Measurements of $C P$ observables in $B^\pm \rightarrow D K^\pm$ and $B^\pm \rightarrow D \pi^\pm$ decays are presented where the $D$ meson is reconstructed in the final states $K^\pm\pi^\mp$, $\pi^\pm K^\mp$, $K^+K^$, $\pi^+\pi^$, $K^\pm\pi^\mp \pi^+ \pi^$, $\pi^\pm K^\mp \pi^+ \pi^$ and $\pi^+ \pi^ \pi^+ \pi^$. This analysis uses a sample of charged $B$ mesons from $pp$ collisions collected by the LHCb experiment in 2011 and 2012, corresponding to an integrated luminosity of 3.0 fb$^{1}$. Various \CPviolating effects are reported and together these measurements provide important input for the determination of the unitarity triangle angle $\gamma$. The analysis of the fourpion $D$ decay mode is the first of its kind.
Invariant mass distributions of selected $ B ^\pm \rightarrow [ K ^\pm \pi ^\mp ]_{D}h^{\pm}$ candidates, separated by charge, with $ B ^ {\rm(} B ^+ {\rm)}$ candidates on the left (right). The top plots contain the $ B ^\pm \rightarrow DK^{\pm}$ candidate sample, as defined by a PID requirement on the bachelor particle. The remaining candidates are placed in the bottom row, reconstructed with a pion hypothesis for the bachelor. The red (thick, open) and green (hatchedarea) curves represent the $ B ^\pm \rightarrow D K ^\pm $ and $ B ^\pm \rightarrow D \pi ^\pm $ signals. The shaded part indicates partially reconstructed decays, the dotted line, where visible, shows the combinatorial component, and the total PDF is drawn as a thin blue line. 
Fig1.eps [47 KiB] HiDef png [361 KiB] Thumbnail [206 KiB] *.C file 

Invariant mass distributions of selected $ B ^\pm \rightarrow [\pi ^\pm K ^\mp ]_{D}h^{\pm}$ decays, separated by charge. The dashed pink line left of the signal peak shows partially reconstructed $ B _{s}^{0} \rightarrow [ K ^+ \pi ^ ]_D K ^ \pi ^+ $ decays, where the bachelor pion is missed. The favoured mode crossfeed is also included in the fit, but is too small to be seen. See the caption of Fig. 1 for other definitions. 
Fig2.eps [49 KiB] HiDef png [392 KiB] Thumbnail [231 KiB] *.C file 

Invariant mass distributions of selected $ B ^\pm \rightarrow [\pi ^+ \pi ^ ]_{D}h^{\pm}$ candidates, separated by charge. The dashed black line represents the residual contribution from charmless decays. This component is present in the $D$ final states considered, but is most visible in this case. See the caption of Fig. 1 for other definitions. 
Fig3.eps [49 KiB] HiDef png [383 KiB] Thumbnail [211 KiB] *.C file 

Invariant mass distributions of selected $ B ^\pm \rightarrow [ K ^+ K ^ ]_{D}h^{\pm}$ candidates, separated by charge. The dashed cyan line represents partially reconstructed $\Lambda ^0_ b \rightarrow [p^+ K ^ \pi ^+ ]_\Lambda ^+_ c h^$ decays, where the pion is missed and the proton is misidentified as a kaon. See the caption of Fig. 1 for other definitions. 
Fig4.eps [52 KiB] HiDef png [399 KiB] Thumbnail [223 KiB] *.C file 

Invariant mass distributions of selected $ B ^\pm \rightarrow [ K ^\pm \pi ^\mp \pi ^+ \pi ^ ]_{D}h^{\pm}$ candidates, separated by charge. See the caption of Fig. 1 for the definitions. 
Fig5.eps [64 KiB] HiDef png [364 KiB] Thumbnail [203 KiB] *.C file 

Invariant mass distributions of selected $ B ^\pm \rightarrow [\pi ^\pm K ^\mp \pi ^+ \pi ^ ]_{D}h^{\pm}$ candidates, separated by charge. The dashed pink line left of the signal peak shows partially reconstructed $ B _{s}^{0} \rightarrow [ K ^+ \pi ^ \pi ^+ \pi ^ ]_D K ^ \pi ^+ $ decays, where the bachelor pion is missed. See the caption of Fig. 1 for other definitions. 
Fig6.eps [61 KiB] HiDef png [407 KiB] Thumbnail [241 KiB] *.C file 

Invariant mass distributions of selected $ B ^\pm \rightarrow [\pi ^+ \pi ^ \pi ^+ \pi ^ ]_{D}h^{\pm}$ candidates, separated by charge. The dashed black line represents the residual contribution from charmless decays. See the caption of Fig. 1 for other definitions. 
Fig7.eps [67 KiB] HiDef png [383 KiB] Thumbnail [218 KiB] *.C file 

Comparison of selected results with the SM expectation (shaded) based on existing knowledge of the underlying parameters and $ D $ decay measurements, as described in the text. The first five rows show $ B ^ \rightarrow D K ^ $ observables, twobody $D$ decay on the left and fourbody on the right. The last three rows show $ B ^ \rightarrow D\pi ^ $ observables. 
Fig8a.eps [13 KiB] HiDef png [258 KiB] Thumbnail [211 KiB] *.C file 

Fig8b.eps [13 KiB] HiDef png [222 KiB] Thumbnail [178 KiB] *.C file 

Fig8c.eps [9 KiB] HiDef png [166 KiB] Thumbnail [136 KiB] *.C file 

Fig8d.eps [9 KiB] HiDef png [143 KiB] Thumbnail [119 KiB] *.C file 

Animated gif made out of all figures. 
PAPER2016003.gif Thumbnail 
Signal yields as measured in the $ B ^ \rightarrow [h^+h^]_{D}h^$ and $ B ^ \rightarrow [h^+h^\pi ^+ \pi ^ ]_{D}h^$ invariant mass fits, together with their statistical uncertainties. 
Table_1.pdf [56 KiB] HiDef png [180 KiB] Thumbnail [90 KiB] tex code 

Systematic uncertainties for the $ B ^ \rightarrow [h^+h^]_{D}h^$ $ C P$ observables quoted as a percentage of the statistical uncertainty on the observable. PID refers to the PID calibration procedure. Bkg refers to the choice of background shapes and yields in the fit. Sim refers to the use of finite samples of simulated events to determine efficiency ratios. Asym refers to the fixed pion and kaon detection asymmetries, and the assumption of no $ C P$ violation in $ B ^ \rightarrow D ^0 \pi ^ $ decays. 
Table_2.pdf [37 KiB] HiDef png [23 KiB] Thumbnail [8 KiB] tex code 

Statistical correlation matrix from for the 2body fit. 
Table_4.pdf [33 KiB] HiDef png [53 KiB] Thumbnail [22 KiB] tex code 

Statistical correlation matrix from for the 4body fit. 
Table_5.pdf [34 KiB] HiDef png [44 KiB] Thumbnail [18 KiB] tex code 

Correlation matrix for the systematic uncertainties in the 2body analysis. 
Table_6.pdf [34 KiB] HiDef png [51 KiB] Thumbnail [21 KiB] tex code 

Correlation matrix for the systematic uncertainties in the 4body analysis. 
Table_7.pdf [34 KiB] HiDef png [44 KiB] Thumbnail [19 KiB] tex code 
Created on 14 January 2021.