The SO(6) Scalar Product and Three-Point Functions from Integrability

In 1012.2475 Escobedo, Gromov, Sever and Vieira suggested a formula for an SU(2) three-point correlation function at weak coupling based on integrability techniques. We generalize it to the SO(6) sector, thus including all possible single-trace scalar operators in $\mathcal{N}=4$ super Yang-Mills, and prove by direct comparison to a perturbative SO(6) calculations that our generalization is valid.