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Recently, the BaBar Collaboration reported a broad resonance structure near 2GeV when analyzing the $e^+e^-\to f_1(1285)\pi^+\pi^-$ process, which providesa good opportunity to study the higher $\rho$-mesonic states. When consideringthe $\rho(1900)$ and $\rho(2150)$ contributions, the experimental data of thecross section of $e^+e^-\to f_1(1285)\pi^+\pi^-$ around 2 GeV can be welldepicted, especially the observed broad resonance structure in $e^+e^-\tof_1(1285)\pi^+\pi^-$ containing two substructures is suggested by the presentwork. Additionally, we also indicate a possible signal of $\rho(5S)$ around 2.5GeV in the $e^+e^-\to f_1(1285)\pi^+\pi^-$ process. The obtained result mayprovide a valuable hint to identify higher $\rho$ mesons, which will be a newtask for the BESIII and Belle II experiments with the accumulation of higherprecision data.

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