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.
Highlights
The discovery of the χc1ð3872Þ in 2003 [1] may be considered as the initio of a new era in heavy-quark meson spectroscopy
As a matter of fact, the nonrelativistic Cornell quark model [3,4] incorporates some of these effects through meson loops where the interaction connecting QQ and open flavor meson-meson is derived from the QQ binding potential
The formalism we have developed in the previous sections can be tested in charmoniumlike mesons where, unlike in the bottomoniumlike case, there are several well-established experimental candidates for unconventional isoscalar states, presumably containing significant meson-meson components
Summary
The discovery of the χc1ð3872Þ in 2003 [1] may be considered as the initio of a new era in heavy-quark meson spectroscopy. An intermediate step in this direction was taken in [16] by identifying the unquenched lattice energy for static Q and Q sources, when the QQ configuration mixes with one or two open flavor meson-meson ones [17,18], with a QQ potential This unquenched approximation allows for some physical understanding of threshold effects beyond hadron loops. For this purpose we use the diabatic approach developed in molecular physics for tackling the configuration mixing problem (see for instance [19]) This allows us to establish a general framework for a unified description of conventional and unconventional heavyquark meson states.
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