A bstractIn this paper, we investigate tree-level scattering amplitude relations in U(N) non-linear sigma model. We use Cayley parametrization. As was shown in the recent works [23,24], both on-shell amplitudes and off-shell currents with odd points have to vanish under Cayley parametrization. We prove the off-shell U(1) identity and fundamental BCJ relation for even-point currents. By taking the on-shell limits of the off-shell relations, we show that the color-ordered tree amplitudes with even points satisfy U(1)-decoupling identity and fundamental BCJ relation, which have the same formations within Yang-Mills theory. We further state that all the on-shell general KK, BCJ relations as well as the minimal-basis expansion are also satisfied by color-ordered tree amplitudes. As a consequence of the relations among color-ordered amplitudes, the total 2 m-point tree amplitudes satisfy DDM form of color decomposition as well as KLT relation.

中文翻译：

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非线性 sigma 模型中的幅度关系

摘要在本文中，我们研究了 U(N) 非线性 sigma 模型中的树级散射幅度关系。我们使用 Cayley 参数化。正如最近的工作 [23,24] 所示，在 Cayley 参数化下，壳上振幅和具有奇数点的壳外电流都必须消失。我们证明了偶数点电流的壳外 U(1) 恒等式和基本 BCJ 关系。通过取壳外关系的壳上极限，我们表明具有偶数点的颜色排序树振幅满足 U(1)-解耦恒等式和基本 BCJ 关系，它们在 Yang-Mills 理论中具有相同的形式。我们进一步指出，颜色排序的树振幅也满足所有壳上一般 KK、BCJ 关系以及最小基扩展。由于颜色排序幅度之间的关系，