Coupled-channel meson-meson scattering in the diabatic framework

TL;DR

This paper introduces a nonperturbative, QCD-based diabatic framework for coupled-channel meson-meson scattering, providing a unified approach to analyze open-flavor meson interactions and quarkoniumlike states, with results consistent with experimental data.

Contribution

The paper develops a numerical scheme and a general formula for calculating meson-meson scattering amplitudes within the diabatic framework, connecting lattice QCD and scattering phenomenology.

Findings

Identified structures like Breit-Wigner peaks, threshold cusps, and minimums in scattering cross sections.

Performed a comprehensive analysis of open-charm and open-bottom meson-meson scattering.

Results are fully compatible with experimental data and previous bound-state analyses.

Abstract

We apply the diabatic framework, a QCD-based formalism for the unified study of quarkoniumlike systems in terms of heavy quark-antiquark and open-flavor meson-meson components, to the description of coupled-channel meson-meson scattering. For this purpose, we first introduce a numerical scheme to find the solutions of the diabatic Schr\"odinger equation for energies in the continuum, then we derive a general formula for calculating the meson-meson scattering amplitudes from these solutions. We thus obtain a completely nonperturbative procedure for the calculation of open-flavor meson-meson scattering cross sections from the diabatic potential, which is directly connected to lattice QCD calculations. A comprehensive analysis of various elastic cross sections for open-charm and open-bottom meson-meson pairs is performed in a wide range of the center-of-mass energies. The relevant structures are identified, showing a spectrum of quasi-conventional and unconventional quarkoniumlike states. In addition to the customary Breit-Wigner peaks we obtain nontrivial structures such as threshold cusps and minimums. Finally, our results are compared with existing data and with results from our previous bound-state--based analysis, finding full compatibility with both.