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

The resonant substructure of D⁰ → 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 D⁰ → a₁(1260)⁺ π⁻, D⁰ → σ f₀(1370) and D⁰ → ρ(770)⁰ρ(770)⁰. The broad resonances a₁(1260)⁺, π(1300)⁺ and a₁(1640)⁺ are studied in detail, including quasi-modelindependent parametrizations of their lineshapes. The mass and width of the a₁(1260)⁺ meson are determined to be m_a1(1260)⁺ = [1225 ± 9 (stat) ± 17 (syst) ± 10 (model)] MeV/c² and Γ_a1(1260)⁺ = [430 ± 24 (stat) ± 25 (syst) ± 18 (model)] MeV. The amplitude model of D⁰ → 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 D⁰ → ϕ(1020)ρ(770)⁰, D⁰ → K₁(1270)⁺K⁻ and D⁰ → K(1400)⁺K⁻. The fractional CP -even content of the decay D⁰ → 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)] %, consistent with that obtained from a previous model-independent measurement. For D⁰ → K⁺K⁻π⁺π⁻ decays, the CP -even fraction is measured for the first time and found to be F₊ ^KKππ = [75.3 ± 1.8 (stat) ± 3.3 (syst) ± 3.5 (model)] %. The global decay rate asymmetries between D⁰ and D¯ ⁰ decays are measured to be ACP4π=[+0.54±1.04(stat)±0.51(syst)]% and ACPKKππ=[+1.84±1.74(stat)±0.30(syst)]%. A search for CP asymmetries in the amplitude components yields no evidence for CP violation in either decay mode.