Resolving ambiguities in model-independent partial-wave analysis of three-body decay

TL;DR

This paper addresses mathematical ambiguities in model-independent partial-wave analysis of three-body decays, proposing techniques to identify and correct these issues to improve analysis accuracy.

Contribution

It introduces methods to detect and resolve ambiguities in freed-isobar partial-wave analysis, enhancing the reliability of model-independent decay studies.

Findings

Identified how ambiguities arise in freed-isobar analysis.

Developed techniques to detect and correct analysis ambiguities.

Validated methods with examples in meson decay and scattering.

Abstract

Partial wave analysis is an important tool for analyzing large data sets in hadronic decays of light and heavy mesons. It commonly relies on the isobar model, which assumes multihadron final states originate from successive two-body decays of well-known undisturbed intermediate states. Recently, analyses of heavy-meson decays and diffractively produced states have attempted to overcome the strong model dependences of the isobar model. These analyses have overlooked that model-independent, or freed-isobar, partial-wave analysis can break the orthogonality of partial waves and introduce mathematical ambiguities into results. We show how these ambiguities arise and present general techniques for identifying their presence and for correcting for them. We demonstrate these techniques with specific examples in both heavy-meson decay and pion--proton scattering.