# Measurement of $C P$ observables in $B^\pm \rightarrow D K^\pm$ and $B^\pm \rightarrow D \pi^\pm$ with two- and four-body $D$ decays

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## Abstract

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 \CP-violating effects are reported and together these measurements provide important input for the determination of the unitarity triangle angle $\gamma$. The analysis of the four-pion $D$ decay mode is the first of its kind.

## Figures and captions

 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 (hatched-area) 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 [362 KiB] Thumbnail [203 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 cross-feed 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 [395 KiB] Thumbnail [228 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 [386 KiB] Thumbnail [209 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 [403 KiB] Thumbnail [221 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 [365 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 [409 KiB] Thumbnail [243 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 [386 KiB] Thumbnail [219 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, two-body $D$ decay on the left and four-body on the right. The last three rows show $B ^- \rightarrow D\pi ^-$ observables. Fig8a.eps [13 KiB] HiDef png [256 KiB] Thumbnail [211 KiB] *.C file Fig8b.eps [13 KiB] HiDef png [220 KiB] Thumbnail [179 KiB] *.C file Fig8c.eps [9 KiB] HiDef png [164 KiB] Thumbnail [137 KiB] *.C file Fig8d.eps [9 KiB] HiDef png [141 KiB] Thumbnail [119 KiB] *.C file Animated gif made out of all figures. PAPER-2016-003.gif Thumbnail

## Tables and captions

 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 [218 KiB] Thumbnail [107 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 [25 KiB] Thumbnail [10 KiB] tex code Statistical correlation matrix from for the 2-body fit. Table_4.pdf [33 KiB] HiDef png [63 KiB] Thumbnail [28 KiB] tex code Statistical correlation matrix from for the 4-body fit. Table_5.pdf [34 KiB] HiDef png [53 KiB] Thumbnail [23 KiB] tex code Correlation matrix for the systematic uncertainties in the 2-body analysis. Table_6.pdf [34 KiB] HiDef png [61 KiB] Thumbnail [28 KiB] tex code Correlation matrix for the systematic uncertainties in the 4-body analysis. Table_7.pdf [34 KiB] HiDef png [53 KiB] Thumbnail [24 KiB] tex code

## Supplementary Material [file]

 Fig10a.pdf [28 KiB] HiDef png [540 KiB] Thumbnail [318 KiB] *C file Fig10b.pdf [28 KiB] HiDef png [566 KiB] Thumbnail [327 KiB] *C file Fig11a.pdf [27 KiB] HiDef png [522 KiB] Thumbnail [311 KiB] *C file Fig11b.pdf [27 KiB] HiDef png [614 KiB] Thumbnail [357 KiB] *C file Fig12a.pdf [29 KiB] HiDef png [572 KiB] Thumbnail [331 KiB] *C file Fig9a.pdf [26 KiB] HiDef png [499 KiB] Thumbnail [298 KiB] *C file Fig9b.pdf [28 KiB] HiDef png [522 KiB] Thumbnail [326 KiB] *C file

Created on 21 October 2019.