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We evaluate in detail the string scattering amplitude to compute differentinteractions of two massless scalars, one tachyon and one closed stringRamond-Ramond field in type II super string theory. In particular we find twoscalar field and two tachyon couplings to all orders of $\alpha'$ up toon-shell ambiguity. We then obtain the momentum expansion of this amplitude andapply this infinite number of couplings to actually check that the infinitenumber of tachyon poles of S-matrix element of this amplitude for the $p=n$case (where $p$ is the spatial dimension of a D$_p$-brane and $n$ is the rankof a Ramond-Ramond field strength) to all orders of $\alpha'$ is preciselyequal to the infinite number of tachyon poles of the field theory. In additionto confirming the couplings of closed string Ramond-Ramond field to theworld-volume gauge field and scalar fields including commutators, we alsopropose an extension of the Wess-Zumino action which naturally reproduces thesenew couplings in field theory such that they could be confirmed with directS-matrix computations. Finally we show that the infinite number of masslesspoles and contact terms of this amplitude for the $p=n+1$ case can bereproduced by Chern-Simons, higher derivative corrections of the Wess-Zuminoand symmetrized trace tachyon DBI actions.

On higher derivative corrections to Wess-Zumino and Tachyonic actions in type II super string theory