Model-independent $D^0-\bar{D^0}$ mixing and CP violation studies with $D^0 \to K^0_{\rm S}\pi^+\pi^-$ and $D^0 \to K^0_{\rm S}K^+K^-$

TL;DR

This study evaluates a model-independent method for analyzing $D^0$ decays to measure mixing and CP violation, demonstrating high precision potential with large data samples and minimal systematic uncertainties.

Contribution

It introduces a model-independent analysis approach for $D^0$ decays that leverages quantum-correlated data to improve sensitivity to mixing and CP violation.

Findings

Achieves ~0.01 precision on $r_{CP}$ with 100M decays.

Attains ~0.7° precision on $a_{CP}$ with large data sets.

Systematic uncertainties are manageable with existing $ ext{CLEO-c}$ and $ ext{BES-III}$ data.

Abstract

Simulation studies are performed to assess the sensitivity of a model-independent analysis of the flavour-tagged decays $D^0 \to K^0_{\rm S}\pi^+\pi^-$ and $D^0 \to K^0_{\rm S}K^+K^-$ to mixing and CP violation. The analysis takes as input measurements of the $D$ decay strong-phase parameters that are accessible in quantum-correlated $D-\bar{D}$ pairs produced at the $\psi(3770)$ resonance. It is shown that the model-independent approach is well suited to the very large data sets expected at an upgraded LHCb experiment, or future high luminosity $e^+e^-$ facility, and that with 100M $K^0_{\rm S}\pi^+\pi^-$ decays a statistical precision of around 0.01 and $0.7^\circ$ is achievable on the CP violation parameters $r_{CP}$ and $a_{CP}$, respectively. Even with this very large sample the systematic uncertainties associated with the strong-phase parameters will not be limiting, assuming that full use is made of the available $\psi(3770)$ data sets of CLEO-c and BES-III. Furthermore, it is demonstrated that large flavour-tagged samples can themselves be exploited to provide information on the strong-phase parameters, a feature that will be beneficial in the measurement of the CKM angle $\gamma/\phi_3$ with $B^- \to DK^-$ decays.