Patterns of High energy Massive String Scatterings in the Regge regime

Abstract

We calculate high energy massive string scattering amplitudes of open bosonic string in the Regge regime (RR). We found that the number of high energy amplitudes for each fixed mass level in the RR is much more numerous than that of Gross regime (GR) calculated previously. Moreover, we discover that the leading order amplitudes in the RR can be expressed in terms of the Kummer function of the second kind. In particular, based on a summation algorithm for Stirling number identity, we discover that the ratios calculated previously among scattering amplitudes in the GR can be extracted from this Kummer function in the RR. We conjecture and give evidences that the existence of these GR ratios in the RR persists to subleading orders in the Regge expansion of all string scattering amplitudes. Finally, we demonstrate the universal power-law behavior for all massive string scattering amplitudes in the RR.

25 pages,1 figure, typos corrected, refs added

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• Review on High energy String Scattering Amplitudes and Symmetries of String Theory
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• Higher Spin String States Scattered from D-particle in the Regge Regime and Factorized Ratios of Fixed Angle Scatterings
• The Appell Function $F_1$ and Regge String Scattering Amplitudes
• High-Energy String Scattering Amplitudes and Signless Stirling Number Identity
• Regge Closed String Scattering and its Implication on Fixed angle Closed String Scattering
• Solving Lauricella String Scattering Amplitudes through Recurrence Relations
• To see Symmetry in a Forest of Trees
• Kummer function and High energy String Scatterings
• Recent developments of the Lauricella string scattering amplitudes and their exact SL(K+3,C) Symmetry
• Recurrence Relations of Higher Spin BPST Vertex Operators for Open String
• High-Energy Symmetry of Bosonic Open String Theory in the Light-like Linear Dilaton Background
• Stirling number Identities and High energy String Scatterings
• The exact SL(K+3,C) symmetry of string theory
• Vertex Operators and Scattering Amplitudes of the Bosonic Open String Theory in the Linear Dilaton Background
• Residues of bosonic string scattering amplitudes and the Lauricella functions
• String Scattering Amplitudes in High Energy Limits