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We derive the generalized partial wave expansion for M → N scattering amplitude in terms of spinor helicity variables. The basis amplitudes of the expansion with definite angular momentum j consist of the Poincare Clebsch-Gordan coefficients, while j constrains the UV physics that could generate the corresponding operators at tree level. Moreover, we obtain a series of selection rules that restrict the anomalous dimension matrix of effective operators and the way how effective operators contribute to some 2 → N amplitudes at the loop level.arXiv:2001.04481v1 fatcat:6u3boecxkfh7foogfhklpvapsu