Towards a four-loop form factor

TL;DR

This paper advances the calculation of a four-loop form factor in N=4 SYM, including non-planar corrections, by developing master integral bases and computational methods, with implications for QCD.

Contribution

It introduces new master integral bases for four-loop form factors and extends computational techniques, addressing non-planar corrections in N=4 SYM.

Findings

Master integrals basis obtained via IBP reduction and Mint package methods.

Consistency between different computational approaches with minor exceptions.

Potential applicability of master integrals to QCD beyond N=4 SYM.

Abstract

The four-loop, two-point form factor contains the first non-planar correction to the lightlike cusp anomalous dimension. This anomalous dimension is a universal function which appears in many applications. Its planar part in N = 4 SYM is known, in principle, exactly from AdS/CFT and integrability while its non-planar part has been conjectured to vanish. The integrand of the form factor of the stress-tensor multiplet in N = 4 SYM including the non-planar part was obtained in previous work. We parametrise the difficulty of integrating this integrand. We have obtained a basis of master integrals for all integrals in the four-loop, two-point class in two ways. First, we computed an IBP reduction of the integrand of the N = 4 form factor using massive computer algebra (Reduze). Second, we computed a list of master integrals based on methods of the Mint package, suitably extended using Macaulay2 / Singular. The master integrals obtained in both ways are consistent with some minor exceptions. The second method indicates that the master integrals apply beyond N = 4 SYM, in particular to QCD. The numerical integration of several of the master integrals will be reported and remaining obstacles will be outlined