Scatterings of Massive String States from D-brane and Their Linear Relations at High Energies

TL;DR

This paper analyzes high-energy scattering amplitudes of massive closed string states from D-branes, revealing they can be expressed via hypergeometric functions that simplify to beta functions, and uncovers linear relations among these amplitudes.

Contribution

It introduces a novel expression of scattering amplitudes in terms of hypergeometric functions and derives infinite linear relations at high energies for arbitrary mass levels.

Findings

Amplitudes reduce to beta functions at high energies.

Linear relations among scattering amplitudes are established.

Ratios of amplitudes align with zero-norm state decoupling.

Abstract

We study scatterings of bosonic massive closed string states at arbitrary mass levels from D-brane. We discover that all the scattering amplitudes can be expressed in terms of the generalized hypergeometric function with special arguments, which terminates to a finite sum and, as a result, the whole scattering amplitudes consistently reduce to the usual beta function. For the simple case of D-particle, we explicitly calculate high-energy limits of a series of the above scattering amplitudes for arbitrary mass levels, and derive infinite linear relations among them for each fixed mass level. The ratios of these high-energy scattering amplitudes are found to be consistent with the decoupling of high-energy zero-norm states of our previous works.