Two Ramond-Ramond corrections to type II supergravity via field-theory amplitude

Motivated by the standard form of the string theory amplitude, we calculate the field-theory amplitude to complete the higher-derivative terms in type II supergravity theories in their conventional form. We derive explicitly the O(alpha'(3)) interactions for the RR (Ramond-Ramond) fields with graviton, B-field and dilaton in the low-energy effective action of type II superstrings. We check our results by comparison with previous work that has been done by the other methods, and we find exact agreement.