Note on high energy scattering of open superstrings

We study the Regge and hard-scattering limits of the one-loop amplitude for massless open string states in the type I theory in flat space. For hard scattering we find the exact kinematic dependence in terms of the scattering angle of the factor multiplying the known exponential falloff, without relying on a saddle point approximation for the integration over the cross ratio. This bypasses the issues of estimating the contributions from flat directions as well as those that arise from fluctuations of the Gaussian integration about the saddle point. This result allows for a straightforward computation of the small-angle behavior of the hard-scattering regime and we find complete agreement with the Regge limit at high momentum transfer, as expected.