Patterns of High energy Massive String Scatterings in the Regge regime

TL;DR

This paper analyzes high energy massive string scattering amplitudes in the Regge regime, revealing a richer structure than previously known in the Gross regime, with new mathematical expressions and universal power-law behavior.

Contribution

It introduces a detailed calculation of scattering amplitudes in the Regge regime, expressing leading order amplitudes via Kummer functions, and uncovers persistent ratios and universal power-law behavior.

Findings

More numerous high energy amplitudes in RR than GR

Leading amplitudes expressed with Kummer functions

Universal power-law behavior in RR amplitudes

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.