A model-independent Dalitz plot analysis of $B^\pm \to D K^\pm$ with $D \to K^0_{\rm S} h^+h^-$ ($h=\pi, K$) decays and constraints on the CKM angle $\gamma$

Understand

A binned Dalitz plot analysis of $B^\pm \to D K^\pm$ decays, with $D \to K^0_{\rm S} \pi^+\pi^-$ and $D \to K^0_{\rm S} K^+ K^-$, is performed to measure the CP-violating observables $x_{\pm}$ and $y_{\pm}$ which are sensitive to the CKM angle $\gamma$.

• The analysis exploits 1.0 $\rm fb^{-1}$ of data collected by the LHCb experiment.
• The study makes no model-based assumption on the variation of the strong phase of the D decay amplitude over the Dalitz plot, but uses measurements of this quantity from CLEO-c as input.
• The values of the parameters are found to be $x_- = (0.0 \pm 4.3 \pm 1.5 \pm 0.6) \times 10^{-2}$, $y_- = (2.7 \pm 5.2 \pm 0.8 \pm 2.3) \times 10^{-2}$, $x_+ = (-10.3 \pm 4.5 \pm 1.8 \pm 1.4)\times 10^{-2}$ and $y_+ = (-0.9 \pm 3.7 \pm 0.8 \pm 3.0)\times 10^{-2}$.