  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.
