Rotation-invariant observables in parity-violating decays of vector particles to fermion pairs

TL;DR

This paper introduces rotation-invariant observables for analyzing parity-violating decays of vector particles into fermion pairs, enabling more robust and comparable measurements of spin alignment and parity violation.

Contribution

It presents a general, frame-independent formulation of polarization and parity asymmetry observables for J=1 states, applicable across different production processes.

Findings

Derived frame-independent observables for vector particle decays.

Showed these observables improve measurement robustness.

Facilitated better comparison between experiment and theory.

Abstract

The di-fermion angular distribution observed in decays of inclusively produced vector particles is characterized by two frame-independent observables, reflecting the average spin-alignment of the produced particle and the magnitude of parity violation in the decay. The existence of these observables derives from the rotational properties of angular momentum eigenstates and is a completely general result, valid for any J=1 state and independent of the production process. Rotation-invariant formulations of polarization and of the decay parity-asymmetry can provide more significant measurements than the commonly used frame-dependent definitions, also improving the quality of the comparisons between the measurements and the theoretical calculations.