Measurement of the CKM angle $\gamma$ and $B^0_s$-$\bar{B}^0_s$ mixing frequency with $B^0_s \rightarrow D_s^\mp h^\pm \pi^\pm \pi^\mp$ decays

Understand

The CKM angle $\gamma$ is measured for the first time from mixing-induced $CP$ violation between $B^0_s \rightarrow D_s^\mp K^\pm \pi^\pm \pi^\mp$ and $\bar{B}^0_s \rightarrow D_s^\pm K^\mp \pi^\mp \pi^\pm$ 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 $\gamma-2\beta_s$ and, subsequently, $\gamma$ by taking the $B^0_s$-$\bar{B}^0_s$ mixing phase $\beta_{s}$ as an external input.
• The measurement yields $\gamma = (44 \pm 12)^\circ$ 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 $\gamma = (44^{\,+\,20}_{\,-\,13})^\circ$ modulo $180^\circ$.