Studying the $D_{1}D$ molecule in the Bethe-Salpeter equation approach

Abstract

We study the possible bound states of the $D_{1}D$ system in the Bethe-Salpeter (BS) formalism in the ladder and instantaneous approximations. By solving the BS equation numerically with the kernel containing one-particle exchange diagrams and introducing three different form factors (monopole, dipole, and exponential form factors) at the vertices, we investigate whether the isoscalar and isovector $D_{1}D$ bound states may exist, respectively. We find that $Y(4260)$ could be accommodated as a $D_{1}D$ molecule, whereas the interpretation of $Z_2^{+}(4250)$ as a $D_{1}D$ molecule is disfavored. The bottom analog of $Y(4260)$ may exist but that of $Z_2^{+}(4250)$ does not.

Comments: 17 pages, 6 figures, and 4 tables