A bstractIn this paper, we study the single and double soft behaviors of tree level off-shell currents and on-shell amplitudes in nonlinear sigma model (NLSM). We first propose and prove the leading soft behavior of the tree level currents with a single soft particle. In the on-shell limit, this single soft emission becomes the Adler’s zero. Then we establish leading and subleading soft behaviors of tree level currents with two adjacent soft particles. With a careful analysis of the on-shell limit, we obtain the double soft behaviors of on-shell amplitudes where the two soft particles are adjacent to each other. By applying Kleiss-Kuijf (KK) relation, we further obtain the leading and subleading behaviors of amplitudes with two nonadjacent soft particles.

中文翻译：

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NLSM 中的单和双软行为

摘要在本文中，我们研究了非线性 sigma 模型 (NLSM) 中树级壳外电流和壳上振幅的单软和双软行为。我们首先提出并证明了具有单个软粒子的树级电流的领先软行为。在壳上极限中，这个单一的软发射成为阿德勒零。然后我们建立了两个相邻软粒子的树级电流的引导和子引导软行为。通过对壳上极限的仔细分析，我们获得了壳上振幅的双软行为，其中两个软粒子彼此相邻。通过应用 Kleiss-Kuijf (KK) 关系，我们进一步获得了两个不相邻的软粒子振幅的领先和次领先行为。