Can Locality, Unitarity, and Hidden Zeros Completely Determine Tree-Level Amplitudes?

TL;DR

This paper demonstrates that locality, unitarity, and hidden zeros fully determine tree-level amplitudes in Yang-Mills and NLSM theories by reconstructing soft theorems from these principles.

Contribution

It shows that soft theorems, derived from locality, unitarity, and hidden zeros, can reconstruct full tree-level amplitudes in YM and NLSM theories, establishing their sufficiency.

Findings

Full YM and NLSM amplitudes reconstructed from soft theorems.

Soft theorems derived from locality, unitarity, and hidden zeros.

Complete determination of tree-level amplitudes from these principles.

Abstract

In this note, we address the question of whether locality, unitarity, and newly discovered hidden zeros can completely determine tree-level amplitudes, from the perspective of soft limit. We reconstruct the single-soft theorems of tree YM amplitudes and the double-soft theorems of tree NLSM amplitudes from locality, unitarity, and hidden zeros. A series of studies have shown that the full YM and NLSM amplitudes can be constructed from these soft theorems; therefore, we conclude that locality, unitarity, and hidden zeros completely determine the tree-level YM and NLSM amplitudes.