Quark structure of the $X(3872)$ and ${\chi }_b(3P)$ resonances

Abstract

We discuss the nature of the ${\chi }_b(3P)$ and $X(3872)$ mesons: Are the ${\chi }_b(3P)$'s standard $b\bar{b}$ mesons or $b\bar{b}$ states with a significative continuum component? Is the $X(3872)$ a $c\bar{c}$ state with continuum coupling effects or a meson-meson molecule? To do that, we compare quark model and unquenched quark model results for the mass barycenter and splittings of the ${\chi }_b(3P)$ multiplet. Future and more precise experimental results will discriminate between the two interpretations. In the case of the $X(3872)$, we interpret it a $c\bar{c}$ core plus higher Fock components due to the coupling to the meson-meson continuum, thus we think that it is compatible with the meson ${\chi }_{c1}(2P)$, with $J^{PC}=1^{++}$. The $J^{PC}=1^{++}$ quantum numbers are in agreement with the experimental results found by the LHCb collaboration. In our view, the $X(3872)$'s mass is lower than the quark model's predictions because of self energy shifts. We also provide an estimation of the open charm/bottom strong decay modes of the $X(3872)$ and ${\chi }_b(3P)$ mesons, such as $X(3872)\to D{\bar{D}}^{\ast }$ and ${\chi }_{b2}(3P)\to B\bar{B}$, and radiative transitions.

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• Decays of the X(3872) and ${\chi }_{c1}(2P)$ charmonium
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• Radiative decay of the X(3872) as a mixed molecule-charmonium state in QCD Sum Rules
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• QCD Sum Rules for the production of the X(3872) as a mixed molecule-charmonium state in B meson decay

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