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

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.Comment: 31 pages. Updated to reflect new functionality through v1.4 May 2016 and new information about use with C++. Source code and documentation are available at http://www.niu.edu/spmartin/TSIL or http://faculty.otterbein.edu/DRobertson/tsil

Investigating the near-criticality of the Higgs boson

“…[109]. The evaluation of the basis functions was done numerically using the code TSIL [110]. The two loop correction to λ is the sum of a QCD term and of an electroweak (EW) term.…”

Two-loop contributions of the order O α t α s $$ \mathcal{O}\left({\alpha}_t{\alpha}_s\right) $$ to the masses of the Higgs bosons in the CP-violating NMSSM

“…The one-loop one-point and two-point functions have been defined in [75,76]. For the two-loop vacuum functions we use the existing results in [77][78][79][80][81][82][83]. Inserting these expansions into the two-loop expressions, we can easily extract the coefficients of the double pole, single pole and finite parts.…”

The m W − m Z interdependence in the Standard Model: a new scrutiny

“…[50]. The evaluation of the basis functions was done numerically using the code TSIL [51] that, according to the authors, reaches a relative accuracy better than 10 −10 in the evaluation of integrals without large hierarchies in the masses.…”