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arXiv · 2607.27345

NLSM amplitudes from a quartic two-derivative theory

Qu Cao·Zhenqi Han·Fan Zhu
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Abstract

We revisit the well-known nonlinear sigma model (NLSM), an effective field theory describing the scattering of $\mathrm{SU}(N)$ Goldstone bosons and characterized by an infinite tower of two-derivative interactions. We introduce a local scalar Lagrangian involving two scalar fields $\psi^\pm$ carrying opposite "polarities", whose interacting part consists of a single polynomial quartic two-derivative operator, and prove that it reproduces planar NLSM amplitudes at all loop orders. This quartic two-derivative formulation reveals a previously hidden simplicity of the NLSM: its Feynman rules involve only a single quartic interaction vertex, making the Adler zero and the leading double-soft factor manifest at all loop orders on generalized cuts and significantly improving the efficiency of high-multiplicity computations. We also suggest a possible analogous description of the NLSM +$ \phi^3 $ theory in terms of a finite tower of local interactions.

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Qu Cao, Zhenqi Han, Fan Zhu. 2026-07-29. NLSM amplitudes from a quartic two-derivative theory. https://arxiv.org/abs/2607.27345

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