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 summary Program title: BOKASUN Catalogue identifier: AECG_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AECG-v1-0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac,uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 9404 No. of bytes in distributed program, including test data, etc.: 104123 Distribution format. tar.gz Programming language: FORTRAN77 Computer: Any computer with a Fortran compiler accepting FORTRAN77 standard. Tested on various PC's with LINUX Operating system: LINUX RAM: 120 kbytes Classification: 4.4 Nature 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 p(2). The method is a combination of an accelerated expansion in 1/p(2) in its (pretty largel) 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 mu s for series expansion with pre-calculated coefficients, 80 mu s 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). (C) 2008 Elsevier B.V. All rights reserved.