A new recursion relation for tree-level NLSM amplitudes based on hidden zeros

TL;DR

This paper introduces a new recursion relation for tree-level NLSM amplitudes that leverages hidden zeros to simplify calculations and reproduce key amplitude features.

Contribution

It presents a novel BCFW-like recursion relation for NLSM amplitudes that avoids boundary term computations by exploiting hidden zeros.

Findings

Reproduces the Adler zero in NLSM amplitudes

Derives the $ ext{delta}$-shift construction from the recursion

Shows universal expansion into bi-adjoint scalar amplitudes

Abstract

In this note, we propose a novel BCFW-like recursion relation for tree-level non-linear sigma model (NLSM) amplitudes, which circumvents the computation of boundary terms by exploiting the recently discovered hidden zeros. Using this recursion, we reproduce three remarkable features of tree-level NLSM amplitudes: (i) the Adler zero, (ii) the $\delta$-shift construction, which generates NLSM amplitudes from ${\rm Tr}(\phi^3)$ amplitudes, and (iii) the universal expansion of NLSM amplitudes into bi-adjoint scalar amplitudes. Our results demonstrate that the hidden zeros, combined with standard factorization on physical poles, uniquely determine all tree-level NLSM amplitudes.