Toward $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}$ annihilation inspired by higher $\rho$ mesonic states around 2.2 GeV

Abstract

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

Comments: 6 pages, 1 table and 2 figures. Accepted by Phys. Rev. D