Measurement of the CKM angle $γ$ and $B^0_s$-$\bar{B}^0_s$ mixing frequency with $B^0_s \rightarrow D_s^\mp h^\pm π^\pm π^\mp$ decays
The CKM angle $γ$ is measured for the first time from mixing-induced $CP$ violation between $B^0_s \rightarrow D_s^\mp K^\pm π^\pm π^\mp$ and $\bar{B}^0_s \rightarrow D_s^\pm K^\mp π^\mp π^\pm$ decays reconstructed in proton-proton collision data corresponding to an integrated luminosity of 9 ${\rm fb}^{-1}$ recorded with the LHCb detector. A time-dependent amplitude analysis is performed to extract the $CP$-violating weak phase $γ-2β_s$ and, subsequently, $γ$ by taking the $B^0_s$-$\bar{B}^0_s$ mixing phase $β_{s}$ as an external input. The measurement yields $γ= (44 \pm 12)^\circ$ modulo $180^\circ$, where statistical and systematic uncertainties are combined. An alternative model-independent measurement, integrating over the five-dimensional phase space of the decay, yields $γ= (44^{\,+\,20}_{\,-\,13})^\circ$ modulo $180^\circ$. Moreover, the $B^0_s$-$\bar{B}^0_s$ oscillation frequency is measured from the flavour-specific control channel $B^0_s \rightarrow D_s^- π^+ π^+ π^-$ to be $Δm_s = (17.757 \pm 0.007 \,({\rm stat.}) \pm 0.008 \,({\rm syst.})) \text{ps}^{-1}$, consistent with and more precise than the current world-average value.