Analytic evaluation of the three-loop three-point form factor of tr ϕ3 in $$ \mathcal{N} $$ = 4 sYM

A bstract We compute analytically the three-loop correlation function of the local operator tr ϕ 3 inserted into three on-shell states, in maximally supersymmetric Yang-Mills theory. The result is expressed in terms of Chen iterated integrals. We also present our result using generalised polylogarithms, and evaluate them numerically, finding agreement with a previous numerical result in the literature. We observe that the result depends on fewer kinematic singularities compared to individual Feynman integrals. Furthermore, upon choosing a suitable definition of the finite part, we find that the latter satisfies powerful symbol adjacency relations similar to those previously observed for the tr ϕ 2 case.