Strong decays of the $Y(4660)$ as a vector tetraquark state in solid quark-hadron duality

Abstract

In this article, we choose the $[sc{]}_P[\bar{s}\bar{c}{]}_A-[sc{]}_A[\bar{s}\bar{c}{]}_P$ type tetraquark current to study the hadronic coupling constants in the strong decays $Y(4660)\to J/\psi f_0(980)$, ${\eta }_c\varphi (1020)$, ${\chi }_{c0}\varphi (1020)$, $D_s{\bar{D}}_s$, $D_s^{\ast }{\bar{D}}_s^{\ast }$, $D_s{\bar{D}}_s^{\ast }$, $D_s^{\ast }{\bar{D}}_s$, ${\psi }^{\prime }{\pi }^{+}{\pi }^{-}$, $J/\psi \varphi (1020)$ with the QCD sum rules based on solid quark-hadron quality. The predicted width $\Gamma (Y(4660))=74.2_{-19.2}^{+29.2}\mathrm{MeV}$ is in excellent agreement with the experimental data $68\pm 11\pm 1\text{mbox}MeV$ from the Belle collaboration, which supports assigning the $Y(4660)$ to be the $[sc{]}_P[\bar{s}\bar{c}{]}_A-[sc{]}_A[\bar{s}\bar{c}{]}_P$ type tetraquark state with $J^{PC}=1^{--}$. In calculations, we observe that the hadronic coupling constants $|G_{Y{\psi }^{\prime }{f}_0}|\gg |G_{YJ/\psi f_0}|$, which is consistent with the observation of the $Y(4660)$ in the ${\psi }^{\prime }{\pi }^{+}{\pi }^{-}$ mass spectrum, and favors the ${\psi }^{\prime }{f}_0(980)$ molecule assignment. It is important to search for the process $Y(4660)\to J/\psi \varphi (1020)$ to diagnose the nature of the $Y(4660)$, as the decay is greatly suppressed.

Comments: 19 pages, 7 figures. arXiv admin note: text overlap with arXiv:1811.12821, arXiv:1901.06938