Covariant orbital-spin scheme for any spin based on irreducible tensor

TL;DR

This paper introduces a Lorentz covariant scheme for orbital-spin coupling in hadron physics, utilizing irreducible tensors to systematically construct partial wave amplitudes for particles of any spin.

Contribution

It develops a general covariant orbital-spin coupling framework based on irreducible Lorentz tensors, applicable to both massive and massless particles, with explicit construction procedures.

Findings

Provides a systematic method for covariant partial wave analysis.

Applicable to particles of any spin, enhancing analysis flexibility.

Includes specific examples demonstrating the scheme's effectiveness.

Abstract

In hadron spectrum physics, the partial wave analysis is a primary method used to extract properties of hadronic resonances. The covariant orbital-spin coupling scheme holds unique advantages over other partial wave methods due to its Lorentz covariant form and determined orbital-spin quantum numbers. This paper presents a general form of the covariant orbital-spin coupling scheme based on the irreducible tensor of the homogeneous proper Lorentz group and its little groups. A systematic procedure for constructing partial wave amplitude in a Lorentz covariant way is provided, which can be applied to both massive and massless particles. Specific examples are also included.