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

## TL;DR

This paper investigates the nature of the $Y(4390)$ and $Z(4430)$ states as molecular states arising from the $D^*(2010)ar{D}_1(2420)$ interaction, proposing $Y(4390)$ as an isoscalar partner of $Z(4430)$ based on theoretical modeling.

## Contribution

The study introduces a quasipotential Bethe-Salpeter approach to identify molecular states from the $D^*(2010)ar{D}_1(2420)$ interaction, linking them to observed exotic states.

## Key findings

- A bound state at 4384 MeV related to $Y(4390)$.
- A resonance at 4461+i39 MeV related to $Z(4430)$.
- $Y(4390)$ is proposed as an isoscalar partner of $Z(4430)$.

## Abstract

Invoked by the recent observation of $Y(4390)$ at BESIII, which is about 40 MeV below the $D^*(2010)\bar{D}_1(2420)$ threshold, we investigate possible bound and resonance states from the $D^*(2010)\bar{D}_1(2420)$ 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 $D^*(2010)\bar{D}_1(2420)$ 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 $D^*(2010)\bar{D}_1(2420)$ interaction.