Assignments of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>Y</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>2040</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math>, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>ρ</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>1900</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math>, and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>ρ</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>2150</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math> in the quark model
Zheng-Ya Li, Demin Li, En Wang, W. C. Yan, Qin-Tao Song
Abstract
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.