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 ⁰π⁺π⁻ and D → K_S ⁰K⁺K⁻, is used to perform a measurement of the CP-violating observables x_± and y_±, which are sensitive to the Cabibbo-Kobayashi-Maskawa angle γ. The analysis is performed without assuming any D decay model, through the use of information on the strong-phase variation over the Dalitz plot from the CLEO collaboration. Using a sample of proton-proton collision data collected with the LHCb experiment in 2015 and 2016, and corresponding to an integrated luminosity of 2.0 fb⁻¹, the values of the CP violation parameters are found to be x₋ = (9.0 ± 1.7 ± 0.7 ± 0.4) × 10⁻², y₋ = (2.1 ± 2.2 ± 0.5 ± 1.1) × 10⁻², x₊ = (−7.7 ± 1.9 ± 0.7 ± 0.4) × 10⁻², and y₊ = (−1.0 ± 1.9 ± 0.4 ± 0.9) × 10⁻². The first uncertainty is statistical, the second is systematic, and the third is due to the uncertainty (on the strong-phase measurements. These values are used to obtain γ = (87_{− 12} ^{+ 11})^∘, r_B = 0.086_{− 0.014} ^{+ 0.013}, and δ_B = (101±11)°, where r_B is the ratio between the suppressed and favoured B-decay amplitudes and δ_B is the corresponding strong-interaction phase difference. This measurement is combined with the result obtained using 2011 and 2012 data collected with the LHCb experiment, to give γ = (80_{− 9} ^{+ 10})^∘, r_B = 0.080 ± 0.011, and δ_B = (110 ± 10)°.[Figure not available: see fulltext.]