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Double pion photoproduction off nuclei - are there effects beyond final-state interaction?

Photoproduction of $π^{0}π^{0}$ and $π^{0}π^{\pm}$ pairs from nuclei has been measured over a wide mass range ($^2$H, $^{7}$Li, $^{12}$C, $^{40}$Ca, and $^{\rm nat}$Pb) for photon energies from threshold to 600 MeV. The experiments were performed at the MAMI accelerator in Mainz, using the Glasgow photon tagging spectrometer and a 4$π$ electromagnetic calorimeter consisting of the Crystal Ball and TAPS detectors. A shift of the pion-pion invariant mass spectra for heavy nuclei to small invariant masses has been observed for $π^0$ pairs but also for the mixed-charge pairs. The precise results allow for the first time a model-independent analysis of the influence of pion final-state interactions. The corresponding effects are found to be large and must be carefully considered in the search for possible in-medium modifications of the $σ$-meson. Results from a transport model calculation reproduce the shape of the invariant-mass distributions for the mixed-charge pairs better than for the neutral pairs, but also for the latter differences between model results and experiment are not large, leaving not much room for $σ$-in-medium modification.