Measurement of the CKM angle $\gamma$ and $B_s^0-\overline{B_s^0}$ mixing frequency with $B_s^0 \to D_s^{\mp} h^{\pm} \pi^{\pm}\pi^{\mp}$ decays

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