Phenomenology of near-threshold states: a practical parametrisation for the line shapes

F.-K Guo,C Hanhart,Q Wang,J.-L Wynen,A V Nefediev,P Matuschek,Yu S Kalashnikova,R.V Mizuk,Y Foka,N Brambilla,V Kovalenko

doi:10.1051/epjconf/201713706020

Abstract

In the last decade many states in the spectrum of charmonium and bottomonium have been observed experimentally above the lowest open-flavour threshold. Most of these states reside in the vicinity of strong thresholds and show properties that cannot be captured by simple quark models. Description and understanding of such exotic states is a challenge for the phenomenology of strong interactions, since it requires building adequate theoretical tools and approaches. In this work, a practical parametrisation for the line shapes of near threshold resonance(s) is derived in the framework of a coupled-channel model which includes an arbitrary number of elastic and inelastic channels as well as of bare pole terms. Parameters of the distribution have a direct relation to phenomenology and the resulting analytical parametrisation is therefore ideally suited to harvest the full information content provided by the measurements and to establish a link between the experimental data and their theoretical interpretation.

Highlights

In the last decade many states in the spectrum of charmonium and bottomonium have been observed experimentally above the lowest open-flavour threshold
Description and understanding of such exotic states is a challenge for the phenomenology of strong interactions, since it requires building adequate theoretical tools and approaches
Parameters of the distribution have a direct relation to phenomenology and the resulting analytical parametrisation is ideally suited to harvest the full information content provided by the measurements and to establish a link between the experimental data and their theoretical interpretation

Summary

Introduction

To arrive soon from the new upcoming experiments [2,3,4,5] the task of building adequate approaches for the data analysis for exotic states becomes urgent. The Breit-Wigner formula violates analyticity, for it only account for a single pole in the amplitude. Such an approach provides only limited information on the states studied, since the Breit-Wigner parameters are reaction-dependent and the naive algebraic sum of the Breit-Wigner distributions violates unitary. We build a model-independent parametrisation for near-threshold states consistent with all requirements from unitarity and analyticity. The formulae derived are well suited for a simultaneous analysis of the entire bulk of data for all production and decay channels for the given near-threshold state(s).

Coupled-channel problem

Practical parametrisation

Fits for the data and the nature of the Zb’s

Conclusions