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.Subject Index: 129 §1. IntroductionRecently high-energy, fixed angle behavior of string scattering amplitudes 1)-3) was intensively investigated for massive higher-spin string states at arbitrary mass levels. 4)-12) The motivation was to uncover the fundamental hidden stringy spacetime symmetry. An important new ingredient of this calculation was the zero-norm states (ZNS) 13)-15) in the old covariant first quantized string spectrum, in particular, the identification of inter-particle symmetries induced by the inter-particle ZNS 13) in the spectrum. An infinite number of linear relations among high-energy fixed angle scattering amplitudes of different string states at each fixed but arbitrary mass levels can be derived. Moreover, these linear relations can be used to fix the ratios among high-energy scattering amplitudes of different string states at each fixed mass level. On the other hand, 2D discrete zero-norm states were also shown 14) to carry the spacetime ω ∞ symmetry charges of toy 2D string theory. Furthermore, in the high-energy limit, these discrete zero-norm states approach 8), 9) the discrete Polyakov positive-norm states which generate the well-known ω ∞ symmetry of the 2D string. 16)-18) This strongly suggests that the linear relations obtained from zeronorm states are indeed related to the hidden symmetry of the 26 dimensional string.

Review on High energy String Scattering Amplitudes and Symmetries of String Theory

“…The complete ratios were then calculated through a correspondence between HSS ratios and RSS ratios to be discussed in Eq. (0.76) below, and were found to be factorized [43] (see section XIV.C) T N ;2m,2m ′ ;q,q ′ SD T (N ;0,0;0,0)…”

Overview of High Energy String Scattering Amplitudes and Symmetries of String Theory

“…The complete ratios were then calculated through the open string HSS ratios Eq. (3.22), and were found to be factorized [52] T N ;2m,2m ′ ;q,q ′ SD T (N ;0,0;0,0…”

High-Energy String Scattering Amplitudes and Signless Stirling Number Identity

“…For all four classes of high-energy superstring scattering amplitudes, L is an integer too [17]. A recent work on string D-particle scattering amplitudes [26]…”