TSIL: a program for the calculation of two-loop self-energy integrals

TSIL is a library of utilities for the numerical calculation of dimensionally regularized two-loop self-energy integrals. A convenient basis for these functions is given by the integrals obtained at the end of O.V. Tarasov's recurrence relation algorithm. The program computes the values of all of these basis functions, for arbitrary input masses and external momentum. When analytical expressions in terms of polylogarithms are available, they are used. Otherwise, the evaluation proceeds by a Runge-Kutta integration of the coupled first-order differential equations for the basis integrals, using the external momentum invariant as the independent variable. The starting point of the integration is provided by known analytic expressions at (or near) zero external momentum. The code is written in C, and may be linked from C/C++ or Fortran. A Fortran interface is provided. We describe the structure and usage of the program, and provide a simple example application. We also compute two new cases analytically, and compare all of our notations and conventions for the two-loop self-energy integrals to those used by several other groups.

Program summary

Title of program:TSILVersion number: 1.0Catalogue identifier: ADWSProgram summary URL:http://cpc.cs.qub.ac.uk/summaries/ADWSProgram obtainable from: CPC Program Library, Queen's University of Belfast, N. IrelandProgramming language: CPlatform: Any platform supporting the GNU Compiler Collection (gcc), the Intel C compiler (icc), or a similar C compiler with support for complex mathematicsNo. of lines in distributed program, including test data, etc.: 42 730No. of bytes in distributed program, including test data, etc.: 297 101Distribution format: tar.gzNature of physical problem: Numerical evaluation of dimensionally regulated Feynman integrals needed in two-loop self-energy calculations in relativistic quantum field theory in four dimensions.Method of solution: Analytical evaluation in terms of polylogarithms when possible, otherwise through Runge-Kutta solution of differential equations.Limitations: Loss of accuracy in some unnatural threshold cases that do not have vanishing masses.Typical running time: Less than a second.