Constructing the general partial waves and renormalization in EFT

TL;DR

This paper develops a comprehensive framework for partial wave analysis in scattering processes using Lorentz-invariant spinor-helicity variables, facilitating algebraic computations and addressing infrared divergences in effective field theories.

Contribution

It introduces a general partial wave basis for N→M scattering, incorporating Lorentz invariance and spinor-helicity variables, and develops techniques for partial wave expansion of amplitudes with infrared divergences.

Findings

Constructed the partial wave amplitude basis using Poincaré Clebsch-Gordan coefficients.

Converted phase space integration into an algebraic problem via an inner product.

Applied the method to compute anomalous dimension matrices with unitarity cuts.

Abstract

We construct the general partial wave amplitude basis for the $N\to M$ scattering, which consists of Poincar\'e Clebsch-Gordan coefficients, with Lorentz invariant forms given in terms of spinor-helicity variables. The inner product of the Clebsch-Gordan coefficients is defined, which converts on-shell phase space integration into an algebraic problem. We also develop the technique of partial wave expansions of arbitrary amplitudes, including those with infrared divergence. These are applied to the computation of anomalous dimension matrix for general effective operators, where unitarity cuts for the loop amplitudes, with an arbitrary number of external particles, are obtained via partial wave expansion.