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 } Bs0→Ds∓K±π±π∓ and {\overline{B}}_s^0\to {D}_s^{\pm }{K}^{\mp xmlns:mml="http://www.w3.org/1998/Math/MathML">B¯s0→Ds±K∓π∓π± decays reconstructed in proton-proton collision data corresponding to an integrated luminosity of 9 fb − 1 recorded with LHCb detector. time-dependent amplitude analysis performed extract -violating weak phase 2 β s and, subsequently, by taking {B}_s^0\hbox{-} {\overline{B}}_s^0 xmlns:mml="http://www.w3.org/1998/Math/MathML">Bs0‐B¯s0 mixing as external input. measurement yields = (44 ± 12)° modulo 180°, where statistical systematic uncertainties are combined. An alternative model-independent measurement, integrating over five-dimensional space decay, \gamma =\left({44}_{-13}^{+20}\right){}^{\circ} xmlns:mml="http://www.w3.org/1998/Math/MathML">γ=44−13+20° 180°. Moreover, oscillation frequency flavour-specific control channel {D}_s^{-}{\pi}^{+}{\pi}^{+}{\pi}^{-} xmlns:mml="http://www.w3.org/1998/Math/MathML">Bs0→Ds−π+π+π− be ∆ m (17 . 757 0 007(stat) 008(syst)) ps , consistent more precise than current world-average value.