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arXiv · 2508.12894

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

Xiaodi Li·Kang Zhou
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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.

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Xiaodi Li, Kang Zhou. 2025-08-18. A new recursion relation for tree-level NLSM amplitudes based on hidden zeros. https://arxiv.org/abs/2508.12894

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