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 $Y(4660)\to J/ψf_0(980)$, $η_c ϕ(1020)$, $χ_{c0}ϕ(1020)$, $D_s\bar{D}_s$, $ D_s^* \bar{D}^*_s$, $ D_s \bar{D}^*_s$, $D_s^* \bar{D}_s$, $ψ^\prime π^+π^-$, $J/ψϕ(1020)$ with the QCD sum rules based on solid quark-hadron quality. The predicted width $Γ(Y(4660) )= 74.2^{+29.2}_{-19.2}\,{\rm{MeV}}$ is in excellent agreement with the experimental data $68\pm 11\pm 1 {\mbox{ MeV}}$ 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_{Yψ^\prime f_0}|\gg |G_{Y J/ψf_0}|$, which is consistent with the observation of the $Y(4660)$ in the $ψ^\primeπ^+π^-$ mass spectrum, and favors the $ψ^{\prime}f_0(980)$ molecule assignment. It is important to search for the process $Y(4660)\to J/ψϕ(1020)$ to diagnose the nature of the $Y(4660)$, as the decay is greatly suppressed.