High energy scattering on distant branes

We consider the elastic scattering of two open strings living on two D-branes separated by a distance r. We compute the high-energy behavior of the amplitude, to leading order in string coupling, as a function of the scattering angle and of the dimensionless parameter v = r/(πα'√s) with √s the center-of-mass energy. The result exhibits an interesting phase diagram in the (v,) plane, with a transition at the production threshold for stretched strings at v = 1. We also discuss some more general features of the open-string semiclassical world-sheets, and use T-duality to give a quantum tunneling interpretation of the exponential suppression at high-energy.