epsilon : A tool to find a canonical basis of master integrals

Abstract 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 − 2 ϵ 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. Program summary Program Title: epsilon Program Files doi: http://dx.doi.org/10.17632/j59sy5n729.1 Licensing provisions: GPLv3 Programming language: C++ Nature of problem: For a certain class of master integrals, a canonical basis can be found in which they fulfill a differential equation with the right hand side proportional to ϵ . In such a basis the solution of the master integrals in an ϵ -expansion becomes trivial. Unfortunately, the problem of finding a canonical basis is challenging. Solution method: Algorithm by Lee [1] Restrictions: The normalization step of Lee’s algorithm will fail if the eigenvalues of the matrix residues are not of the form a + b ϵ with a , b ∈ Z . Multi-scale problems are not supported. [1] R.N. Lee, JHEP 1504 (2015) 108 [ arXiv:1411.0911 [hep-ph]].