Amplitude analysis of the decays D⁰ → π⁺π⁻π⁺π⁻ and D⁰ → π⁺π⁻π⁰π^0*

Using e⁺e⁻ annihilation data corresponding to an integrated luminosity of 2.93 fb⁻¹ taken at the center-of-mass energy ^√s = 3.773 GeV with the BESIII detector, a joint amplitude analysis is performed on the decays D⁰ → π⁺π⁻π⁺π⁻ and D⁰ → π⁺π⁻π⁰π⁰ (non-η). The fit fractions of individual components are obtained, and large interferences among the dominant components of the decays D⁰ → a₁(1260)π, D⁰ → π(1300)π, D⁰ → ρ(770)ρ(770), and D⁰ → 2(ππ)S are observed in both channels. With the obtained amplitude model, the CP-even fractions of D⁰ → π⁺π⁻π⁺π⁻ and D⁰ → π⁺π⁻π⁰π⁰ (non-η) are determined to be (75.2 ± 1.1stat. ± 1.5syst.) % and (68.9 ± 1.5stat. ± 2.4syst.)%, respectively. The branching fractions of D⁰ → π⁺π⁻π⁺π⁻ and D⁰ → π⁺π⁻π⁰π⁰ (non-η) are measured to be (0.688 ± 0.010stat. ± 0.010syst.)% and (0.951 ± 0.025stat. ± 0.021syst.)%, respectively. The amplitude analysis provides an important model for the binning strategy in measuring the strong phase parameters of D⁰ → 4π when used to determine the CKM angle γ(ϕ₃) via the B⁻ → DK⁻ decay.