High-Energy String Scattering Amplitudes and Signless Stirling Number Identity

Abstract

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.

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Cited by in corpus (7)

• The Lauricella Functions and Exact String Scattering Amplitudes
• Higher Spin String States Scattered from D-particle in the Regge Regime and Factorized Ratios of Fixed Angle Scatterings
• The SL(K+3,C) Symmetry of the Bosonic String Scattering Amplitudes
• Solving Lauricella String Scattering Amplitudes through Recurrence Relations
• The Exact SL(K+3,C) Symmetry of String Scattering Amplitudes
• Residues of bosonic string scattering amplitudes and the Lauricella functions
• String Scattering Amplitudes in High Energy Limits