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

Abstract

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.