Photoproduction of $\pi^+ \pi^-$ meson pairs on the proton

The exclusive reaction $\gamma p \to p \pi^+ \pi^-$ was studied in the photon energy range 3.0 - 3.8 GeV and momentum transfer range $0.4<-t<1.0$ GeV$^2$. Data were collected with the CLAS detector at the Thomas Jefferson National Accelerator Facility. In this kinematic range the integrated luminosity was about 20 pb$^{-1}$. The reaction was isolated by detecting the $\pi^+$ and proton in CLAS, and reconstructing the $\pi^-$ via the missing-mass technique. Moments of the di-pion decay angular distributions were derived from the experimental data. Differential cross sections for the $S$, $P$, and $D$-waves in the $M_{\pi^+\pi^-}$ mass range $0.4-1.4$ GeV were derived performing a partial wave expansion of the extracted moments. Besides the dominant contribution of the $\rho(770)$ meson in the $P$-wave, evidence for the $f_0(980)$ and the $f_2(1270)$ mesons was found in the $S$ and $D$-waves, respectively. The differential production cross sections $d\sigma/dt$ for individual waves in the mass range of the above-mentioned mesons were extracted. This is the first time the $f_0(980)$ has been measured in a photoproduction experiment.