Does the bottomonium counterpart of $X(3872)$ exist?

Abstract

A narrow line shape peak at about 10615 MeV, just above the threshold in the $B{\bar{B}}^{\ast }$ channel, which can be regarded as the signal of bottomonium counterpart of $X(3872)$, $X_b$, is predicted by using the extended Friedrichs scheme. Though a virtual state is found at about 10593 MeV in this scheme, we point out that the peak is contributed mainly by the coupling form factor, which comes from the convolution of the interaction term and meson wave functions including the one from ${\chi }_{b1}(4P)$, but not mainly by the virtual-state pole. In this picture, the reason why $X_b$ signal is not observed in the ${\rm Y}{\pi }^{+}{\pi }^{-}$ and ${\rm Y}{\pi }^{+}{\pi }^{-}{\pi }^0$ channels can also be understood. The ${\chi }_{b1}(4P)$ mass and width are found to be about 10771 MeV and 6 MeV, respectively and a dynamically generated broad resonance is also found with its mass and width at about 10672 MeV and 78 MeV, respectively. The line shapes of these two states are also affected by the form factor effect. Thus, this study also emphasizes the importance of the structure of the wave functions of high radial excitations in the analysis of the line shapes, and provides a caveat that some signals may be generated from the structures of the form factors rather than from poles.

5 pages, 3 figures; v2, the final published version

References in corpus (11)

• Hadronic molecules
• Multiquark Resonances
• Exotics: Heavy Pentaquarks and Tetraquarks
• Is the X(3872) Production Cross Section at Tevatron Compatible with a Hadron Molecule Interpretation?
• Line Shapes of the X(3872)
• Observation of $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}{\pi }^0{\chi }_{bJ}$ and search for $X_b\to \omega {\rm Y}(1S)$ at $\sqrt{s}\sim 10.867$ GeV
• Searching for the Bottom Counterparts of X(3872) and Y(4260) via ${\pi }^{+}{\pi }^{-}{\rm Y}$
• Search for the $X_b$ and other hidden-beauty states in the ${\pi }^{+}{\pi }^{-}{\rm Y}(1\mathrm{S})$ channel at ATLAS
• $X(3872)$, $X_b$, and the ${\chi }_{b1}(3P)$ state
• Virtual states and generalized completeness relation in the Friedrichs Model
• Comprehending Isospin breaking effects of $X(3872)$ in a Friedrichs-model-like scheme

Cited by in corpus (9)

• The $XYZ$ states: experimental and theoretical status and perspectives
• Pentaquark and Tetraquark states
• Spectrum of the Hidden-Bottom and the Hidden-Charm/Strange Exotics in the Dynamical Diquark Model
• Observation of $e^{+}{e}^{-}\to \omega {\chi }_{bJ}(1P)$ and search for $X_b\to \omega {\rm Y}(1S)$ at $\sqrt{s}$ near 10.75 GeV
• $X(3872)$ as virtual companion pole of the charm-anticharm state ${\chi }_{c1}(2P)$
• Status and Prospects of Exotic Hadrons at Belle II
• Bottomonium spectrum with a Dirac potential model in the momentum space
• Hunting for $X_b$ via hidden bottomonium decays $X_b\to \pi \pi {\chi }_{bJ}$
• Exotic hadrons associated with $b$-quark