Measurement of the CKM angle $\gamma$ in $B^\pm\to D K^\pm$ and $B^\pm \to D \pi^\pm$ decays with $D \to K_\mathrm S^0 h^\pm h^\mp$

A measurement of $CP$-violating observables is performed using the decays ${B^\pm \to D K^\pm}$ and ${B^\pm \to D \pi^\pm}$, where the $D$ meson is reconstructed in one of the self-conjugate three-body final states $K_\mathrm S^0\pi^+\pi^-$ and $K_\mathrm S^0 K^+ K^-$ ($h^\pm h^\mp = \pi^\pm \pi^\mp, K^\pm K^\mp$). The decays are analysed in bins of the $D$-decay phase space, leading to a measurement that is independent of the modelling of the $D$-decay amplitude. Using the full Run 1 and 2 LHCb data sample, the observables of interest are measured to be \begin{align*} x_-^{DK} & = (\phantom{-}5.6 \pm 1.0 \pm 0.2\pm 0.3) \times 10^{-2}, \\ y_-^{DK} & = (\phantom{-}6.5\pm 1.1 \pm 0.3\pm 0.4) \times 10^{-2}, \\ x_+^{DK} & = ( - 9.2 \pm 1.0 \pm 0.2\pm 0.2) \times 10^{-2}, \\ y_+^{DK} & = ( - 1.2 \pm 1.2 \pm 0.3\pm 0.3) \times 10^{-2}, \\ x_\xi^{D\pi} & = ( - 5.3 \pm 2.0 \pm 0.3\pm 0.2) \times 10^{-2}, \\ y_\xi^{D\pi} & = (\phantom{-}1.0 \pm 2.3 \pm 0.5\pm 0.3) \times 10^{-2}, \end{align*} where the first uncertainty is statistical, the second arises from systematic effects in the method or other experimental effects, and the third from external inputs of strong-phase measurements from CLEO and BESIII. The measurements can be interpreted in terms of the CKM angle $\gamma$, leading to $\gamma=(69 \pm 5)^\circ$. Measurements of the hadronic parameters $r_B^{DK}$, $r_B^{D\pi}$, $\delta_B^{DK}$, and $\delta_B^{D\pi}$ are also reported