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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 $D \to K_\mathrm S^0 h^+ h^-$

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Abstract

A measurement of $CP$-violating observables is performed using the decays $B^\pm\to D K^\pm$ and $B^\pm\to D \pi^\pm$, where the $D$ meson is reconstructed in one of the self-conjugate three-body final states $K_{\mathrm S}\pi^+\pi^-$ and $K_{\mathrm S}K^+K^-$ (commonly denoted $K_{\mathrm S} h^+h^-$). 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. The observables are interpreted in terms of the CKM angle $\gamma$. Using a data sample corresponding to an integrated luminosity of $9 \text{fb}^{-1}$ collected in proton-proton collisions at centre-of-mass energies of $7$, $8$, and $13 \text{TeV}$ with the LHCb experiment, $\gamma$ is measured to be $\left(68.7^{+5.2}_{-5.1}\right)^\circ$. The hadronic parameters $r_B^{DK}$, $r_B^{D\pi}$, $\delta_B^{DK}$, and $\delta_B^{D\pi}$, which are the ratios and strong-phase differences of the suppressed and favoured $B^\pm$ decays, 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. The horizontal and vertical axes are interchanged between the $ B ^+ $ and $ B ^- $ decay plots to aid visualisation of the $ C P$ asymmetries between the two distributions.

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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}}$ candidate is long (downstream). A particle within square brackets in the legend denotes the particle that has not been reconstructed.

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pretty_fit_d2kspp_DD.pdf

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}}$ candidate is long (downstream). A particle within square brackets in the legend denotes the particle that has not been reconstructed.

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pretty_fit_d2kskk_DD.pdf

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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likelihood_plot_paper.pdf

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 vertical dashed line separates the $ K ^0_{\mathrm{S}} \pi ^+ \pi ^- $ and $ K ^0_{\mathrm{S}} K ^+ K ^- $ bins on the horizontal axis.

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Confidence limits for the CKM angle $\gamma$ obtained using the method described in Ref. [45].

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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. [45].

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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 region $m_B\in[5249, 5309]\text{ Me V /}c^2 $ as obtained in the fit. For the $ B ^\pm \rightarrow D K ^\pm $ candidates, the yield of the partially reconstructed background includes the contributions from $ B ^0_ s $ decays and misidentified partially reconstructed backgrounds.

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Overview of all sources of uncertainty, $\sigma$, on $ x_\pm^{ D K }$ , $ y_\pm^{ D K }$ , $ x_\xi^{ D \pi}$ , and $ y_\xi^{ D \pi}$ . All uncertainties are quoted $\times 10^{-2}$.

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Statistical uncertainties, $\sigma$, and correlation matrix for $ x_\pm^{ D K }$ , $ y_\pm^{ D K }$ , $ x_\xi^{ D \pi}$ , and $ y_\xi^{ D \pi}$ .

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Total LHCb -related systematic uncertainties, $\sigma$, for $ x_\pm^{ D K }$ , $ y_\pm^{ D K }$ , $ x_\xi^{ D \pi}$ , and $ y_\xi^{ D \pi}$ , and the corresponding correlation matrix.

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Systematic uncertainties, $\sigma$, for $ x_\pm^{ D K }$ , $ y_\pm^{ D K }$ , $ x_\xi^{ D \pi}$ , and $ y_\xi^{ D \pi}$ due to strong-phase inputs, the corresponding correlation matrix.

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Supplementary Material [file]

Supplementary material full pdf

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Created on 05 March 2021.