AI 中文总结
本文通过引入含ψ^±的局域标量拉格朗日量，用单一四次两导数算符的相互作用项在所有圈阶重现平面NLSM振幅，提升了高多重度计算效率，并提出NLSM + φ³理论的类似描述方案。
AI 中文摘要
我们重新研究著名的非线性σ模型（NLSM），这是一种描述SU(N)戈德斯通玻色子散射的有效场论，其特征是包含无穷多的两导数相互作用项。我们引入一个包含两个标量场ψ^±的局域标量拉格朗日量，这两个标量场带有相反的“极性”，其相互作用部分由一个单一的多项式四次两导数算符构成，并证明它能在所有圈阶下重现平面NLSM振幅。这种四次两导数表述揭示了NLSM此前隐藏的简洁性：其费曼规则仅涉及一个单一的四次相互作用顶点，这使得Adler零和领先的双软因子在广义割上的所有圈阶都显现出来，并显著提高了高多重度计算的效率。我们还提出了用有限层局域相互作用对NLSM + φ³理论进行类似描述的可能性。
英文摘要
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 $ψ^\pm$ 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 +$ ϕ^3 $ theory in terms of a finite tower of local interactions.
Comments12 pages, 14 figures
