Hexagons and the classical limit

In planar maximally supersymmetric Yang-Mills, we can compute three-point functions at weak coupling using the so-called hexagonalization formalism. The main objects in this framework are called hexagons. We are interested in two sectors of the theory, spanned by operators built entirely from scalar fields, and by spinning operators, respectively. By reviewing the analytic properties of these building blocks, we find new representations for them at weak coupling where the two sectors are on equal footing. We compute the classical limit of the hexagons and of correlation functions in both sectors for some choices of polarizations and our results match previous predictions in the literature.