Measurement of $CP$ asymmetry in $B^0_s \rightarrow D^{\mp}_s K^{\pm}$ decays

A measurement of the $CP$-violating parameters in $B^0_s \rightarrow D^{\mp}_s K^{\pm}$ decays obtained from $pp$ collisions is reported, using a data set corresponding to an integrated luminosity of $6\,\textrm{fb}^{-1}$ at a centre-of-mass energy of ${\sqrt{s}=13 \,\textrm{TeV}}$ recorded with the LHCb detector between 2015 and 2018. The measured values are: \begin{equation} $C_f = 0.791 \pm 0.061 \pm 0.022$, \\ $A_f^{\Delta \Gamma} = 0.051 \pm 0.134 \pm 0.037$, \\ $A_{\bar{f}}^{\Delta \Gamma} = 0.303 \pm 0.125 \pm 0.036$, \\ $S_f = -0.571 \pm 0.084 \pm 0.023$, \\ $S_{\bar{f}} = -0.503 \pm 0.084 \pm 0.025$, \\ \end{equation} where the uncertainties are statistical and systematic, respectively. Together with the value of the $B_s^0$ mixing phase $-2 \beta{_s}$, these parameters are used to obtain a measurement of the CKM angle $\gamma$ from $B^0_s \rightarrow D^{\mp}_s K^{\pm}$ decays of $\gamma = ( 74\pm11)^{\circ}$ modulo $180^{\circ}$, where the uncertainty contains both statistical and systematic contributions.