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.