From Lattice QCD Potentials to the Heavy-Quark Meson Spectrum: the Diabatic Approach

Understanding the hadron spectrum from the fundamental QCD Lagrangian is possibly the ultimate challenge in hadronic physics. As a matter of fact, the Born-Oppenheimer approximation provides a description of heavy-quark mesons firmly based on quenched (without sea quarks) Lattice QCD, where they are identified as bound states of a heavy quark-antiquark pair in effective potentials. However, the incorporation of unquenched (including sea quarks) Lattice potentials requires to take into account the effect of meson-meson components as well. This can be done in the diabatic framework, a formalism first introduced in molecular physics, where the dynamics is governed by a potential matrix treating the confining quark-antiquark interaction on equal grounds with the string breaking one, responsible for the coupling with meson-meson. Heavy-quark mesons are then identified as either bound states or scattering resonances containing both quark-antiquark and meson-meson components. A unified spectrum of quark-antiquark and molecular states comes out, which may accommodate many of the experimental charmoniumlike and bottomoniumlike mesons, including the notoriously "unconventional" ones like X(3872).