Amplitude analysis of the decays D0 → π+π−π+π− and D0 → π+π−π0π0

Using e+e- annihilation data corresponding to an integrated luminosity of 2.93 fb^-1 taken at the center-of-mass energy sqrt(s) = 3.773 GeV with the BESIII detector, a joint amplitude analysis is performed on the decays D0 -> pi+pi-pi+pi- and D0 -> pi+pi-pi0pi0(non-eta). The fit fractions of individual components are obtained, and large interferences among the dominant components of the decays D0 -> alpha_1(1260)pi, D0 -> pi(1300)pi, D0 -> rho(770)rho(770), and D0 -> 2(pi pi)_s are observed in both channels. With the obtained amplitude model, the CP-even fractions of D0 -> pi+pi-pi+pi- and D0 -> pi+pi-pi0pi0(non-eta) are determined to be (75.2 +/- 1.1(stat.) +/- 1.5(syst))% and (68.9 +/- 1.5(stat.) +/- 2.4(syst.))%, respectively. The branching fractions of D0 -> pi+pi-pi+pi- and D0 -> pi+pi-pi0pi0(non-eta) are measured to be (0.688 +/- 0.010(stat). +/- 0.010(syst.)) % and (0.951 +/- 0.025(stat.) +/- 0.021(syst.))%, respectively. The amplitude analysis provides an important model for the binning strategy in measuring the strong phase parameters of D0 -> 4pi when used to determine the CKM angle gamma(phi_3) via the B^- -> DK- decay.