Assignments of the Y ( 2040 ) , ρ ( 1900 ) , and ρ ( 2150 ) in the quark model

Recently, the BESIII Collaboration reported a resonance $Y(2040)$ with $M=2034\\ifmmode\\pm\\else\\textpm\\fi{}13\\ifmmode\\pm\\else\\textpm\\fi{}9\\text{ }\\text{ }\\mathrm{MeV}$ and $\\mathrm{\\ensuremath{\\Gamma}}=234\\ifmmode\\pm\\else\\textpm\\fi{}30\\ifmmode\\pm\\else\\textpm\\fi{}25\\text{ }\\text{ }\\mathrm{MeV}$ in the process of ${e}^{+}{e}^{\\ensuremath{-}}\\ensuremath{\\rightarrow}\\ensuremath{\\omega}{\\ensuremath{\\pi}}^{0}$. In addition, new measurements with much higher precision for the $\\ensuremath{\\rho}(1900)$ and $\\ensuremath{\\rho}(2150)$ states are obtained by the BESIII and BABAR Collaborations. In this work, we perform a systematic study on the mass spectrum of the excited $\\ensuremath{\\rho}$ resonances using the modified Godfrey-Isgur model, and the strong decays of $Y(2040)$, $\\ensuremath{\\rho}(1900)$, and $\\ensuremath{\\rho}(2150)$ within the $^{3}{P}_{0}$ model. We find that $Y(2040)$, $\\ensuremath{\\rho}(1900)$, and $\\ensuremath{\\rho}(2150)$ can be interpreted as the $\\ensuremath{\\rho}(2{^{3}D}_{1})$, $\\ensuremath{\\rho}(3{^{3}S}_{1})$, and $\\ensuremath{\\rho}(4{^{3}S}_{1})$ states, respectively. Meanwhile, the mass and strong decays of the $\\ensuremath{\\rho}(3{^{3}D}_{1})$ state are predicted as well, which could be helpful to search for this state in the future.