Model-independent constraints on the shape parameters of dilepton angular distributions

TL;DR

This paper derives model-independent positivity and invariance constraints on dilepton angular distribution parameters, providing a universal framework applicable regardless of production mechanisms and clarifying the interpretation of violations of known relations.

Contribution

It establishes universal, model-independent constraints on dilepton angular distribution shape parameters based on covariance and positivity, extending understanding beyond specific production models.

Findings

Positivity constraints are derived for angular distribution coefficients.

A rotation-invariant identity generalizes the Lam-Tung relation.

Violations of the Lam-Tung relation can be characterized by a single shape coefficient.

Abstract

The coefficients determining the dilepton decay angular distribution of vector particles obey certain positivity constraints and a rotation-invariant identity. These relations are a direct consequence of the covariance properties of angular momentum eigenstates and are independent of the production mechanism. The Lam-Tung relation can be derived as a particular case, simply recognizing that the Drell-Yan dilepton is always produced transversely polarized with respect to one or more quantization axes. The dilepton angular distribution continues to be characterized by a frame-independent identity also when the Lam-Tung relation is violated. Moreover, the violation can be easily characterized by measuring a one-dimensional distribution depending on one shape coefficient.