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We classify the 3-point functions of local gauge-invariant single-traceoperators in the scalar sector of planar N=4 supersymmetric Yang-Millsinvolving at least one su(3) operator. In the case of two su(3) and one su(2)operators, the tree-level 3-point function can be expressed in terms of scalarproducts of su(3) Bethe vectors. Moreover, if the second level Bethe roots ofone of the su(3) operators is trivial (set to infinity), this 3-point functioncan be written in a determinant form. Using the determinant representation, weevaluate the structure constant in the semi-classical limit, when the number ofroots goes to infinity.

A tree-level 3-point function in the su(3)-sector of planar N=4 SYM