A coupled-channel approach is applied to the charged tetraquark state $T_{cc}^{+}$ recently discovered by the LHCb Collaboration. The parameters of the interaction are fixed by a fit to the observed line shape in the three-body $D^0{D}^0{\pi }^{+}$ channel. Special attention is paid to the three-body dynamics in the $T_{cc}^{+}$ due to the finite life time of the $D^{*}$. An approach to the $T_{cc}^{+}$ is argued to be self-consistent only if both manifestations of the three-body dynamics, the pion exchange between the $D$ and $D^{*}$ mesons and the finite $D^{*}$ width, are taken into account simultaneously to ensure that three-body unitarity is preserved. This is especially important to precisely extract the pole position in the complex energy plane whose imaginary part is very sensitive to the details of the coupled-channel scheme employed. The $D^0{D}^0$ and $D^0{D}^{+}$ invariant mass distributions, predicted based on this analysis, are in good agreement with the LHCb data. The low-energy expansion of the $D^{*}D$ scattering amplitude is performed and the low-energy constants (the scattering length and effective range) are extracted. The compositeness parameter of the $T_{cc}^{+}$ is found to be close to unity, which implies that the $T_{cc}^{+}$ is a hadronic molecule generated by the interactions in the $D^{*+}{D}^0$ and $D^{*0}{D}^{+}$ channels. Employing heavy-quark spin symmetry, an isoscalar $D^{*}{D}^{*}$ molecular partner of the $T_{cc}^{+}$ with $J^P=1^{+}$ is predicted under the assumption that the $D{D}^{*}\text{−}{D}^{*}{D}^{*}$ coupled-channel effects can be neglected.

We investigate the enhancement in the $D^0{\overline{D}}^0{\pi }^0$ final state with the mass $M=3875.2\pm {0.7}_{-1.6}^{+0.3}\pm 0.8\mathrm{MeV}$ found recently by the Belle Collaboration in the $B\to K{D}^0{\overline{D}}^0{\pi }^0$ decay and test the possibility that this is yet another manifestation of the well-established resonance $X(3872)$. We perform a combined Flattè analysis of the data for the $D^0{\overline{D}}^0{\pi }^0$ mode and for the ${\pi }^{+}{\pi }^{-}J/\psi$ mode of the $X(3872)$. Only if the $X(3872)$ is a virtual state in the $D^0{\overline{D}}^{*0}$ channel do the data on the new enhancement comply with those on the $X(3872)$. In our fits, the mass distribution in the $D^0{\overline{D}}^{*0}$ mode exhibits a peak at 2–3 MeV above the $D^0{\overline{D}}^{*0}$ threshold, with a distinctive non-Breit-Wigner shape.

We investigate the role played by the three-body $D\overline{D}\pi$ dynamics on the near-threshold resonance $X(3872)$ charmonium state, which is assumed to be formed by nonperturbative $D{\overline{D}}^{*}$ dynamics. It is demonstrated that, as compared to the naive static-pions approximation, the imaginary parts that originate from the inclusion of dynamical pions reduce substantially the width from the $D\overline{D}\pi$ intermediate state. In particular, for a resonance peaked at 0.5 MeV below the $D^0{\overline{D}}^{*0}$ threshold, this contribution to the width is reduced by about a factor of 2, and the effect of the pion dynamics on the width grows as long as the resonance is shifted towards the $D^0{\overline{D}}^0{\pi }^0$ threshold. Although the physical width of the $X$ is dominated by inelastic channels, our finding should still be of importance for the $X$ line shapes in the $D\overline{D}\pi$ channel below $D{\overline{D}}^{*}$ threshold. For example, in the scattering length approximation, the imaginary part of the scattering length includes effects of all the pion dynamics and does not only stem from the $D^{*}$ width. Meanwhile, we find that another important quantity for the $X$ phenomenology, the residue at the $X$ pole, is weakly sensitive to dynamical pions. In particular, we find that the binding energy dependence of this quantity from the full calculation is close to that found from a model with pointlike $D{\overline{D}}^{*}$ interactions only, consistent with earlier claims. Coupled-channel effects (inclusion of the charged $D{\overline{D}}^{*}$ channel) turn out to have a moderate impact on the results.

We revisit the consequences of the heavy-quark spin symmetry for the possible spin partners of the X(3872). We confirm that, if the X(3872) were a DD¯⁎ molecular state with the quantum numbers JPC=1++, then in the strict heavy-quark limit there should exist three more hadronic molecules degenerate with the X(3872), with the quantum numbers 0++, 1+−, and 2++ in line with previous results reported in the literature. We demonstrate that this result is robust with respect to the inclusion of the one-pion exchange interaction between the D mesons. However, this is true only if all relevant partial waves as well as particle channels which are coupled via the pion-exchange potential are taken into account. Otherwise, the heavy-quark symmetry is destroyed even in the heavy-quark limit. Finally, we solve the coupled-channel problem in the 2++ channel with nonperturbative pions beyond the heavy-quark limit and, contrary to the findings of previous calculations with perturbative pions, find for the spin-2 partner of the X(3872) a significant shift of the mass as well as a width of the order of 50 MeV