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

Abstract

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 − 2β_s and, subsequently, γ by taking the ${B}_s^0\hbox{-} {\overline{B}}_s^0$ 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 $\gamma =\left({44}_{-13}^{+20}\right){}^{\circ}$ 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 ∆m_s = (17.757 ± 0.007(stat) ± 0.008(syst)) ps⁻¹, consistent with and more precise than the current world-average value.