A. V. Nefediev

In the original version of this manuscript, an error was introduced on pp352. '2.7nb:1.6nb' has been corrected to '2.4nb:1.3nb' in the current online and printed version. doi:10.1093/ptep/ptz106.

We investigate the enhancement in the ${D}^{0}{\overline{D}}^{0}{\ensuremath{\pi}}^{0}$ final state with the mass $M=3875.2\ifmmode\pm\else\textpm\fi{}{0.7}_{\ensuremath{-}1.6}^{+0.3}\ifmmode\pm\else\textpm\fi{}0.8\text{ }\text{ }\mathrm{MeV}$ found recently by the Belle Collaboration in the $B\ensuremath{\rightarrow}K{D}^{0}{\overline{D}}^{0}{\ensuremath{\pi}}^{0}$ decay and test the possibility that this is yet another manifestation of the well-established resonance $X(3872)$. We perform a combined Flatt\`e analysis of the data for the ${D}^{0}{\overline{D}}^{0}{\ensuremath{\pi}}^{0}$ mode and for the ${\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}J/\ensuremath{\psi}$ 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.

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 ${D}^{0}{D}^{0}{\ensuremath{\pi}}^{+}$ 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 $D{D}^{*}\text{\ensuremath{-}}{D}^{*}{D}^{*}$ coupled-channel effects can be neglected.

The spectra of light-light and heavy-light mesons are calculated within the framework of the QCD string model, which is derived from QCD in the Wilson loop approach. Special attention is paid to the proper string dynamics that allows us to reproduce the straight-line Regge trajectories with the inverse slope being $2\ensuremath{\pi}\ensuremath{\sigma}$ for light-light and twice as small for heavy-light mesons. We use the model of the rotating QCD string with quarks at the ends to calculate the masses of several light-light mesons lying on the lowest Regge trajectories and compare them with the experimental data as well as with the predictions of other models. The masses of several low-lying orbitally and radially excited heavy-light states in the D, ${D}_{s},$ B, and ${B}_{s}$ mesons spectra are calculated in the einbein (auxiliary) field approach, which has proven to be rather accurate in various calculations for relativistic systems. The results for the spectra are compared with the experimental and recent lattice data. It is demonstrated that an account of the proper string dynamics encoded in the so-called string correction to the interquark interaction leads to an extra negative contribution to the masses of orbitally excited states that resolves the problem of the identification of the $D(2637)$ state recently claimed by the DELPHI Collaboration. For heavy-light system we extract the constants $\overline{\ensuremath{\Lambda}},$ ${\ensuremath{\lambda}}_{1},$ and ${\ensuremath{\lambda}}_{2}$ used in heavy quark effective theory and find good agreement with the results of other approaches.