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We reconsider the two-point string scattering amplitudes of masslessNeveu-Schwarz--Neveu-Schwarz states of Type IIB orientifold superstring theoryon the disk and projective plane in ten dimensions and analyse its $\alpha'$expansion. We also discuss the unoriented Type IIB theory on$T^6/\mathbb{Z}_2\times\mathbb{Z}_2$ where two-point string scatteringamplitudes of the complex K\"ahler moduli and complex structures of theuntwisted sector are computed on the disk and projective plane. New results areobtained together with known ones. Finally, we compare string scatteringamplitudes results at $\alpha'^2$-order with the (curvature)$^2$ terms in thelow energy effective action of D-branes and $\Omega$-planes in both cases.

Closed superstring moduli tree-level two-point scattering amplitudes in Type IIB orientifold on $T^6/(Z_2\times Z_2)$