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

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. Tarasovʹs 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.