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

We discuss the nature of the ${\chi }_b(3P)$ and $X(3872)$ mesons. Are the ${\chi }_b(3P)$’s standard $b\overline{b}$ mesons or $b\overline{b}$ states with a significative continuum component? Is the $X(3872)$ a $c\overline{c}$ 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 as a $c\overline{c}$ core plus higher Fock components due to the coupling to the meson-meson continuum, and 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 $X(3872)\to D{\overline{D}}^{*}$ and ${\chi }_{b2}(3P)\to B\overline{B}$, and radiative transitions.

Figure 1

Comparison between the calculated masses (black lines) of $1S$, $2S$, $1P$, $2P$, and $1D$ charmonium states via Eq. (1) [15] and the experimental ones [43] (blue boxes). The new values of the parameters of Godfrey and Isgur’s model are taken from Ref. [15]. Picture from Ref. [15]; APS copyright.

Figure 2

Mass barycenter (in GeV) of the ${\chi }_b(3P)$ system in our UQM calculation, from Ref. [36].