Solving Lauricella String Scattering Amplitudes through Recurrence Relations

TL;DR

This paper demonstrates that an infinite set of recurrence relations can be used to solve all Lauricella string scattering amplitudes, expressing them in terms of a single four tachyon amplitude, extending previous high-energy and Regge limit results.

Contribution

The paper introduces a new method to solve all Lauricella SSA using recurrence relations, unifying various scattering amplitude calculations.

Findings

Infinite recurrence relations exist for all energies.

All Lauricella SSA can be expressed via a single four tachyon amplitude.

Extends previous high-energy and Regge limit solvability results.

Abstract

We show that there exist infinite number of recurrence relations valid for all energies among the open bosonic string scattering amplitudes (SSA) of three tachyons and one arbitrary string state, or the Lauricella SSA. Moreover, these infinite number of recurrence relations can be used to solve all the Lauricella SSA and express them in terms of one single four tachyon amplitude. These results extend the solvability of SSA at the high energy, fixed angle scattering limit and those at the Regge scattering limit discovered previously.