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.
Stephen Sekula
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