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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.

81-04 Software, source code, etc. for problems pertaining to quantum theory
81Q30 Feynman integrals and graphs; applications of algebraic topology and algebraic geometry
Full Text: DOI
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