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

TL;DR

This paper investigates high-energy scattering amplitudes of compactified open strings, revealing exponential fall-off behavior and extending known amplitude ratios, with implications for understanding string dynamics in compactified dimensions.

Contribution

It introduces a novel analysis of Regge scattering amplitudes, including arbitrary real parameters and new kinematic regimes with winding modes, extending previous fixed angle results.

Findings

Discovered exponential fall-off behavior in Regge string scatterings.

Extended amplitude ratio calculations to include arbitrary real values.

Identified a kinematic regime with highly winding modes showing exponential decay.

Abstract

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 String