Extracting Angular Observables without a Likelihood and Applications to Rare Decays

TL;DR

This paper introduces a likelihood-free method using moments and Monte Carlo techniques to extract angular observables in multi-body decays, enabling analysis with few events and robustness against mismodeling.

Contribution

It presents a novel likelihood-free algorithm for extracting angular observables, accounting for systematic uncertainties, applicable to various rare decay processes.

Findings

Method is effective with limited data

Robust against angular distribution mismodeling

Provides explicit formulas for specific rare decays

Abstract

Our goal is to obtain a complete set of angular observables arising in a generic multi-body process. We show how this can be achieved without the need to carry out a likelihood fit of the angular distribution to the measured events. Instead, we apply the method of moments that relies both on the orthogonality of angular functions and the estimation of integrals by Monte Carlo techniques. The big advantage of this method is that the joint distribution of all observables can be easily extracted, even for very few events. The method of moments is shown to be robust against mismodeling of the angular distribution. Our main result is an explicit algorithm that accounts for systematic uncertainties from detector-resolution and acceptance effects. Finally, we present the necessary process-dependent formulae needed for direct application of the method to several rare decays of interest.