Measurement of the CKM angle $\gamma$ using $B^\pm\to DK^\pm$ with $D\to K_\text{S}^0\pi^+\pi^-$, $K_\text{S}^0K^+K^-$ 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 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)°.