# Observation of the suppressed ADS modes $B^\pm \to [\pi^\pm K^\mp \pi^+\pi^-]_D K^\pm$ and $B^\pm \to [\pi^\pm K^\mp \pi^+\pi^-]_D \pi^\pm$

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## Abstract

An analysis of $B^{\pm}\to DK^{\pm}$ and $B^{\pm}\to D\pi^{\pm}$ decays is presented where the $D$ meson is reconstructed in the four-body final state $K^{\pm}\pi^{\mp} \pi^+ \pi^-$. Using LHCb data corresponding to an integrated luminosity of $1.0{\rm fb}^{-1}$, first observations are made of the suppressed ADS modes $B^{\pm}\to [\pi^{\pm} K^{\mp}\pi^+\pi^-]_D K^{\pm}$ and $B^{\pm}\to [\pi^{\pm} K^{\mp} \pi^+\pi^- ]_D\pi^{\pm}$ with a significance of $5.1\sigma$ and greater than $10\sigma$, respectively. Measurements of CP asymmetries and CP-conserving ratios of partial widths from this family of decays are also performed. The magnitude of the ratio between the suppressed and favoured $B^{\pm}\to DK^{\pm}$ amplitudes is determined to be $r^K_B = 0.097 \pm{0.011}$.

## Figures and captions

 Invariant mass distributions of selected $B ^\pm \rightarrow [ K ^\pm \pi^{\mp}\pi ^+ \pi ^- ]_Dh^{\pm}$ candidates, separated by charge. The left plots are $B ^-$ candidates, $B ^+$ are on the right. In the top plots, the bachelor track passes the PID cut and the $B ^\pm$ candidates are reconstructed assigning this track the kaon mass. The remaining candidates are placed in the sample displayed on the bottom row and are reconstructed with a pion mass hypothesis. The dark (red) and light (green) curves represent the fitted $B ^\pm \rightarrow D K ^\pm$ and $B ^\pm \rightarrow D \pi ^\pm$ components, respectively. The shaded contribution indicates partially reconstructed decays and the total PDF includes the combinatorial component. canvas[..].pdf [25 KiB] HiDef png [269 KiB] Thumbnail [163 KiB] *.C file Invariant mass distributions of selected $B ^\pm \rightarrow [\pi ^\pm K^{\mp} \pi ^+ \pi ^- ]_Dh^{\pm}$ decays, separated by charge. See the caption of Fig. 1 for a full description. The dashed line here represents the partially reconstructed, but Cabibbo favoured, $B ^0_ s \rightarrow D K ^- \pi ^+$, and charge-conjugated, decays where the pion is not reconstructed. The favoured mode cross-feed is included in the fit, but is too small to be seen. canvas[..].pdf [23 KiB] HiDef png [304 KiB] Thumbnail [202 KiB] *.C file Charge-integrated invariant mass distributions of those candidates shown in Fig. 2 passing the $B ^\pm \rightarrow [\pi ^\pm K^{\mp} \pi ^+ \pi ^- ]_Dh^{\pm}$ selection. canvas[..].pdf [17 KiB] HiDef png [403 KiB] Thumbnail [276 KiB] *.C file Animated gif made out of all figures. PAPER-2012-055.gif Thumbnail

## Tables and captions

 Favoured ($[ K \pi \pi \pi]_{D} h$) and suppressed ($[ \pi K \pi \pi]_{D} h$) signal yields together with their corresponding statistical uncertainties. Table_1.pdf [47 KiB] HiDef png [60 KiB] Thumbnail [28 KiB] tex code Systematic uncertainties on the observables. Bachelor PID refers to the fixed efficiency for the bachelor track ${\rm DLL}_{K\pi}$ requirement determined using the $D ^{*\pm}$ calibration sample. PDFs refers to the variations of the fixed shapes in the mass fit. Simulation refers to the use of simulation to estimate relative efficiencies of the signal modes, and also includes the contribution from the uncertainty in the residual background from charmless $B$ decays. $A_{\rm instr.}$ quantifies the uncertainty on the production, interaction and detection asymmetries. Table_2.pdf [52 KiB] HiDef png [42 KiB] Thumbnail [20 KiB] tex code

Created on 06 March 2021.