Invariant mass distributions for: (a) $ K ^+ K ^- \pi ^+ $ and (b) $ K ^+ K ^- \pi ^- $ candidates for magnet up, (c) $ K ^+ K ^- \pi ^+ $ and (d) $ K ^+ K ^- \pi ^- $ candidates for magnet down with $ K ^+ K ^- $ invariant mass within $\pm$20 $\mathrm{ Me V} $ of the $\phi$ meson mass. The $ D ^+_ s $ [yellow (grey) shaded area] and $ D ^+$ [red (dark) shaded area] signal shapes are described in the text. The $\chi ^2$/ndf for these fits are 1.28, 1.25, 1.53, and 1.27 respectively, the corresponding p-values are 7%, 8%, 4%, 7%.

Invariant $\mu ^+ \mu ^- $ mass distributions of the kinematically-selected $ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu}$ candidates in magnet up data, where the red (open) circles represent entries where the muon candidate, kinematically selected, is rejected and the black (filled) circles those where it is accepted by the muon identification algorithm. The dashed lines represent the combinatorial background.

Relative muon efficiency as a function of muon momentum determined using the kinematically-selected $ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu}$ sample.

(a) Spectrum of the logarithm of the IP calculated with respect to the primary vertex for $ D ^+_ s $ candidates in combination with muons; the insert shows a magnified view of the region where the prompt $ D ^+_ s $ contribution peaks. The blue dashed line is the component coming from $B$ hadron decays, the black dashed line the false $ D ^+_ s $ background, the red line the prompt background, (b) the invariant mass distributions for $ D ^+_ s \rightarrow \phi\pi$ candidates. These distributions are for the magnet down sample. (For interpretation of the reference to colour in this figure legend, the reader is referred to the web version of this Letter.)

Asymmetries corrected for relative muon efficiencies, $A_{\mu}^{\text{c}}$, examined in the five muon momentum intervals for (a) magnet up data, (b) magnet down data and (c) average, using the KS muon calibration method. Then (d) magnet up data, (e) magnet down data and (f) average, using the MS muon calibration method in the two different binning scheme.

Measurements of semileptonic decay asymmetries. The bands correspond to the central values $\pm$1 standard deviation uncertainties, defined as the sum in quadrature of the statistical and systematic errors. The solid dot indicates the SM prediction.

Animated gif made out of all figures.

Yields for $ D ^+_ s \mu ^- $ and $ D ^-_ s \mu ^+ $ events separately for magnet up and down data. These yields contain very small contributions from prompt $ D _s$ and b-hadron backgrounds.

Muon efficiency ratio corrected asymmetry $A_{\mu}^c$. The errors account for the statistical uncertainties in the $ B ^0_ s $ signal yields.

Sources of systematic uncertainty on $A_{\rm meas}$.