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Measurement of the CKM angle $\gamma$ in $B^\pm\to D K^\pm$ and $B^\pm \to D \pi^\pm$ decays with $D \to K_\mathrm S^0 h^\pm h^\mp$

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Abstract

A measurement of $ C P$ -violating observables is performed using the decays $ B ^\pm \rightarrow D K ^\pm $ and $ B ^\pm \rightarrow D \pi ^\pm $ , where the $ D $ meson is reconstructed in one of the self-conjugate three-body final states $ K ^0_{\mathrm{S}} \pi ^+ \pi ^- $ and $ K ^0_{\mathrm{S}} K ^+ K ^- $ ($h^\pm h^\mp = \pi ^\pm \pi ^\mp , K ^\pm K ^\mp $). The decays are analysed in bins of the $ D $ -decay phase space, leading to a measurement that is independent of the modelling of the $ D $ -decay amplitude. Using the full Run 1 and 2 LHCb data sample, the observables of interest are measured to be \begin{align*} x_-^{ D K } & = (\phantom{-}5.6 \pm 1.0 \pm 0.2\pm 0.3) \times 10^{-2}, \\ y_-^{ D K } & = (\phantom{-}6.5\pm 1.1 \pm 0.3\pm 0.4) \times 10^{-2}, \\ x_+^{ D K } & = ( - 9.2 \pm 1.0 \pm 0.2\pm 0.2) \times 10^{-2}, \\ y_+^{ D K } & = ( - 1.2 \pm 1.2 \pm 0.3\pm 0.3) \times 10^{-2}, \\ x_\xi^{ D \pi} & = ( - 5.3 \pm 2.0 \pm 0.3\pm 0.2) \times 10^{-2}, \\ y_\xi^{ D \pi} & = (\phantom{-}1.0 \pm 2.3 \pm 0.5\pm 0.3) \times 10^{-2}, \end{align*} where the first uncertainty is statistical, the second arises from systematic effects in the method or other experimental effects, and the third from external inputs of strong-phase measurements from CLEO and BESIII . The measurements can be interpreted in terms of the CKM angle $\gamma$, leading to $\gamma =(69 \pm 5)^\circ$. Measurements of the hadronic parameters $ r_ B ^{ D K }$ , $ r_ B ^{ D \pi}$ , $\delta_ B ^{ D K }$ , and $\delta_ B ^{ D \pi}$ are also reported.

Figures and captions

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.

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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.

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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.

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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.

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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

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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.

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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].

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Animated gif made out of all figures.

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Tables and captions

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.

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Table_1.pdf

Overview of all sources of uncertainty on the measurement.

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Created on 06 March 2021.