Amplitude analyses of D 0 → π + π − π + π − and D 0 → K + K − π + π − decays

The resonant substructure of D 0 → π + π − π + π − decays is studied using data collected by the CLEO-c detector. An amplitude analysis is performed in order to disentangle the various intermediate state contributions. To limit the model complexity a data driven regularization procedure is applied. The prominent contributions are the decay modes D 0 → a 1 (1260) + π − , D 0 → σ f 0 (1370) and D 0 → ρ (770) 0 ρ (770) 0 . The broad resonances a 1 (1260) + , π(1300) + and a 1 (1640) + are studied in detail, including quasi-modelindependent parametrizations of their lineshapes. The mass and width of the a 1 (1260) + meson are determined to be m a1 (1260) + = [1225 ± 9 (stat) ± 17 (syst) ± 10 (model)] MeV /c 2 and Γ a1 (1260) + = [430 ± 24 (stat) ± 25 (syst) ± 18 (model)] MeV. The amplitude model of D 0 → K + K − π + π − decays obtained from CLEO II.V, CLEO III, and CLEO-c data is revisited with improved lineshape parametrizations. The largest components are the decay modes D 0 → ϕ (1020) ρ (770) 0 , D 0 → K 1 (1270) + K − and D 0 → K (1400) + K − . The fractional CP -even content of the decay D 0 → π + π − π + π − is calculated from the amplitude model to be F + 4π = [72.9 ± 0.9(stat) ± 1.5(syst) ± 1.0(model)]