On-shell S-matrix and tachyonic effective actions
  We evaluate various disk level four-point functions involving the massless scalar and tachyon vertex operators in the presence of background B-flux in superstring theory. By studying these amplitudes in specific limits, we find couplings of two scalars with two tachyons, and couplings of four tachyons on the world-volume of non-BPS D-branes of superstring theory. They are fully consistent with the non-commutative tachyonic Dirac-Born-Infeld effective action. They also fix the coefficient of $T^4$ term in the expansion of the tachyon potential around its maximum. 
Mohammad R. Garousi