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

Abstract

The resonant substructure of $D^0\to {\pi }^{+}{\pi }^{-}{\pi }^{+}{\pi }^{-}$ 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 $D^0\to a_1(1260{)}^{+}{\pi }^{-}$, $D^0\to \sigma f_0(1370)$ and $D^0\to \rho (770{)}^0\rho (770{)}^0$. The broad resonances $a_1(1260{)}^{+}$, $\pi (1300{)}^{+}$ 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 $m_{a_1(1260{)}^{+}}=[1225\pm 9\text{(stat)}\pm 17\text{(syst)}\pm 10\text{(model)}]\text{MeV}/c^2$ and ${\Gamma }_{a_1(1260{)}^{+}}=[430\pm 24\text{(stat)}\pm 25\text{(syst)}\pm 18\text{(model)}]\text{MeV}$. The amplitude model of $D^0\to K^{+}{K}^{-}{\pi }^{+}{\pi }^{-}$ 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 $D^0\to \varphi (1020)\rho (770{)}^0$, $D^0\to K_1(1270{)}^{+}{K}^{-}$ and $D^0\to K(1400{)}^{+}{K}^{-}$. The fractional $CP$-even content of the decay $D^0\to {\pi }^{+}{\pi }^{-}{\pi }^{+}{\pi }^{-}$ is calculated from the amplitude model to be $F_{+}^{4\pi }=[72.9\pm 0.9\text{(stat)}\pm 1.5\text{(syst)}\pm 1.0\text{(model)}]\%$, consistent with that obtained from a previous model-independent measurement. For $D^0\to K^{+}{K}^{-}{\pi }^{+}{\pi }^{-}$ decays, the $CP$-even fraction is measured for the first time and found to be $F_{+}^{KK\pi \pi }=[75.3\pm 1.8\text{(stat)}\pm 3.3\text{(syst)}\pm 3.5\text{(model)}]\%$. The global decay rate asymmetries between $D^0$ and ${\overline{D}}^0$ decays are measured to be $A_{CP}^{4\pi }=[+0.54\pm 1.04\text{(stat)}\pm 0.51\text{(syst)}]\%$ and $A_{CP}^{KK\pi \pi }=[+1.84\pm 1.74\text{(stat)}\pm 0.30\text{(syst)}]\%$.

62 pages, 18 figures, 24 tables

References in corpus (12)

• Observation of the resonant character of the $Z(4430{)}^{-}$ state
• Branching fractions, polarisation and asymmetries of B -> VV decays
• Analysis of the resonant components in B0->J/ψpi+pi-
• A Study in Depth of f0(1370)
• First determination of the $CP$ content of $D\to {\pi }^{+}{\pi }^{-}{\pi }^{+}{\pi }^{-}$ and updated determination of the $CP$ contents of $D\to {\pi }^{+}{\pi }^{-}{\pi }^0$ and $D\to K^{+}{K}^{-}{\pi }^0$
• The mass of the sigma pole
• Determining the unitarity triangle angle $\gamma$ with a four-body amplitude analysis of ${\mathrm{B}}^{\pm }\to ({\mathrm{K}}^{+}{\mathrm{K}}^{-}{\pi }^{+}{\pi }^{-}{)}_{\mathrm{D}}{\mathrm{K}}^{\pm }$ decays
• Model independent determination of the CKM phase $\gamma$ using input from $D^0-{\bar{D}}^0$ mixing
• Measurement of Branching Fraction and First Evidence of CP Violation in B0 --> a1+-(1260) pi-+ Decays
• Covariant tensor formalism for partial wave analyses of psi decay to mesons
• On model-independent measurement of the angle phi_3 using Dalitz plot analysis
• An alternative parametrization of the pion form factor and the mass and width of rho(770)

Cited by in corpus (22)

• 50 Years of Quantum Chromodynamics
• Axial-vector transition form factors and $e^{+}{e}^{-}\to f_1{\pi }^{+}{\pi }^{-}$
• Studies of the resonance structure in $D^0\to K^{\mp }{\pi }^{\pm }{\pi }^{\pm }{\pi }^{\mp }$ decays
• Direct CP violation in beauty and charm hadron decays
• Search for $CP$ violation through an amplitude analysis of $D^0\to K^{+}{K}^{-}{\pi }^{+}{\pi }^{-}$ decays
• Model-independent determination of the strong phase difference between $D^0$ and ${\bar{D}}^0\to {\pi }^{+}{\pi }^{-}{\pi }^{+}{\pi }^{-}$ amplitudes
• The f0(1370) controversy from dispersive meson-meson scattering data analyses
• Search for $CP$ violation in the phase space of $D^0\to {\pi }^{+}{\pi }^{-}{\pi }^{+}{\pi }^{-}$ decays
• Amplitude analysis and branching fraction measurement of $D_s^{+}\to K^{-}{K}^{+}{\pi }^{+}{\pi }^0$
• A study of $CP$ violation in the decays $B^{\pm }\to [K^{+}{K}^{-}{\pi }^{+}{\pi }^{-}{]}_D{h}^{\pm }$ ($h=K,\pi$) and $B^{\pm }\to [{\pi }^{+}{\pi }^{-}{\pi }^{+}{\pi }^{-}{]}_D{h}^{\pm }$
• $S$-wave contribution to rare $D^0\to {\pi }^{+}{\pi }^{-}{\ell }^{+}{\ell }^{-}$ decays in the Standard Model and sensitivity to New Physics
• Amplitude analysis of $B^{+}\to \psi (2S)K^{+}{\pi }^{+}{\pi }^{-}$ decays
• Using an amplitude analysis to measure the photon polarisation in $B\to K\pi \pi \gamma$ decays
• Novel correlated $D^0\overline{D}{}^0$ systems for $c/b$ physics and tests of $T/CPT$
• Resolving the ${\varphi }_2$ ($\alpha$) ambiguity in $B^0\to a_1^{\pm }{\pi }^{\mp }$
• Study of $a_1(1260)$ in the $\gamma p\to {\pi }^{+}{\pi }^{+}{\pi }^{-}n$ reaction
• Observation of the semileptonic decays $D^0\to K_S^0{\pi }^{-}{\pi }^0{e}^{+}{\nu }_e$ and $D^{+}\to K_S^0{\pi }^{+}{\pi }^{-}{e}^{+}{\nu }_e$
• Resolving the ${\varphi }_2$ ($\alpha$) ambiguity in $B\to \rho \rho$
• Amplitude analysis and branching fraction measurement of $D_s^{+}\to K^{-}{K}^{+}{\pi }^{+}{\pi }^{+}{\pi }^{-}$
• Emergence of the $\pi (1300)$ Resonance from Lattice QCD
• A model-independent measurement of the CKM angle $\gamma$ in the decays $B^{\pm }\to [K^{+}{K}^{-}{\pi }^{+}{\pi }^{-}{]}_D{h}^{\pm }$ and $B^{\pm }\to [{\pi }^{+}{\pi }^{-}{\pi }^{+}{\pi }^{-}{]}_D{h}^{\pm }$ ($h=K,\pi$)
• Charge asymmetry in the process $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}{\pi }^0\gamma$