Towards extending the Chern-Simons couplings at order $O(\alpha'^2)$

Using the compatibility of the anomalous Chern-Simons couplings on D$_p$-branes with the linear T-duality and with the antisymmetric B-field gauge transformations, some couplings have been recently found for $C^{(p-3)}$ at order $O(\alpha'^2)$. We examine these couplings with the S-matrix element of one RR and two antisymmetric B-field vertex operators. We find that the S-matrix element reproduces these couplings as well as some other couplings. Each of them is invariant under the linear T-duality and the B-field gauge transformations.