Diabatic description of charmonium-like mesons

TL;DR

This paper introduces a diabatic formalism adapted from molecular physics to describe heavy-quark mesons, providing a unified framework for conventional and unconventional charmonium-like states, especially near meson-meson thresholds.

Contribution

It applies a diabatic potential matrix approach derived from lattice QCD to heavy-quark mesons, extending beyond the Born-Oppenheimer approximation to include meson-meson components nonperturbatively.

Findings

Unified description of conventional and unconventional resonances.

Effective modeling of meson states near and above thresholds.

Spectral results for $c\overline{c}$ mesons below 4.1 GeV.

Abstract

We apply the diabatic formalism, first introduced in molecular physics, to the description of heavy-quark mesons. In this formalism the dynamics is completely described by a diabatic potential matrix whose elements can be derived from unquenched lattice QCD studies of string breaking. For energies far below the lowest open flavor meson-meson threshold, the resulting diabatic approach reduces to the well-known Born-Oppenheimer approximation where heavy-quark meson masses correspond to energy levels in an effective quark-antiquark potential. For energies close below or above that threshold, where the Born-Oppenheimer approximation fails, this approach provides a set of coupled Schr\"{o}dinger equations incorporating meson-meson components nonperturbatively, i.e. beyond loop corrections. A spectral study of heavy mesons containing $c\overline{c}$ with masses below $4.1$ GeV is carried out within this framework. From it a unified description of conventional as well as unconventional resonances comes out.