BOKASUN: A fast and precise numerical program to calculate the Master Integrals of the two-loop sunrise diagrams

We present the program BOKASUN for fast and precise evaluation of the Master Integrals of the two-loop self-mass sunrise diagram for arbitrary values of the internal masses and the external four-momentum. We use a combination of two methods: a Bernoulli accelerated series expansion and a Runge–Kutta numerical solution of a system of linear differential equations.Program summaryProgram title: BOKASUNCatalogue identifier: AECG_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AECG_v1_0.htmlProgram obtainable from: CPC Program Library, Queen's University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 9404No. of bytes in distributed program, including test data, etc.: 104 123Distribution format: tar.gzProgramming language: FORTRAN77Computer: Any computer with a Fortran compiler accepting FORTRAN77 standard. Tested on various PC's with LINUXOperating system: LINUXRAM: 120 kbytesClassification: 4.4Nature of problem: Any integral arising in the evaluation of the two-loop sunrise Feynman diagram can be expressed in terms of a given set of Master Integrals, which should be calculated numerically. The program provides a fast and precise evaluation method of the Master Integrals for arbitrary (but not vanishing) masses and arbitrary value of the external momentum.Solution method:   The integrals depend on three internal masses and the external momentum squared p2p2. The method is a combination of an accelerated expansion in 1/p21/p2 in its (pretty large!) region of fast convergence and of a Runge–Kutta numerical solution of a system of linear differential equations.Running time: To obtain 4 Master Integrals on PC with 2 GHz processor it takes 3 μs for series expansion with pre-calculated coefficients, 80 μs for series expansion without pre-calculated coefficients, from a few seconds up to a few minutes for Runge–Kutta method (depending on the required accuracy and the values of the physical parameters).