Binning schemes for (left) $ D \rightarrow K ^0_{\mathrm{S}} \pi ^+ \pi ^- $ decays and (right) $ D \rightarrow K ^0_{\mathrm{S}} K ^+ K ^- $ decays. The diagonal line separates the positive and negative bins, where the positive bins are in the region in which $ m^2_- > m^2_+ $ is satisfied.

Dalitz plot for $ D $ decays of (left) $ B ^+ \rightarrow D K ^+ $ and (right) $ B ^- \rightarrow D K ^- $ candidates in the signal region, in the (top) $ D \rightarrow K ^0_{\mathrm{S}} \pi ^+ \pi ^- $ and (bottom) $ D \rightarrow K ^0_{\mathrm{S}} K ^+ K ^- $ channels.

Invariant mass distributions for the (left) $ B ^\pm \rightarrow D K ^\pm $ channel and (right) $ B ^\pm \rightarrow D \pi ^\pm $ channel with $ D \rightarrow K ^0_{\mathrm{S}} \pi ^+ \pi ^- $ . The top (bottom) plots show data where the $ K ^0_{\mathrm{S}}$ type is long (downstream). The particle within square brackets in the legend denotes the particle that has not been reconstructed.

Invariant mass distributions for the (left) $ B ^\pm \rightarrow D K ^\pm $ channel and (right) $ B ^\pm \rightarrow D \pi ^\pm $ channel with $ D \rightarrow K ^0_{\mathrm{S}} K ^+ K ^- $ . The top (bottom) plots show data where the $ K ^0_{\mathrm{S}}$ type is long (downstream). The particle within square brackets in the legend denotes the particle that has not been reconstructed.

Confidence levels at 68.2 % and 95.5 % probability for (left, blue) $( x_+ ^{ D K ^\pm }, y_+ ^{ D K ^\pm })$, (left, red) $( x_- ^{ D K ^\pm }, y_- ^{ D K ^\pm })$, and (right, green) $(x_\xi^{ D \pi ^\pm },y_\xi^{ D \pi ^\pm }) $ as measured in $ B ^\pm \rightarrow D K ^\pm $ and $ B ^\pm \rightarrow D \pi ^\pm $ decays with a profile likelihood scan. The black dots show the central values

The bin-by-bin asymmetries $(N^-_{-i}-N^+_{+i})/(N^-_{-i}+N^+_{+i})$ for each Dalitz-plot bin number for (left) $ B ^\pm \rightarrow D K ^\pm $ decays and (right) $ B ^\pm \rightarrow D \pi ^\pm $ decays. The prediction from the central values of the $ C P$ -violation observables is shown with a solid line and the asymmetries obtained in fits with independent bin yields are shown with the error bars. The predicted asymmetries in a fit that does not allow for $ C P$ violation are shown with a dotted line.

The 68 % and 95 % confidence regions for combinations of the physics parameters $(\gamma , r_ B ^{ D K } , \delta_ B ^{ D K } , r_ B ^{ D \pi} , \delta_ B ^{ D \pi} )$ obtained using the methods described in Ref. [44].

Animated gif made out of all figures.

The signal and background yields in the signal region $m_B\in[5249, 5309]\text{ Me V /}c^2 $. In the $ B ^\pm \rightarrow D K ^\pm $ channels, the yield of the partially reconstructed background includes contributions from the $ B ^0_ s $ background and partially reconstructed decays where a pion is misidentified as a kaon.

Overview of all sources of uncertainty on the measurement.