A universal splitting of string and particle scattering amplitudes

TL;DR

This paper introduces a universal splitting behavior of string and particle scattering amplitudes, revealing a factorization into two parts across various theories, with implications for soft theorems and amplitude structures.

Contribution

It uncovers a new universal splitting of tree-level amplitudes into two stringy currents, applicable to multiple theories including string, gauge, and scalar models.

Findings

Amplitudes split into two parts in specific Mandelstam subspaces.

Splitting applies to open- and closed-string amplitudes with Parke-Taylor factors.

The splitting extends to soft theorems and various theories.

Abstract

We propose a new splitting behavior of tree-level string/particle amplitudes for scalars, gluons and gravitons. We identify certain subspaces in the space of Mandelstam variables, where the universal Koba-Nielsen factor splits into two parts (each with an off-shell leg). Both open- and closed-string amplitudes with Parke-Taylor factors naturally factorize into two stringy ${\it currents}$, which implies the splitting of bi-adjoint $\phi^3$ amplitudes and via a simple deformation to unified stringy amplitudes, the splitting of amplitudes in the non-linear sigma model and Yang-Mills-scalar theory; the same splitting holds for scalar amplitudes without color such as the special Galileon. Remarkably, if we impose similar constraints on Lorentz products involving polarizations, gluon and graviton amplitudes in bosonic string and superstring theories also split into two (stringy) currents. A special case of the splitting implies soft theorems, and more generally it extends recently proposed smooth splittings and new factorizations near zeros to all these theories.