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

Area of Science:

• High Energy Physics
• Quantum Field Theory
• Particle Physics

Background:

• Partial wave expansion is a standard technique for analyzing scattering amplitudes.
• Spinor helicity variables offer a powerful framework for relativistic scattering calculations.

Purpose of the Study:

• To derive a generalized partial wave expansion for N→M scattering amplitudes.
• To identify selection rules governing effective operators and their contributions to scattering processes.

Main Methods:

• Derivation of the generalized partial wave expansion using spinor helicity variables.
• Identification of Poincaré Clebsch-Gordan coefficients as basis amplitudes.
• Analysis of selection rules for anomalous dimension matrices.

Main Results:

• The generalized partial wave expansion for N→M scattering amplitudes is established.
• Poincaré Clebsch-Gordan coefficients are identified as key components of the expansion.
• A series of selection rules are derived, constraining effective operator properties.

Conclusions:

• The derived expansion and selection rules provide new tools for studying quantum field theories.
• This work offers insights into the behavior of effective operators at loop level.
• The findings facilitate a deeper understanding of particle interactions and scattering phenomena.