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

TL;DR

This paper investigates high-energy scattering of higher spin closed string states from D-particles, revealing factorized ratios in fixed angle regimes despite non-factorizable amplitudes, and employs combinatorial identities for calculations.

Contribution

It introduces an indirect method using combinatorial identities to derive fixed angle scattering ratios from Regge regime amplitudes, confirming their factorization.

Findings

Derived complete ratios including previous results

Discovered factorization of ratios despite non-factorizable amplitudes

Confirmed ratios are consistent with zero norm state decoupling

Abstract

We study scattering of higher spin closed string states at arbitrary mass levels from D-particle in the Regge regime. We extract the 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. 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.