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

TL;DR

This study uses the Bethe-Salpeter equation to explore possible molecular states of heavy meson pairs, finding that certain isoscalar configurations can form bound states, supporting some experimental candidates as molecular states.

Contribution

It provides a systematic Bethe-Salpeter equation analysis with various form factors, identifying which heavy meson pairs can form bound molecular states and clarifying the nature of several exotic hadrons.

Findings

Isoscalar $Dar{D}^*$ and $Bar{B}^*$ systems can form bound states.

Supports $X(3872)$ and $T^+_{cc}$ as molecular states.

Excludes molecular explanations for $Z_b(10610)$ and $Z_c(3900)$.

Abstract

In this work, we systematically study the $D\bar{D}^*$/$B\bar{B}^*$ and $DD^*$/$\bar{B}\bar{B}^*$ 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 $D\bar{D}^*$/$B\bar{B}^*$ and $DD^*$/$\bar{B}\bar{B}^*$ systems can exist as bound states. This indicate that the $X(3872)$ and $T^+_{cc}$ could be accommodated as $I^G(J^{PC})=0^+(1^{++})$ $D\bar{D}^*$ and $(I)J^P =(0)1^+$ $DD^*$ molecular states while the molecular state explanations for $Z_b(10610)$ and $Z_c(3900)$ are excluded.