Broad resonance structure in $e^{+}{e}^{-}\to f_1(1285){\pi }^{+}{\pi }^{-}$ and higher $\rho$-meson excitations

Recently, the BaBar Collaboration reported a broad resonance structure near 2 GeV when analyzing the $e^{+}{e}^{-}\to f_1(1285){\pi }^{+}{\pi }^{-}$ process, which provides a good opportunity to study the higher $\rho$-mesonic states. When considering the $\rho (1900)$ and $\rho (2150)$ contributions, the experimental data of the cross section of $e^{+}{e}^{-}\to f_1(1285){\pi }^{+}{\pi }^{-}$ around 2 GeV can be well depicted, especially the observed broad resonance structure in $e^{+}{e}^{-}\to f_1(1285){\pi }^{+}{\pi }^{-}$ containing two substructures is suggested by the present work. Additionally, we also indicate a possible signal of $\rho (5S)$ around 2.5 GeV in the $e^{+}{e}^{-}\to f_1(1285){\pi }^{+}{\pi }^{-}$ process. The obtained result may provide a valuable hint to identify higher $\rho$ mesons, which will be a new task for the BESIII and Belle II experiments with the accumulation of higher precision data.