Higher Spin String States Scattered from D-Particle in the Regge Regime and Factorized Ratios of Fixed Angle Scatterings

Abstract

We study scattering of higher spin closed string states at arbitrary mass levels from D-particle in the Regge regime. We extract the complete infinite ratios among high-energy amplitudes of different string states in the fixed angle regime from these Regge string scattering amplitudes. In this calculation, we have used an identity proved recently based on a signless Stirling number identity in combinatorial theory. The complete ratios calculated by this indirect method include a subset of ratios calculated previously by direct fixed angle calculation [C. T. Chan, J. C. Lee and Y. Yang, Nucl. Phys. B 764 (2007), 1]. Moreover, we discover that in spite of the non-factorizability of the closed string D-particle scattering amplitudes, the complete ratios derived for the fixed angle regime are found to be factorized. These ratios are consistent with the decoupling of high-energy zero norm states calculated previously.