New Selection Rules from Angular Momentum Conservation

Understand

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.