Toward $e^+e^-\to π^+π^-$ annihilation inspired by higher $ρ$ mesonic states around 2.2 GeV

Very recently, the {\it BABAR} Collaboration indicated that there exist an explicit enhancement structure near 2.2 GeV when focusing on the $e^+e^-\toπ^+π^-$ process again, which inspires our interest in studying the production of higher $ρ$ mesonic states. Since the branching ratio of $π^+π^-$ channel of $D-$wave $ρ$ states are much smaller than $S-$wave states, we choose $ρ(1900)$ and $ρ(2150)$ as the intermediate states in $e^+e^-\toπ^+π^-$, where $ρ(1900)$ and $ρ(2150)$ are treated as $ρ(3S)$ and $ρ(4S)$ states, respectively. Our result indicates that the $BABAR$'s data of $e^+e^-\toπ^+π^-$ around 2 GeV can be depicted well, which shows that this enhancement structure near 2.2 GeV existing in $e^+e^-\toπ^+π^-$ can be due to the contribution from two $ρ$ mesons, $ρ(1900)$ and $ρ(2150)$. Additionally, this conclusion can be enforced by the consistence of the extracted values of $Γ_{e^+e^-}\mathcal{B}(π^+π^-)$ of $ρ(1900)$ and $ρ(2150)$ in the whole fitting processes and the corresponding theoretical calculations. The present study of $e^+e^-\toπ^+π^-$ data may provide valuable information to establish the $ρ$ meson family.

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