Interpretation of ${\rm Y}(11020)$ as an $S$-Wave $B_1\bar{B}$--$B_1{\bar{B}}^{\ast }$ Molecular State

Abstract

Although heavy-quark symmetry predicts a $B_1\bar{B}$ molecular partner of the $D_1\bar{D}$ molecule, no such state has been observed. We propose that the experimentally observed ${\rm Y}(11020)$ may be a candidate for such a state, possibly containing a $B_1{\bar{B}}^{\ast }$ component. To test this, we interpret ${\rm Y}(11020)$ as an $S$-wave $B_1\bar{B}$--$B_1{\bar{B}}^{\ast }$ molecule and compute its strong decay widths using the compositeness condition and effective Lagrangians. The couplings to $B_1$ and ${\bar{B}}^{(\ast )}$ are extracted by fitting ${\rm Y}(11020)\to e^{+}{e}^{-}$ and ${\rm Y}(11020)\to {\chi }_{bJ}\pi \pi \pi$ data. Using these couplings, we evaluate partial widths into $B_{(s)}^{(\ast )}{\bar{B}}_{(s)}^{(\ast )}$, $\pi \pi {\rm Y}(nS)$, $\pi \pi h_b(nP)$, and $\pi \pi \pi {\chi }_{b1}$ via hadronic loops, as well as three-body $B^{\ast }\pi {\bar{B}}^{(\ast )}$ decays via tree diagrams. The results indicate that ${\rm Y}(11020)$ is predominantly a $B_1\bar{B}$ molecule, with its main decay channel being $B_s^{\ast }{\bar{B}}^{\ast }$. The $\pi \pi {\rm Y}(nS)$ and $\pi \pi h_b(nP)$ widths are only a few eV, whereas $\pi \pi \pi {\chi }_{b1}$ reaches 0.167~MeV and the unobserved $\pi \pi \pi {\chi }_{b0}$ could be 0.754~keV. These distinctive decay patterns provide clear experimental signatures of the molecular nature of ${\rm Y}(11020)$ and offer a test of heavy-quark symmetry.