Interpretation of $Y_b (10750)$ as a tetraquark and its production mechanism
Recently, the Belle Collaboration has updated the analysis of the cross sections for the processes $e^+ e^- \to \Upsilon(nS)\, \pi^+ \pi^-$ ($n = 1,\, 2,\, 3$) in the $e^+ e^-$ center-of-mass energy range from 10.52 to 11.02 GeV. A new structure, called here $Y_b (10750)$, with the mass $M (Y_b) = (10752.7 \pm 5.9^{+0.7}_{-1.1})$ MeV and the Breit-Wigner width $\Gamma (Y_b) = (35.5^{+17.6 +3.9}_{-11.3 -3.3})$ MeV was observed \cite{Abdesselam:2019gth}. We interpret $Y_b (10750)$ as a compact $J^{PC} = 1^{--}$ state with a dominant tetraquark component. The mass eigenstate $Y_b (10750)$ is treated as a linear combination of the diquark-antidiquark and $b \bar b$ components due to the mixing via gluonic exchanges shown recently to arise in the limit of large number of quark colors. The mixing angle between $Y_b$ and $\Upsilon(5S)$ can be estimated from the electronic width, recently determined to be $\Gamma_{ee} (Y_b) = (13.7 \pm 1.8)$ eV. The mixing provides a plausible mechanism for $Y_b (10750)$ production in high energy collisions from its $b \bar b$ component and we work out the Drell-Yan and prompt production cross sections for $p p \to Y_b (10750) \to \Upsilon (nS)\, \pi^+ \pi^-$ at the LHC. The resonant part of the dipion invariant mass spectrum in $Y_b (10750) \to \Upsilon (1S)\, \pi^+ \pi^-$ and the corresponding angular distribution of $\pi^+$-meson in the dipion rest frame are presented as an example.