  We have examined the momentum expansion of the disk level S-matrix element of
two tachyons and two gauge fields to find, up to on-shell ambiguity, the
couplings of these fields in the world volume theory of N coincident non-BPS
D-branes to all order of $\alpha'$. Using the proposal that the action of
D-brane-anti-D-brane is given by the projection of the action of two non-BPS
D-branes with $(-1)^{F_L}$, we find the corresponding couplings in the world
volume theory of the brane-anti-brane system. Using these infinite tower of
couplings, we then calculate the massless pole of the scattering amplitude of
one RR field, two tachyons and one gauge field in the brane-anti-brane theory.
We find that the massless pole of the field theory amplitude is exactly equal
to the massless pole of the disk level S-matrix element of one RR, two tachyons
and one gauge field to all order of $\alpha'$.
