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

Abstract

Recently, the BESIII Collaboration reported a resonance $Y(2040)$ with $M=2034\pm 13\pm 9$ MeV and $\Gamma =234\pm 30\pm 25$ MeV in the process of $e^{+}{e}^{-}\to \omega {\pi }^0$. 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 ${}^3{P}_0$ model.We find that $Y(2040)$, $\rho (1900)$, and $\rho (2150)$ can be interpreted as the $\rho (2^3{D}_1)$, $\rho (3^3{S}_1)$, and $\rho (4^3{S}_1)$ states, respectively. Meanwhile, the mass and strong decays of the $\rho (3^3{D}_1)$ state are predicted as well, which could be helpful to search for this state in future.

Comments: 9 pages, 5 figures, typos are corrected