FORCER, a FORM program for the parametric reduction of four-loop massless propagator diagrams

Abstract

We explain the construction of FORCER, a FORM program for the reduction of four-loop massless propagator-type integrals to master integrals. The resulting program performs parametric IBP reductions similar to the three-loop MINCER program. We show how one can solve many systems of IBP identities parametrically in a computer-assisted manner. Next, we discuss the structure of the FORCER program, which involves recognizing reduction actions for each topology, applying symmetries, and transitioning between topologies after edges have been removed. This part is entirely precomputed and automatically generated. We give examples of recent applications of FORCER, and study the performance of the program. Finally we demonstrate how to use the FORCER package and sketch how to prepare physical diagrams for evaluation by FORCER. Program summary: Program title: Forcer. Program files doi: http://dx.doi.org/10.17632/d4jy7mfjxf.1 Licensing provisions: GNU General Public License, version 3. Programming language: FORM. The generating scripts are written in Python. Nature of problem: Some physical quantities in perturbative quantum field theories require the evaluation of dimensionally regularized massless propagator-type Feynman integrals. This can be achieved by reducing the integrals in the problem to a set of master integrals and then substituting their values. At the four-loop level, such a reduction becomes highly non-trivial and very time-consuming. One needs an efficient program for the reduction. Solution method: The program recursively applies pre-derived parametric reduction rules for four-loop massless propagator-type Feynman integrals. Many rules were derived from topology substructures and were automatically generated by Python code. Some special cases were carefully optimized in a computer-assisted manner. Restrictions: Limitations come from the fact that reducing too complicated integrals requires too much CPU time and storage space. If rational coefficients become too large to be handled in FORM, then one needs to consider using truncated expansions. © 2020 Elsevier