Stringy scaling of n-point hard string scattering amplitudes

TL;DR

This paper uncovers a universal stringy scaling behavior in n-point hard string scattering amplitudes across all loop orders, extending previous conjectures and calculations for four-point functions to arbitrary n-point cases.

Contribution

It introduces a general stringy scaling law for all n-point hard string scattering amplitudes, based on recent symmetry calculations, and extends known four-point relations to arbitrary n-point amplitudes.

Findings

Discovered a universal scaling behavior for n-point HSSA.

Extended four-point amplitude relations to arbitrary n-point cases.

Confirmed the scaling behavior across all string loop orders.

Abstract

Motivated by the recent calculation of the SL(K+3,C) symmetry of n-point Lauricella string scattering amplitudes (SSA) of open bosonic string theory, we calculate ratios of the solvable infinite linear relations of arbitrary n-point hard SSA (HSSA). We discover a general stringy scaling behavior for all n-point HSSA to all string loop orders. For the special case of n=4, the stringy scaling behavior reduces to the infinite linear relations and constant ratios among HSSA conjectured by Gross [8] and later corrected and calculated by the method of decoupling of zero-norm states [11].