Measurement of the CKM angle γ using B ± → DK ± with D  →  K S 0 π + π − , K S 0 K + K − decays

A binned Dalitz plot analysis of B ± → DK ± decays, with D → K S 0 π + π − and D → K S 0 K + K − , is performed to measure the CP -violating observables x ± and y ± , which are sensitive to the Cabibbo-Kobayashi-Maskawa angle γ . The analysis exploits a sample of proton-proton collision data corresponding to 3.0 fb −1 collected by the LHCb experiment. Measurements from CLEO-c of the variation of the strong-interaction phase of the D decay over the Dalitz plot are used as inputs. The values of the parameters are found to be x +  = (−7.7 ± 2.4 ± 1.0 ± 0.4) × 10 − 2 , x −  = (2.5 ± 2.5 ± 1.0 ± 0.5) × 10 − 2 , y +  = (−2.2 ± 2.5 ± 0.4 ± 1.0) × 10 − 2 and y −  = (7.5 ± 2.9 ± 0.5 ± 1.4) × 10 − 2 . The first, second, and third uncertainties are the statistical, the experimental systematic, and that associated with the precision of the strong-phase parameters. These are the most precise measurements of these observables and correspond to γ  = (62 − 14 + 15 ) ° , with a second solution at γ  →  γ  + 180 ° , and r B  = 0.080 − 0.021 + 0.019 , where r B is the ratio between the suppressed and favoured B decay amplitudes.