Massive three loop form factors in the planar limit

TL;DR

This paper computes three-loop heavy quark form factors in QCD for various currents, using a novel differential equations method to evaluate master integrals, and expresses results with harmonic polylogarithms.

Contribution

Introduces a new differential equations approach for evaluating master integrals in three-loop form factors, applicable to general bases.

Findings

Analytic expressions for three-loop form factors obtained.

Method applicable to any first order factorizing systems.

Results expressed in harmonic polylogarithms and cyclotomic harmonic polylogarithms.

Abstract

We present the color planar and complete light quark QCD contributions to the three loop heavy quark form factors in the case of vector, axial-vector, scalar and pseudo-scalar currents. We evaluate the master integrals applying a new method based on differential equations for general bases, which is applicable for any first order factorizing systems. The analytic results are expressed in terms of harmonic polylogarithms and real-valued cyclotomic harmonic polylogarithms.