On the Computation of Form Factors in Massless QCD with Finite Master Integrals

TL;DR

This paper computes massless QCD form factors at multiple loops using finite master integrals, providing new insights into their structure and an automated software tool for such calculations.

Contribution

It introduces a method to express form factors with finite master integrals and reveals a phenomenon where only integrals with fewer propagators influence cusp anomalous dimensions.

Findings

Reproduces known results via symbolic integration.

Identifies a pattern in propagator contributions to cusp anomalous dimensions.

Provides software for automated finite master integral computation.

Abstract

We present the bare one-, two-, and three-loop form factors in massless Quantum Chromodynamics as linear combinations of finite master integrals. Using symbolic integration, we compute their $\epsilon$ expansions and thereby reproduce all known results with an independent method. Remarkably, in our finite basis, only integrals with a less-than-maximal number of propagators contribute to the cusp anomalous dimensions. We report on indications of this phenomenon at four loops, including the result for a finite, irreducible, twelve-propagator form factor integral. Together with this article, we provide our automated software setup for the computation of finite master integrals.