Heavy-quark mesons in the diabatic approach: string breaking and the quarkoniumlike spectrum

Roberto Bruschini

doi:10.1051/epjconf/202225804001

Abstract

The Born-Oppenheimer approximation provides a description of heavy-quark mesons firmly based on lattice QCD, but its validity is limited to the lightest states lying far below the first open-flavour meson-meson threshold. This limitation can be overcome in the diabatic framework, a formalism first introduced in molecular physics, where the dynamics is encoded in a potential matrix whose elements can be derived from unquenched lattice QCD studies of string breaking. The off-diagonal elements of the potential matrix provide interaction between heavy quark-antiquark and meson-meson pairs, from which the mixing of quarkonium states with molecular components and the OZI-allowed strong decay widths are directly calculated. This allows for a QCD-based unified description of conventional quarkonium and unconventional mesons containing quark-antiquark and meson-meson components, what has proved to be successful for charmoniumlike and bottomoniumlike resonances.

Highlights

For many years the spectrum of heavy-quark mesons has been successfully described by the quark model, in its nonrelativistic [1, 2] and semi-relativistic [3] realizations, from the bound states of a heavy quark-antiquark (QQ) pair
The validity of the B-O approximation without configuration mixing is limited to states whose mass lies far below any open-flavor meson-meson threshold. In this talk we shall overcome this limitation using the diabatic approach, first developed in molecular physics [24], to obtain a QCD-based description of heavy-quark mesons taking into account the configuration mixing between QQand meson-meson. In this approach the QQ–meson-meson mixing induced by string breaking is incorporated together with the confining Q-Qinteraction in a potential matrix that is directly connected to the static energy levels calculated in lattice QCD
Let us notice that the parameters we use in the diabatic potential matrix are not fitted on lattice data but are instead a mixture of lattice and phenomenology

Summary

Introduction

For many years the spectrum of heavy-quark mesons has been successfully described by the quark model, in its nonrelativistic [1, 2] and semi-relativistic [3] realizations, from the bound states of a heavy quark-antiquark (QQ) pair. The validity of the B-O approximation without configuration mixing is limited to states whose mass lies far below any open-flavor meson-meson threshold In this talk we shall overcome this limitation using the diabatic approach, first developed in molecular physics [24], to obtain a QCD-based description of heavy-quark mesons taking into account the configuration mixing between QQand meson-meson. In this approach the QQ–meson-meson mixing induced by string breaking is incorporated together with the confining Q-Qinteraction in a potential matrix that is directly connected to the static energy levels calculated in lattice QCD.

Born-Oppenheimer approximation

Diabatic approach

E777775

Results

Summary