What is the right formalism to search for resonances? II. The pentaquark chain

TL;DR

This paper compares different partial-wave analysis formalisms for three-body decays involving fermions, focusing on the Lambda_b decay to identify the best approach for pentaquark resonance searches.

Contribution

It provides a detailed analysis of the analytical properties of decay amplitudes, proposing a minimal energy dependence formalism consistent with S-matrix principles.

Findings

Identifies key differences between partial-wave formalisms.

Develops an amplitude with minimal energy dependence.

Supports more accurate resonance searches in three-body decays.

Abstract

We discuss the differences between several partial-wave analysis formalisms used in the construction of three-body decay amplitudes involving fermions. Specifically, we consider the decay Lambda_b -> psi p K- , where the hidden charm pentaquark signal has been reported. We analyze the analytical properties of the amplitudes and separate kinematical and dynamical singularities. The result is an amplitude with the minimal energy dependence compatible with the S-matrix principles.