmetic”, Comput. Phys. Commun., 247 (2020), 106877, 14 pp., arXiv: 1901.07808 | DOI
[19] A. V. Kotikov, “Differential equations method. New technique for massive Feynman diagrams calculation”, Phys. Lett. B, 254:1–2 (1991), 158–164 | DOI | MR
[20] T. Gehrmann, E. Remiddi, “Differential equations for two loop four-point functions”, Nucl. Phys. B, 580:1–2 (2000), 485–518, arXiv: hep-ph/9912329 | DOI | MR
[21] J. M. Henn, “Multiloop integrals in dimensional regularization made simple”, Phys. Rev. Lett., 110:25 (2013), 251601, 4 pp., arXiv: 1304.1806 | DOI
[22] T. Peraro, “Scattering amplitudes over finite fields and multivariate functional reconstruction”, JHEP, 12 (2016), 030, 45 pp., arXiv: 1608.01902 | DOI | MR
[23] T. Peraro, “FiniteFlow: multivariate functional reconstruction using finite fields and dataflow graphs”, JHEP, 07 (2019), 031, 56 pp., arXiv: 1905.08019 | DOI | MR
[24] J. Klappert, F. Lange, “Reconstructing rational functions with FireFly”, Comput. Phys. Commun., 247 (2020), 106951, 18 pp., arXiv: 1904.00009 | DOI
[25] J. Klappert, S. Y. Klein, F. Lange, “Interpolation of dense and sparse rational functions and other improvements in FireFly”, Comput. Phys. Commun., 264 (2021), 107968, 18 pp., arXiv: 2004.01463 | DOI | MR
[26] A. V. Belitsky, A. V. Smirnov, R. V. Yakovlev, “Balancing act: Multivariate rational reconstruction for IBP”, Nucl. Phys. B, 993 (2023), 116253, 16 pp., arXiv: 2303.02511 | DOI | MR
[27] P. A. Baikov, K. G. Chetyrkin, “Four loop massless propagators: An algebraic evaluation of all master integrals”, Nucl. Phys. B, 837:3 (2010), 186–220, arXiv: 1004.1153 | DOI | MR
[28] R. N. Lee, A. V. Smirnov, V. A. Smirnov, “Master integrals for four-loop massless propagators up to transcendentality weight twelve”, Nucl. Phys. B, 856:1 (2012), 95–110, arXiv: 1108.0732 | DOI | MR
[29] B. Ruijl, T. Ueda, J. A. M. Vermaseren, “Forcer, a Form program for the parametric reduction of four-loop massless propagator diagrams”, Comput. Phys. Commun., 253 (2020), 107198, 23 pp., arXiv: 1704.06650 | DOI | MR
[30] S. G. Gorishnii, S. A. Larin, L. R. Surguladze, F. V. Tkachov, “Mincer: Program for multiloop calculations in quantum field theory for the Schoonschip system”, Comput. Phys. Commun., 55:3 (1989), 381–408 | DOI
[31] S. A. Larin, F. V. Tkachov, J. A. M. Vermaseren, The FORM version of MINCER, Report NIKHEF-H-91-18, Netherlands, 1991