Note on tree NLSM amplitudes and soft theorems

Abstract: We use the universality of single soft behavior, together with the double copy structure, to completely determine the tree amplitudes of non-linear sigma model (NLSM). We first figure out the Adler's zero for $4$-point NLSM amplitudes, by considering kinematics. Then, we assume the universality of the Adler's zero, and use this requirement to construct general tree NLSM amplitudes in the expanded formula, i.e., the formula of expanding NLSM amplitudes to bi-adjoint scalar amplitudes. We also derive double soft factors for tree NLSM amplitudes, based on the resulting expanded formula.