On the Rotational Invariance and Non-Invariance of Lepton Angular Distributions in Drell-Yan and Quarkonium Production

TL;DR

This paper discusses the rotational invariance properties of lepton angular distributions in Drell-Yan and quarkonium production, proposing intuitive methods to identify invariant quantities and analyze violations of the Lam-Tung relation.

Contribution

It introduces an intuitive approach to determine rotational invariance of lepton angular distribution quantities and highlights the importance of frame-independent measures for the Lam-Tung relation.

Findings

Rotational invariance of certain angular distribution quantities can be easily established.

Frame-independent quantities are preferable for analyzing Lam-Tung relation violations.

The approach simplifies understanding of angular distribution invariance in high-energy processes.

Abstract

Several rotational invariant quantities for the lepton angular distributions in Drell-Yan and quarkonium production were derived several years ago, allowing the comparison between different experiments adopting different reference frames. Using an intuitive picture for describing the lepton angular distribution in these processes, we show how the rotational invariance of these quantities can be readily obtained. This approach can also be used to determine the rotational invariance or non-invariance of various quantities specifying the amount of violation for the Lam-Tung relation. While the violation of the Lam-Tung relation is often expressed by frame-dependent quantities, we note that alternative frame-independent quantities are preferred.