New Selection Rules from Angular Momentum Conservation

Abstract

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

Comments: 10 pages, 5 figures, 3 tables