Assignments of the $Y(2040)$, $\rho(1900)$, and $\rho(2150)$ in the quark model

Recently, the BESIII Collaboration reported a resonance $Y(2040)$ with $M=2034\pm13\pm9$ MeV and $\Gamma=234\pm30\pm25$ MeV in the process of $e^+e^-\rightarrow\omega\pi^0$. In addition, new measurements with much higher precision for the $\rho(1900)$ and $\rho(2150)$ states are obtained by the BESIII and BABAR Collaborations. In this work, we perform a systematic study on the mass spectrum of the excited $\rho$ resonances using the modified Godfrey-Isgur model, and the strong decays of $Y(2040)$, $\rho(1900)$, and $\rho(2150)$ within the $^3P_0$ model.We find that $Y(2040)$, $\rho(1900)$, and $\rho(2150)$ can be interpreted as the $\rho(2^3D_1)$, $\rho(3^3S_1)$, and $\rho(4^3S_1)$ states, respectively. Meanwhile, the mass and strong decays of the $\rho(3^3D_1)$ state are predicted as well, which could be helpful to search for this state in future.