Massive Superstring Scatterings in the Regge Regime

TL;DR

This paper computes high-energy massive fermionic string scattering amplitudes in the Regge regime, expressing them via Kummer functions, and demonstrates the persistence of known ratios across regimes, revealing deep structural connections.

Contribution

It introduces a method to express all leading order amplitudes in the Regge regime using Kummer functions and links these to previously known ratios from the Gross regime.

Findings

All four leading order amplitudes can be expressed with Kummer functions.

Ratios from the Gross regime can be derived from Regge regime amplitudes.

The ratios persist to subleading orders in the Regge expansion.

Abstract

We calculate four classes of high energy massive string scattering amplitudes of fermionic string theory at arbitrary mass levels in the Regge regime (RR). We show that all four leading order amplitudes in the RR can be expressed in terms of the Kummer function of the second kind. Based on the summation algorithm of a set of extended signed Stirling number identities, we show that all four ratios calculated previously by the method of decoupling of zero-norm states among scattering amplitudes in the Gross Regime (GR) can be extracted from this Kummer function in the RR. Finally, we conjecture and give evidences that the existence of these four GR ratios in the RR persists to subleading orders in the Regge expansion of all high energy fermionic string scattering amplitudes.