Investigation of the possible $D{\bar{D}}^{\ast }$/$B{\bar{B}}^{\ast }$ and $D{D}^{\ast }$/$\bar{B}{\bar{B}}^{\ast }$ molecule states

Abstract

In this work, we systematically study the $D{\bar{D}}^{\ast }$/$B{\bar{B}}^{\ast }$ and $D{D}^{\ast }$/$\bar{B}{\bar{B}}^{\ast }$ systems with the Bethe-Salpeter equation in the ladder and instantaneous approximations for the kernel. By solving the Bethe-Salpeter equation numerically with the kernel containing the direct and crossed one particle-exchange diagrams and introducing three different form factors (monopole, dipole, and exponential form factors) at the vertices, we find only the isoscalar $D{\bar{D}}^{\ast }$/$B{\bar{B}}^{\ast }$ and $D{D}^{\ast }$/$\bar{B}{\bar{B}}^{\ast }$ systems can exist as bound states. This indicate that the $X(3872)$ and $T_{cc}^{+}$ could be accommodated as $I^G(J^{PC})=0^{+}(1^{++})$ $D{\bar{D}}^{\ast }$ and $(I)J^P=(0)1^{+}$ $D{D}^{\ast }$ molecular states while the molecular state explanations for $Z_b(10610)$ and $Z_c(3900)$ are excluded.

arXiv comment13 pages, 2 tables

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• An updated review of the new hadron states
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• Higher molecular $P_{\psi s}^{\Lambda /\Sigma }$ pentaquarks arising from the ${\Xi }_c^{(\prime ,\ast )}{\bar{D}}_1/{\Xi }_c^{(\prime ,\ast )}{\bar{D}}_2^{\ast }$ interactions
• Searching for doubly charmed tetraquark candidates $T_{cc}$ and $T_{cc\bar{s}}$ in $B_c$ decays
• Doubly heavy tetraquark states in a mass splitting model
• The study of possible molecular states of $D_s^{(\ast )}{D}_s^{(\ast )}$ and $B_s^{(\ast )}{B}_s^{(\ast )}$
• Isospin violation effect and three-body decays of the $T_{cc}^{+}$ state
• Spectroscopic Properties of Double-Strangeness Molecular Tetraquarks
• Hunting for the prospective $T_{cc}$ family based on the diquark-antidiquark configuration
• Investigation on the bottom analogs of the $T_{cc}^{+}$
• Electromagnetic characteristics as probes into the inner structures of the predicted ${\Xi }_c^{{(}^{\prime },\ast )}{D}_s^{(\ast )}$ molecular states
• Investigating $S$-wave bound states composed of two pseudoscalar mesons
• Development of Bethe-Salpeter theory for dealing with unstable system
• Calculation of mass and width of unstable molecular state using the developed Bethe-Salpeter theory
• Investigating the two-pion exchange of the double charm $D{D}^{\ast }$ chiral interactions and $T_{cc}$