A model-independent Dalitz plot analysis of B±→DK±B±→DK± with D→KS0h+h− (h=π,Kh=π,K) decays and constraints on the CKM angle γ

A binned Dalitz plot analysis of B±→DK±B±→DK± decays, with D→KS0π+π− and D→KS0K+K−, is performed to measure the CP -violating observables x±x± and y±y± which are sensitive to the CKM angle γ . The analysis exploits 1.0 fb−11.0 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±4.3±1.5±0.6)×10−2x−=(0.0±4.3±1.5±0.6)×10−2, y−=(2.7±5.2±0.8±2.3)×10−2y−=(2.7±5.2±0.8±2.3)×10−2, x+=(−10.3±4.5±1.8±1.4)×10−2x+=(−10.3±4.5±1.8±1.4)×10−2 and y+=(−0.9±3.7±0.8±3.0)×10−2y+=(−0.9±3.7±0.8±3.0)×10−2. The first, second, and third uncertainties are the statistical, the experimental systematic, and the error associated with the precision of the strong-phase parameters measured at CLEO-c, respectively. These results correspond to γ=(44−38+43)°, with a second solution at γ→γ+180°γ→γ+180°, and rB=0.07±0.04rB=0.07±0.04, where rBrB is the ratio between the suppressed and favoured B decay amplitudes.