What is the right formalism to search for resonances?

TL;DR

This paper compares various formalisms used in partial wave analysis for hadron decay chains, emphasizing their analytical properties, and highlights issues like model dependence and crossing symmetry violations affecting resonance extraction.

Contribution

It provides a detailed comparison of helicity and covariant tensor formalisms, analyzing their analytical properties and implications for resonance parameter extraction.

Findings

Covariant tensor approaches have model-dependent energy dependence.

Recursive covariant tensor construction violates crossing symmetry.

Differences in formalisms impact resonance parameter extraction.

Abstract

Hadron decay chains constitute one of the main sources of information on the QCD spectrum. We discuss the differences between several partial wave analysis formalisms used in the literature to build the amplitudes. We match the helicity amplitudes to the covariant tensor basis. Hereby, we pay attention to the analytical properties of the amplitudes and separate singularities of kinematical and dynamical nature. We study the analytical properties of the spin-orbit (LS) formalism, and some of the covariant tensor approaches. In particular, we explicitly build the amplitudes for the B -> psi pi K and B -> Dbar pi pi decays, and show that the energy dependence of the covariant approach is model dependent. We also show that the usual recursive construction of covariant tensors explicitly violates crossing symmetry, which would lead to different resonance parameters extracted from scattering and decay processes.