The Riemann curvature correction to the type II supergravity at eight-derivative level is given schematically as (t_8t_8+ frac{1}{8} eps_{10} eps_{10})R^4 at tree-level. The replacement of the generalized Riemann curvature in t_8t_8R^4 , proposed by Gross and Sloan, produces various NS-NS couplings which are invariant under T-duality. Recently, using the combination of S-duality and T-duality transformations on these couplings, we have found groups of couplings which are invariant under the S-duality transformation. In this paper, we have examined the couplings involving the dilaton with direct scattering amplitude calculations of four NS-NS vertex operators in the superstring theory and found exact agreement. The coupling eps_{10} eps_{10}R^4 is a total derivative term at four-field level. The sigma -model beta function approach implies the presence of this term at the tree-level. By examining the sphere-level scattering amplitude of five gravitons, we have also confirmed the presence of this term in the tree-level effective action.

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