Measurement of $CP$ asymmetry in $B_s^0 \to D_s^{\mp} K^{\pm}$ decays

Abstract

A measurement of the $CP$-violating parameters in $B_s^0 \to D_s^{\mp} K^{\pm}$ decays is reported, based on the analysis of proton-proton collision data collected by the LHCb experiment corresponding to an integrated luminosity of $6\,\mathrm{fb}^{-1}$ at a centre-of-mass energy of $13 \,\mathrm{TeV}$. The measured parameters are obtained with a decay-time dependent analysis yielding $C_f = 0.791 \pm 0.061 \pm 0.022$, $A_f^{\Delta\Gamma} = -0.051 \pm 0.134 \pm 0.058$, $A_{\overline{f}}^{\Delta\Gamma} = -0.303 \pm 0.125 \pm 0.055$, $S_f = -0.571 \pm 0.084 \pm 0.023$ and $S_{\overline{f}} = -0.503 \pm 0.084 \pm 0.025$, where the first uncertainty is statistical and the second systematic. This corresponds to $CP$ violation in the interference between mixing and decay of about $8.6\,\sigma$. Together with the value of the Bs mixing phase $-2\beta_s$, these parameters are used to obtain a measurement of the CKM angle $\gamma$ equal to $ (74\pm12)^\circ$ modulo $180^{\circ}$, where the uncertainty contains both statistical and systematic contributions. This result is combined with the previous LHCb measurement in this channel using $3\,\mathrm{fb}^{-1}$ resulting in a determination of $\gamma= (81^{+12}_{-11})^\circ$.