IBIS: Inverse BInomial sum Solver

Abstract

Ever-increasing experimental precision demands correspondingly more accurate theoretical predictions. This is particularly important in Quantum Chromodynamics (QCD), where significant perturbative corrections make the evaluation of higher-order Feynman integrals all the more essential. By employing the Mellin–Barnes representation, such integrals can be converted into sums of residues. One notable subset of these are the inverse binomial sums. In this work I will introduce IBIS (Inverse BInomial sum Solver), a computational tool developed in FORM that solves these inverse binomial sums in terms of so-called S-sums. I begin by outlining the foundational physics of QCD and the mathematical framework for solving Feynman integrals, motivating the need for tools like IBIS. I then elaborate on the theoretical foundations and implementation of IBIS, detailing its recursion techniques, input/output structure, and performance benchmarks. Additionally, I will showcase the practical utility of IBIS through an application to higher-loop integrals, demonstrating its potential to broaden the scope of possible loop calculations and pave the way for more complex studies in perturbative quantum field theory.