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

We consider a particular case of the 3-point function of local single-trace operators in the scalar sector of planar N=4 supersymmetric Yang-Mills, where two of the fields are su(3) type, while the third one is su(2) type. We show that this tree-level 3-point function can be expressed in terms of scalar products of su(3) Bethe vectors. Moreover, if the second level Bethe roots of one of the su(3) operators is trivial (set to infinity), this 3- point function can be written in a determinant form. Using the determinant representation, we evaluate the structure constant in the semi-classical limit, when the number of roots goes to infinity.