Observation of $e^{+}{e}^{-}\to {\rho }^{+}{\rho }^{-}$ near $\sqrt{s}=10.58\mathrm{GeV}$

We report the first observation of $e^{+}{e}^{-}\to {\rho }^{+}{\rho }^{-}$, in a data sample of $379{\mathrm{fb}}^{-1}$ collected with the BABAR detector at the PEP-II $e^{+}{e}^{-}$ storage ring at center-of-mass energies near $\sqrt{s}=10.58\mathrm{GeV}$. We measure a cross section of $\sigma (e^{+}{e}^{-}\to {\rho }^{+}{\rho }^{-})=8.3\pm 0.7(\mathrm{stat})\pm 0.8(\mathrm{syst})\mathrm{fb}$ within the range of $|\cos {\theta }^{*}|<0.8$ and $|\cos {\theta }_{\pm }|<0.85$, where ${\theta }^{*}$ is the center-of-mass polar angle of the ${\rho }^{\pm }$ meson and ${\theta }_{\pm }$ are the angles in the ${\rho }^{\pm }$ rest frame between the direction of the boost from the laboratory frame and the direction of the ${\pi }^{\pm }$. Assuming production through single-photon annihilation, there are three independent helicity amplitudes. We measure the ratios of their squared moduli to be $|F_{00}{|}^2:|F_{10}{|}^2:|F_{11}{|}^2=0.51\pm 0.14(\mathrm{stat})\pm 0.07(\mathrm{syst}):0.10\pm 0.04(\mathrm{stat})\pm 0.01(\mathrm{syst}):0.04\pm 0.03(\mathrm{stat})\pm 0.01(\mathrm{syst})$. The $|F_{00}{|}^2$ result is inconsistent with the prediction of 1.0 made by QCD models with a significance of 3.1 standard deviations including systematic uncertainties.

Figure 1

Scatter plot of $m_{{\pi }^{+}{\pi }^0{\pi }^{-}{\pi }^0}$ vs $|\Delta p|$ between the ${\pi }^{+}{\pi }^0{\pi }^{-}{\pi }^0$ and initial $e^{+}{e}^{-}$ systems for the on-resonance data.

Figure 2

Scatter plot of $m_{{\pi }^{+}{\pi }^0}$ and $m_{{\pi }^{-}{\pi }^0}$ for the accepted events in the combined data.

Figure 3

The invariant mass projections (a) $m_{{\pi }^{+}{\pi }^0}$ ($m_{{\pi }^{-}{\pi }^0}<1.5\mathrm{GeV}/c^2$) and (b) $m_{{\pi }^{-}{\pi }^0}$ ($m_{{\pi }^{+}{\pi }^0}<1.5\mathrm{GeV}/c^2$) for accepted events in the combined data. The blue-dashed line is the residual linear background, the red dot-dashed line adds (a) ${\rho }^{+}{\pi }^{-}{\pi }^0$ and (b) ${\rho }^{-}{\pi }^{+}{\pi }^0$, and the blue-dotted line includes both ${\rho }^{+}{\pi }^{-}{\pi }^0$ and ${\rho }^{-}{\pi }^{+}{\pi }^0$. The red solid line adds the signal.

Figure 4

The background-subtracted (sWeighted) and efficiency-corrected (a) $\cos {\theta }_{+}$, (b) $\cos {\theta }_{-}$, (c) ${\phi }_{+}$, (d) ${\phi }_{-}$, and (e) $\cos {\theta }^{*}$ distributions. The magenta dashed line is the contribution from the $F_{00}$ component, the blue-dotted line is for the $F_{10}$ component, the blue dot-dashed line is for the $F_{11}$ component, and the red solid line is the total fit function.