Interpretation of $Y_b(10750)$ as a tetraquark and its production mechanism

Abstract

Recently, the Belle Collaboration has updated the analysis of the cross sections for the processes $e^{+}{e}^{-}\to {\rm Y}(nS){\pi }^{+}{\pi }^{-}$ ($n=1,2,3$) 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 $M(Y_b)=(10752.7\pm 5.9_{-1.1}^{+0.7})$ MeV and the Breit-Wigner width $\Gamma (Y_b)=(35.5_{-11.3-3.3}^{+17.6+3.9})$ 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 ${\rm Y}(5S)$ 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 $pp\to Y_b(10750)\to {\rm Y}(nS){\pi }^{+}{\pi }^{-}$ at the LHC. The resonant part of the dipion invariant mass spectrum in $Y_b(10750)\to {\rm Y}(1S){\pi }^{+}{\pi }^{-}$ and the corresponding angular distribution of ${\pi }^{+}$-meson in the dipion rest frame are presented as an example.

Comments: 6 pages, 3 figures; v2: some numerics updated based on new results for ${\Gamma }_{ee}(Y_b)$, references added; v3: accept by Physics Letters B