  We derive the generalized partial wave expansion for $M \rightarrow N$
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 $2
\rightarrow N$ amplitudes at the loop level.
