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

Minyuan Jiang,Jing Shu,Yu-Hui Zheng,Ming-Lei Xiao

doi:10.1103/physrevlett.126.011601

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 Poincaré 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.

Highlights

We derive the generalized partial wave expansion for N → M scattering amplitude in terms of spinor helicity variables
We show that the selection rule from angular momentum conservation could explain many of these nontrivial relations
One of the central roles in the explanation is played by the one-to-one correspondence between effective operators and the on-shell amplitude basis, established in [4,15], where it helps construct a complete operator basis without redundancy in the standard model effective field theory (SMEFT)

Summary

Partial Wave Amplitude Basis and Selection Rules in Effective Field Theories

We derive the generalized partial wave expansion for N → M scattering amplitude in terms of spinor helicity variables. By the operator-amplitude basis correspondence djνν0 induce an operator basis, which inherits the label j as the total angular momentum in the particular scattering channel These operators only contribute to processes with selected total angular momentum, which is the key of our selection rule. The amplitude basis with definite total angular momentum is obtained as a result; based on which, we find two types of selection rules: First, we find nontrivial constraints on the anomalous dimension matrix beyond the non-renormalization relations shown in the literature [11,12]; and second, operators are selected in certain cases while contributing to some one-loop diagrams, verifying the discovery of “vanishing rational terms” in [14] and leading to more nontrivial patterns in one-loop amplitudes. Instead of computing j from the composition of total spin S

Published by the American Physical Society

Together with

The eigenvalue

Our selection rule distinguishes operators with different

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