# Rotation-invariant observables as Density Matrix invariants

## TL;DR

This paper introduces five rotation-invariant observables derived from the hadronic tensor's density matrix, enabling a model-independent analysis of dilepton angular distributions in vector particle decays, including parity violation.

## Contribution

It presents a novel set of five SO(3) rotational-invariant observables as density matrix invariants for analyzing dilepton angular distributions, accounting for parity violation.

## Key findings

- Derived five SO(3) invariants from the hadronic tensor.
- Established positivity constraints on the invariants.
- Calculated invariants for Z and J/ψ decay data.

## Abstract

It is shown that general dilepton angular distribution (with parity violating terms taking into account) in vector particle decays can be described through a set of five SO(3) rotational-invariant observables. These observables are derived as invariants of the spacial part of the hadronic tensor (density matrix) expressed in terms of angular coefficients. The restrictions on the invariants following from the positivity of the hadronic tensor are obtained. Special cases of SO(2) rotations are considered. Calculation of invariants for available data on Z and J/{\psi} decays is performed.