A bstractIn this paper, we investigate multi-soft behaviors of tree amplitudes in nonlinear sigma model (NLSM). The leading behaviors of amplitudes with odd number of all-adjacent soft pions are zero. We further propose and prove that leading soft factors of amplitudes with even number all-adjacent soft pions can be expressed in terms of products of the leading order Berends-Giele sub-currents in Cayley parametrization. Each subcurrent in the expression contains at most one hard pion. Discussions are generalized to amplitudes containing arbitrary number of nonadjacent soft blocks: the leading behaviors of amplitudes where at least one soft block has odd number of adjacent soft pions are zero; the leading soft factors for amplitudes where all soft blocks containing even number of soft pions are given by products of soft factors for these blocks.

中文翻译：

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NLSM中树振幅的领先阶多软行为

摘要在本文中，我们研究了非线性西格玛模型（NLSM）中树振幅的多软行为。奇数个相邻软介子的幅度的领先行为为零。我们进一步提出并证明了具有偶数个所有相邻软π介子的幅度的领先软因子可以用凯莱参数化中的领先阶Berends-Giele子流的乘积来表示。表达式中的每个子流最多包含一个硬π介子。讨论被推广到包含任意数量的非相邻软块的幅度：至少一个软块具有奇数个相邻软 pion 的幅度的领先行为为零；幅度的主要软因子，其中包含偶数个软π介子的所有软块由这些块的软因子的乘积给出。