Kampf Karol, Novotny Jiri, Shifman Mikhail, Trnka Jaroslav
Institute of Particle and Nuclear Physics, Charles University, Prague 18000, Czech Republic.
William I. Fine Theoretical Physics Institute, University of Minnesota, Minneapolis, Minnesota 55455, USA.
Phys Rev Lett. 2020 Mar 20;124(11):111601. doi: 10.1103/PhysRevLett.124.111601.
In this Letter we discuss new soft theorems for the Goldstone-boson amplitudes with nonvanishing soft limits. The standard argument is that the nonlinearly realized shift symmetry leads to the vanishing of scattering amplitudes in the soft limit, known as the Adler zero. This statement involves certain assumptions of the absence of cubic vertices and the absence of linear terms in the transformations of fields. For theories which fail to satisfy these conditions, we derive a new soft theorem which involves certain linear combinations of lower point amplitudes, generalizing the Adler zero statement. We provide an explicit example of the SU(N)/SU(N-1) sigma model which was also recently studied in the context of U(1) fibrated models. The soft theorem can be then used as an input into the modified soft recursion relations for the reconstruction of all tree-level amplitudes.
在本信函中，我们讨论了具有非零软极限的戈德斯通玻色子振幅的新软定理。标准观点认为，非线性实现的平移对称性导致散射振幅在软极限下消失，即所谓的阿德勒零点。该陈述涉及关于不存在三次顶点以及场变换中不存在线性项的某些假设。对于不满足这些条件的理论，我们推导了一个新的软定理，它涉及较低点振幅的某些线性组合，推广了阿德勒零点的陈述。我们给出了SU(N)/SU(N - 1)西格玛模型的一个具体例子，该模型最近也在U(1)纤维化模型的背景下进行了研究。然后，该软定理可作为输入用于修改后的软递归关系，以重建所有树级振幅。
