Helicity amplitudes for generic multi-body particle decays featuring multiple decay chains

TL;DR

This paper derives a general expression for helicity amplitudes in complex multi-body particle decays with multiple decay chains, addressing spin state matching issues crucial for accurate amplitude analysis.

Contribution

It introduces a novel, general method for matching spin states across decay chains, correcting previous inaccuracies and ensuring rotational invariance in amplitude models.

Findings

Provides a comprehensive formula for helicity amplitudes in multi-chain decays.

Identifies and corrects a common spin matching error in existing literature.

Enhances the reliability of amplitude analyses in searches for exotic particles.

Abstract

We present the general expression of helicity amplitudes for generic multi-body particle decays characterised by multiple decay chains. This is achieved by addressing for the first time the issue of the matching of final particle spin states among different decay chains in full generality for generic multi-body decays, proposing a method able to match the exact definition of spin states relative to the decaying particle ones. We stress the importance of our result by showing that one of the matching method used in the literature is incorrect, leading to amplitude models violating rotational invariance. The results presented are therefore relevant for performing numerous amplitude analysis, notably those searching for exotic structures like pentaquarks.