Rotation-invariant observables in polarization measurements

TL;DR

This paper develops a general method to identify all rotation-invariant observables in polarization measurements, enhancing the robustness of tests for the Standard Model and new physics in particle decay processes.

Contribution

It introduces a comprehensive recipe to find rotation-invariant observables in any decay process, extending previous work limited to specific cases.

Findings

Derived explicit expressions for all rotation-invariant observables in spin-1/2 and spin-1 decays.

Provided a robust framework for experimental data analysis and detector acceptance testing.

Enhanced the tools available for testing the Standard Model and searching for new physics.

Abstract

Polarization measurements provide a detailed method to test the Standard Model and to search for new physics. Most previous studies depend on pre-selected coordinates, which blurs the significance of the results. The construction of two rotation-invariant observables in vector boson decay into a fermion pair has been proved to be a big success. In this work, we show that there are more rotation-invariant observables and provide a general recipe to find all of them in an arbitrary decay process. Taking spin-1/2 and spin-1 particle decay processes as examples, we calculate the explicit expressions of all rotation-invariant observables, which can serve as a robust test of the detector acceptance and help the analysis of experimental data.