Amplitude Analyses of $D^0 \to {π^+π^-π^+π^-}$ and $D^0 \to {K^+K^-π^+π^-}$ Decays

Abstract

The resonant substructure of $D^0 \to π^+π^-π^+π^-$ 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 $D^0\to a_1(1260)^+π^-$, $D^0\to σf_0(1370)$ and $D^0 \to ρ(770)^0 ρ(770)^0$. The broad resonances $a_1(1260)^+$, $π(1300)^+$ and $a_1(1640)^+$ are studied in detail, including quasi-model-independent parametrizations of their lineshapes. The mass and width of the $a_1(1260)^+$ meson are determined to be $m_{a_1(1260)^+}=[1225\pm9\text{(stat)}\pm17\text{(syst)}\pm10\text{(model)}]\text{MeV}/c^2$ and $Γ_{a_1(1260)^+}=[430\pm24\text{(stat)}\pm25 \text{(syst)}\pm18\text{(model)}]\text{MeV}$. The amplitude model of $D^0\to K^+K^-π^+π^-$ 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 $D^0\toϕ(1020)ρ(770)^0$, $D^0 \to K_1(1270)^+ K^-$ and $D^0 \to K(1400)^+ K^-$. The fractional $CP$-even content of the decay $D^0\to π^+π^-π^+π^-$ is calculated from the amplitude model to be $F_+^{4π}=[72.9\pm0.9\text{(stat)}\pm1.5\text{(syst)}\pm1.0\text{(model)}]\%$, consistent with that obtained from a previous model-independent measurement. For $D^0 \to K^+K^-π^+π^-$ decays, the $CP$-even fraction is measured for the first time and found to be $F_+^{KKππ}=[75.3\pm1.8\text{(stat)}\pm3.3\text{(syst)}\pm3.5\text{(model)}]\%$. The global decay rate asymmetries between $D^0$ and $\overline{D}^0$ decays are measured to be $A^{4π}_{CP}=[+0.54\pm1.04\text{(stat)}\pm0.51\text{(syst)}]\%$ and $A^{KKππ}_{CP}=[+1.84\pm1.74\text{(stat)}\pm0.30\text{(syst)}]\%$.

62 pages, 18 figures, 24 tables