Abstract
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: TSIL Version number: 1.0 Catalogue identifier: ADWS Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADWS Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Programming language: C Platform: Any platform supporting the GNU Compiler Collection (gcc), the Intel C compiler (icc), or a similar C compiler with support for complex mathematics No. of lines in distributed program, including test data, etc.: 42 730 No. of bytes in distributed program, including test data, etc.: 297 101 Distribution format: tar.gz Nature 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.
Highlights
The precision of measurements within the Standard Model requires a level of accuracy obtained from two-loop, and even higher-order, calculations in quantum field theory
Supersymmetry predicts the existence of many new particle states with perturbative interactions
TSIL is a library of functions written in C, which can be linked from C, C++, or Fortran code.† In addition to the main evaluation functions, it contains a variety of routines for I/O and other utilities
Summary
The precision of measurements within the Standard Model requires a level of accuracy obtained from two-loop, and even higher-order, calculations in quantum field theory. The most important observables in softly broken supersymmetry are just the new particle masses. Comparisons of particular models of supersymmetry breaking with experiment will require systematic methods for two-loop computations of physical pole masses in terms of the underlying Lagrangian parameters. In a general quantum field theory, the necessary dimensionally regularized Feynman integrals can be expressed in the form: μ8−2d ddk ddq [k2. In the remainder of this section, we will describe our notations and conventions‡ for the two-loop basis integrals and some related functions, and describe the strategy used by TSIL to compute them. The loop integrals are functions of a common external momentum invariant s = −p2.
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