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

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.