Precise numerical evaluation of the two loop sunrise graph Master Integrals in the equal mass case

Abstract

We present a double precision routine in Fortran for the precise and fast numerical evaluation of the two Master Integrals (MIs) of the equal mass two-loop sunrise graph for arbitrary momentum transfer in d = 2 and d = 4 dimensions. The routine implements the accelerated power series expansions obtained by solving the corresponding differential equations for the MIs at their singular points. With a maximum of 22 terms for the worst case expansion a relative precision of better than a part in 10 15 is achieved for arbitrary real values of the momentum transfer. Program summary Title of program: sunem Version: 1.0 Release: 1 Catalogue identifier: ADYC_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADYC_v1_0 Program obtainable from: http://www-ttp.physik.uni-karlsruhe.de/Progdata/ Computers: all Operating system: all Program language used: FORTRAN77 No. of lines in distributed program, including test data, etc.:1080 No. of bytes in distributed program, including test data, etc.: 11 835 Memory required to execute: Size: 1532K No. of bits in a word: up to 32 No. of processors used: 1 Distribution format: tar.gz Other programs called: none External files needed: none Nature of the physical problem: Numerical evaluation of the two Master Integrals of the equal mass two-loop sunrise Feynman graph for arbitrary momentum transfer in d = 2 and d = 4 dimensions. Method of solution: Accelerated power series expansions obtained by solving the differential equations for the MIs at their singular points. With a maximum of 22 terms for the worse case expansion a relative precision of better than a part in 10 15 is achieved for arbitrary real values of the momentum transfer. Restrictions on complexity of the problem: Limited to real momentum transfer and equal internal masses. Typical running time: Approximately 1 μs to evaluate the four Master integrals for a fixed momentum transfer value on a Pentium IV/3 GHz Linux PC.