Partial Wave Amplitude Basis and Selection Rules in Effective Field Theories.

TLDR: In this article, the generalized partial wave expansion for N→M scattering amplitude in terms of spinor helicity variables is derived and the basis amplitudes of the expansion with definite angular momentum j consist of the Poincare Clebsch-Gordan coefficients.

Abstract: We derive the generalized partial wave expansion for N→M 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. Moreover, we obtain a series of selection rules that restrict the anomalous dimension matrix of effective operators and how effective operators contribute to some 2→N amplitudes at the loop level.