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.

arXiv comment17 pages, 6 figures, and 4 tables

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Cited by in corpus (6)

• Exotic double-charm molecular states with hidden or open strangeness and around $4.5\sim 4.7$ GeV
• Investigating new type of doubly-charmed molecular tetraquarks composed of the charmed meson in $H$-doublet and the charmed meson in $T$-doublet
• Correlation of the hidden-charm molecular tetraquarks and the charmoniumlike structures existing in the $B\to XYZ+K$
• Newly observed $X(4630)$: a new charmoniumlike molecule
• Investigation of the possible $D{\bar{D}}^{\ast }$/$B{\bar{B}}^{\ast }$ and $D{D}^{\ast }$/$\bar{B}{\bar{B}}^{\ast }$ molecule states
• Investigating $S$-wave bound states composed of two pseudoscalar mesons