The String BCJ Relations Revisited and Extended Recurrence relations of Nonrelativistic String Scattering Amplitudes

TL;DR

This paper revisits and extends high energy string BCJ relations, providing explicit proofs, calculating nonrelativistic scattering amplitudes, and deriving recurrence relations that connect amplitudes across different spins and channels.

Contribution

It offers a comprehensive proof of string BCJ relations at all energies and introduces extended recurrence relations for nonrelativistic string scattering amplitudes.

Findings

BCJ relations hold at all energies for string scattering.

Nonrelativistic string amplitudes relate to hypergeometric functions.

Extended recurrence relations connect amplitudes of different spins and channels.

Abstract

We review and extend high energy string BCJ relations in both the fixed angle and Regge regimes. We then give an explicit proof of four point string BCJ relations for all energy. This calculation provides an alternative proof of the one based on monodromy of integration in string amplitude calculation. In addition, we calculate both s-t and t-u channel nonrelativistic low energy string scattering amplitudes of three tachyons and one leading trojectory string state at arbitrary mass levels. We discover that the mass and spin dependent nonrelativistic string BCJ relations can be expressed in terms of Gauss hypergeometry functions. As an application, for each fixed mass level N, we derive extended recurrence relations among nonrelativistic low energy string scattering amplitudes of string states with different spins and different channels.