Measurement of the beam-helicity asymmetry I⊙ in the photoproduction of $ \pi^{0}$ $ \pi^{\pm}$ pairs off protons and off neutrons

Beam-helicity asymmetries have been measured at the MAMI accelerator in Mainz for the photoproduction of mixed-charge pion pairs in the reactions $ \gamma p\rightarrow n\pi^{0}\pi^{+}$ off free protons and $ \gamma d \rightarrow (p)p\pi^{0}\pi^{-}$ and $ \gamma d\rightarrow (n)n\pi^{0}\pi^{+}$ off quasi-free nucleons bound in the deuteron for incident photon energies up to 1.4GeV. Circularly polarized photons were produced from bremsstrahlung of longitudinally polarized electrons and tagged with the Glasgow-Mainz magnetic spectrometer. The charged pions, recoil protons, recoil neutrons, and decay photons from $ \pi^{0}$ mesons were detected in the $ 4\pi$ electromagnetic calorimeter composed of the Crystal Ball and TAPS detectors. Using a complete kinematic reconstruction of the final state, excellent agreement was found between the results for free and quasi-free protons, suggesting that the quasi-free neutron results are also a close approximation of the free-neutron asymmetries. A comparison of the results to the predictions of the Two-Pion-MAID reaction model shows that the reaction mechanisms are still not well understood, in particular at low incident photon energies in the second nucleon-resonance region.