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

TL;DR

This paper investigates the enhancement near 2.2 GeV in the $e^+e^- o \pi^+\pi^-$ process, attributing it to the contributions of higher $ ho$ mesonic states, specifically $ ho(1900)$ and $ ho(2150)$, and fits experimental data well.

Contribution

It proposes that the 2.2 GeV enhancement is due to two higher $ ho$ mesons, $ ho(1900)$ and $ ho(2150)$, modeled as $ ho(3S)$ and $ ho(4S)$ states, providing new insight into the $ ho$ meson family.

Findings

The enhancement near 2.2 GeV can be explained by contributions from $ ho(1900)$ and $ ho(2150)$.

The model fits BABAR data well, supporting the two-meson explanation.

Extracted parameters are consistent with theoretical expectations.

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.