Interpretation of Y(4390) as an isoscalar partner of Z(4430) from D∗(2010)D¯1(2420) interaction

Invoked by the recent observation of Y(4390) at BESIII, which is about 40 MeV below the D∗(2010)D¯1(2420) threshold, we investigate possible bound and resonance states from the D∗(2010)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)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∗(2010)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∗(2010)D¯1(2420) interaction.