Measurement of the CKM angle γ and $$ {B}_s^0\hbox{-} {\overline{B}}_s^0 $$ mixing frequency with $$ {B}_s^0\to {D}_s^{\mp }{h}^{\pm }{\pi}^{\pm }{\pi}^{\mp } $$ decays

A bstract The CKM angle γ is measured for the first time from mixing-induced CP violation between $$ {B}_s^0\to {D}_s^{\mp }{K}^{\pm }{\pi}^{\pm }{\pi}^{\mp } $$ B s 0 → D s ∓ K ± π ± π ∓ and $$ {\overline{B}}_s^0\to {D}_s^{\pm }{K}^{\mp }{\pi}^{\mp }{\pi}^{\pm } $$ B ¯ s 0 → D s ± K ∓ π ∓ π ± 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 − 2 β s and, subsequently, γ by taking the $$ {B}_s^0\hbox{-} {\overline{B}}_s^0 $$ B s 0 ‐ B ¯ s 0 mixing phase β s 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 $$ \gamma =\left({44}_{-13}^{+20}\right){}^{\circ} $$ γ = 44 − 13 + 20 ° modulo 180°. Moreover, the $$ {B}_s^0\hbox{-} {\overline{B}}_s^0 $$ B s 0 ‐ B ¯ s 0 oscillation frequency is measured from the flavour-specific control channel $$ {B}_s^0\to {D}_s^{-}{\pi}^{+}{\pi}^{+}{\pi}^{-} $$ B s 0 → D s − π + π + π − to be ∆ m s = (17 . 757 ± 0 . 007(stat) ± 0 . 008(syst)) ps − 1 , consistent with and more precise than the current world-average value.