Interpretation of $Y(4390)$ as an isoscalar partner of $Z(4430)$ from $D^{\ast }(2010){\bar{D}}_1(2420)$ interaction

Abstract

Invoked by the recent observation of $Y(4390)$ at BESIII, which is about 40 MeV below the $D^{\ast }(2010){\bar{D}}_1(2420)$ threshold, we investigate possible bound and resonance states from the $D^{\ast }(2010){\bar{D}}_1(2420)$ interaction with the one-boson-exchange model in a quasipotential Bethe-Salpeter equation approach. A bound state with quantum number $0^{-}(1^{--})$ is produced at 4384 MeV from the $D^{(}2010){\bar{D}}_1(2420)$ interaction, which can be related to experimentally observed $Y(4390)$. Another state with quantum number $1^{+}(1^{+})$ is also produced at $4461+i39$ MeV from this interaction. Different from the $0^{-}(1^{--})$ state, the $1^{+}(1^{+})$ state is a resonance state above the $D^{\ast }(2010){\bar{D}}_1(2420)$ threshold. This resonance state can be related to the first observed charged charmonium-like state $Z(4430)$, which has a mass about 4475 MeV measured above the threshold as observed at Belle and LHCb. Our result suggests that $Y(4390)$ is an isoscalar partner of the $Z(4430)$ as a hadronic-molecular state from the $D^{\ast }(2010){\bar{D}}_1(2420)$ interaction.

Comments: 5 pages, 1 figure