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

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 10¹⁵ is achieved for arbitrary real values of the momentum transfer.

Program summary

Title of program:sunemVersion: 1.0Release: 1Catalogue identifier: ADYC_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADYC_v1_0Program obtainable from:http://www-ttp.physik.uni-karlsruhe.de/Progdata/Computers: allOperating system: allProgram language used:FORTRAN77No. of lines in distributed program, including test data, etc.:1080No. of bytes in distributed program, including test data, etc.: 11 835Memory required to execute: Size: 1532KNo. of bits in a word: up to 32No. of processors used: 1Distribution format: tar.gzOther programs called: noneExternal files needed: noneNature 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 10¹⁵ 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.