A model-independent measurement of the CKM angle $\gamma$ in the decays $B^{\pm }\to [K^{+}{K}^{-}{\pi }^{+}{\pi }^{-}{]}_D{h}^{\pm }$ and $B^{\pm }\to [{\pi }^{+}{\pi }^{-}{\pi }^{+}{\pi }^{-}{]}_D{h}^{\pm }$ ($h=K,\pi$)

A model-independent determination of the CKM angle $\gamma$ is presented, using the $B^{\pm }\to [K^{+}{K}^{-}{\pi }^{+}{\pi }^{-}{]}_D{h}^{\pm }$ and $B^{\pm }\to [{\pi }^{+}{\pi }^{-}{\pi }^{+}{\pi }^{-}{]}_D{h}^{\pm }$ decays, with $h=K,\pi$. This measurement is the first phase-space-binned study of these decay modes, and uses a sample of proton-proton collision data collected by the LHCb experiment, corresponding to an integrated luminosity of $9$fb${}^{-1}$. The phase-space bins are optimised for sensitivity to $\gamma$, and in each bin external inputs from the BESIII experiment are used to constrain the charm strong-phase parameters. The result of this binned analysis is $\gamma =(53.9_{-8.9}^{+9.5}{)}^{\circ }$, where the uncertainty includes both statistical and systematic contributions. Furthermore, when combining with existing phase-space-integrated measurements of the same decay modes, a value of $\gamma =(52.6_{-6.4}^{+8.5}{)}^{\circ }$ is obtained, which is one of the most precise determinations of $\gamma$ to date.