How many vector charmonium(-like) states sit in the energy range from 4.2 to 4.35 GeV?

Recently, numerous vector charmonium(-like) states were reported by different electron-positron collider experiments above $4.2$ GeV. However, there is no consensus on the number of these states, as the experimental analysis is based on the Breit-Wigner parametrization, which is channel-dependent. In our work, we focus on the energy region $[4.2,4.35]~\mathrm{GeV}$ and conduct a comprehensive analysis of eight different final states in $e^+ e^-$ annihilation. Our findings indicate that only one single charmonium-like state is sufficient to describe all the data well in the $D_1\bar D$ molecular picture. The extracted pole position is $\sqrt{s_\text{pole}^{Y(4230)}}=\left( 4227{\pm} 4 {-} \frac{i}{2}(50^{+8}_{-2}) \right) \text{MeV}$. Beside the $D_1\bar{D}$ threshold effect which express itself as asymmetric lineshape of the $Y(4230)$, the contribution of the vector charmonium $\psi(4160)$ is necessary included perturbatively.