Using a relativized diquark model Hamiltonian, we calculate the masses of $$J^{PC}=0^{++}$$J PC = 0 + + ground-state tetraquarks in the following systems: $$b s {\bar{b}} {\bar{s}}$$b s b ¯ s ¯ , $$bb {\bar{n}} {\bar{n}}$$b b n ¯ n ¯ ( $$n=u, d$$n = u , d ), $$bb {\bar{s}} {\bar{s}}$$b b s ¯ s ¯ , $$cc{\bar{c}} {\bar{c}}$$c c c ¯ c ¯ , $$b b {\bar{b}} {\bar{b}}$$b b b ¯ b ¯ , $$b c{\bar{b}} {\bar{c}}$$b c b ¯ c ¯ and $$b b {\bar{c}} {\bar{c}}$$b b c ¯ c ¯ . We also compute extensive spectra for the fully-heavy quark flavour combinations. Finally, as a test of the diquark model approach, we compute the masses of fully-heavy baryons in the diquark model. Our results may be compared soon to the forthcoming experimental data for fully-heavy three-quark systems.

We present a quark model calculation of the charmonium spectrum with self-energy corrections due to the coupling to the meson-meson continuum. The bare masses used in the calculation are computed within the relativized quark model by Godfrey and Isgur. The strong decay widths of $3S$, $2P$, $1D$, and $2D$ $c\overline{c}$ states are also calculated, to set the values of the ${}^{3}{P}_{0}$ pair-creation model's parameters we use to compute the vertex functions of the loop integrals. Finally, the nature of the $X(3872)$ resonance is analyzed and the main possibilities ($c\overline{c}$ state or $D{\overline{D}}^{*}$ molecule) are discussed. According to our results, the $X(3872)$ is compatible with the meson ${$\chi${}}_{c1}(2P)$, with ${J}^{\mathrm{PC}}={1}^{++}$, and is thus interpreted as a $c\overline{c}$ core plus higher Fock components due to the coupling to the meson-meson continuum. These ${J}^{\mathrm{PC}}={1}^{++}$ 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 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.

We show the results of a coupled-channel quark model calculation of the bottomonium spectrum with self-energy corrections due to the coupling to the meson-meson continuum. We also provide results for the open-bottom strong decay amplitudes of higher bottomonia in a ${{}^{3}P}_0$ model.

In two recent papers, we used the hadro-quarkonium model to study the properties of hidden-charm and bottom tetraquarks and pentaquarks. Here, we extend the previous results and calculate the masses of heavy-quarkonium-kaon/hyperon systems. We also compute the spectrum of hidden-charm and bottom tetraquarks with strangeness in the compact tetraquark (diquark-antidiquark) model. If heavy-light exotic systems with non-null strangeness content were to be observed experimentally, it might be possible to distinguish among the large variety of available theoretical pictures for tetra- and pentaquark states and, possibly, rule out those which are not compatible with the data.

We investigate the hidden-charm pentaquarks as superpositions of ${\mathrm{\Lambda }}_c{\overline{D}}^{(*)}$ and ${\mathrm{\Sigma }}_c^{(*)}{\overline{D}}^{(*)}$ (isospin $I=1/2$) meson-baryon channels coupled to a $uudc\overline{c}$ compact core by employing an interaction satisfying the heavy quark and chiral symmetries. Our model can consistently explain the masses and decay widths of $P_c^{+}(4312)$, $P_c^{+}(4440)$ and $P_c^{+}(4457)$ with the dominant components of ${\mathrm{\Sigma }}_c\overline{D}$ and ${\mathrm{\Sigma }}_c{\overline{D}}^{*}$ with spin-parity assignments $J^P=1/2^{-}$, $3/2^{-}$ and $1/2^{-}$, respectively. We analyze basic properties of the $P_c$’s such as masses and decay widths, and find that the mass ordering is dominantly determined by the quark dynamics while the decay widths by the tensor force of the one-pion exchange.