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epsilon: a tool to find a canonical basis of master integrals. (English) Zbl 1411.81019
Summary: In [“Multiloop integrals in dimensional regularization made simple”, Phys. Rev. Lett. 110, No. 25, 251601, 4 p. (2013; doi:10.1103/PhysRevLett.110.251601)], J. M. 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 \(\epsilon\) in \(d = 4 - 2 \epsilon\) 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 back end.

MSC:
81-04 Software, source code, etc. for problems pertaining to quantum theory
81Q30 Feynman integrals and graphs; applications of algebraic topology and algebraic geometry
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References:
[1] Tkachov, F. V., Phys. Lett., B100, 65-68, (1981)
[2] Chetyrkin, K. G.; Tkachov, F. V., Nuclear Phys., B192, 159-204, (1981)
[3] Smirnov, V. A., Springer Tracts Mod. Phys., 250, 1-296, (2012)
[4] Kotikov, A. V., Phys. Lett., B254, 158-164, (1991)
[5] Kotikov, A. V., Phys. Lett., B259, 314-322, (1991)
[6] Kotikov, A. V., Phys. Lett., B267, 123-127, (1991), [Erratum: Phys. Lett. B295 (1992) 409]. http://dx.doi.org/10.1016/0370-2693(91)90536-Y, http://dx.doi.org/10.1016/0370-2693(92)91582-T
[7] Henn, J. M., Phys. Rev. Lett., 110, 251601, (2013), arXiv:1304.1806
[8] Lee, R. N., J. High Energy Phys., 04, 108, (2015), arXiv:1411.0911
[9] O. Gituliar, V. Magerya, Fuchsia: a tool for reducing differential equations for Feynman master integrals to epsilon form, 2017. arXiv:1701.04269 · Zbl 1411.81015
[10] R.H. Lewis, Computer Algebra System Fermat, https://home.bway.net/lewis, Accessed: 2016-12-19
[11] Moser, J., Math. Z., 72, 379-398, (1959/60)
[12] Bauer, C. W.; Frink, A.; Kreckel, R., J. Symbolic Comput., 33, 1, (2000), arXiv:cs/0004015
[13] PStreams, http://pstreams.sourceforge.net. Accessed: 2016-12-19
[14] Goncharov, A. B.; Spradlin, M.; Vergu, C.; Volovich, A., Phys. Rev. Lett., 105, 151605, (2010), arXiv:1006.5703
[15] Remiddi, E.; Vermaseren, J. A.M., Internat. J. Modern Phys., A15, 725-754, (2000), arXiv:hep-ph/9905237
[16] Maitre, D., Comput. Phys. Comm., 174, 222-240, (2006), arXiv:hep-ph/0507152
[17] J.A.M. Vermaseren, New features of FORM. arXiv:math-ph/0010025 · Zbl 1309.68231
[18] Binosi, D.; Collins, J.; Kaufhold, C.; Theussl, L., Comput. Phys. Comm., 180, 1709-1715, (2009), arXiv:0811.4113
[19] Vermaseren, J. A.M., Comput. Phys. Comm., 83, 45-58, (1994)
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