Regge Closed String Scattering and its Implication on Fixed angle Closed String Scattering

We calculate the complete closed string high energy scattering amplitudes (HSA) in the Regge regime for arbitrary mass levels. As an application, we deduce the complete ratios among closed string HSA in the fixed angle regime by using Stirling number identities. These results are in contrast with the incomplete set of closed string HSA in the fixed angle regime calculated previously. The complete forms of the fixed angle amplitudes, and hence the ratios, were not calculable previously without the input of zero-norm state calculation. This is mainly due to the lack of saddle point in the fixed angle closed string calculation.Comment: 10 pages. v2: typos correcte

High-Energy String Scattering Amplitudes and Signless Stirling Number Identity

We give a complete proof of a set of identities (7) proposed recently from calculation of high-energy string scattering amplitudes. These identities allow one to extract ratios among high-energy string scattering amplitudes in the fixed angle regime from high-energy amplitudes in the Regge regime. The proof is based on a signless Stirling number identity in combinatorial theory. The results are valid for arbitrary real values $L$ rather than only for $L=0,1$ proved previously. The identities for non-integer real value $L$ were recently shown to be realized in high-energy compactified string scattering amplitudes [He S., Lee J.C., Yang Y., arXiv:1012.3158]. The parameter $L$ is related to the mass level of an excited string state and can take non-integer values for Kaluza-Klein modes

Exponential fall-off Behavior of Regge Scatterings in Compactified Open String Theory

We calculate massive string scattering amplitudes of compactified open string 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. The complete ratios calculated by this indirect method include and extend the subset of ratios calculated previously (Lee and Yang, 2007, and Lee, Takimi, and Yang, 2008) by the more difficult direct fixed angle calculation. In this calculation of compactified open string scattering, we discover a realization of arbitrary real values L in the identity Eq.(4.18), rather than integer value only in all previous high-energy string scattering amplitude calculations. The identity in Eq.(4.18) was explicitly proved recently in Lee, Yan, and Yang to link fixed angle and Regge string scattering amplitudes. In addition, we discover a kinematic regime with stringy highly winding modes, which shows the unusual exponential fall-off behavior in the Regge string scattering. This is in complementary with a kenematic regime discovered previously (Lee, Takimi, and Yang, 2008), which shows the unusual power-law behavior in the high-energy fixed angle compactified string scatterings. Key words: Regge string scatterings; High-energy StringComment: 17 pages. v2:18 pages,corrected Eqs.(3.4),(4.24)-(4.26). v3:19 pages,Eqs.(3.11),(3.12) added, more on conclusion. arXiv admin note: text overlap with arXiv:0805.3168, arXiv:1101.1228, arXiv:0811.4502, arXiv:0812.4190, arXiv:1001.539