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.

13 pages, 2 tables

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