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Measurement of $C P$ asymmetries in two-body $B_{(s)}^{0}$-meson decays to charged pions and kaons

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Abstract

The time-dependent $C P$ asymmetries in $B^0\to\pi^+\pi^-$ and $B_s^0\to K^+ K^-$ decays are measured using a data sample of $pp$ collisions corresponding to an integrated luminosity of 3.0 fb$^{-1}$, collected with the LHCb detector at centre-of-mass energies of 7 and 8 TeV. The same data sample is used to measure the time-integrated $C P$ asymmetries in $B^0\to K^+\pi^-$ and $B_s^0\to\pi^+ K^-$ decays. The results are $C_{\pi^+\pi^-} = -0.34 \pm 0.06 \pm 0.01$, $S_{\pi^+\pi^-} = -0.63 \pm 0.05 \pm 0.01$, $C_{K^+ K^-} = 0.20 \pm 0.06 \pm 0.02$, $S_{K^+ K^-} = 0.18 \pm 0.06 \pm 0.02$, $C_{K^+ K^-}^{\Delta\Gamma} = -0.79 \pm 0.07 \pm 0.10$, $A_{C P}^{B^0} = -0.084 \pm 0.004 \pm 0.003$, and $A_{C P}^{B_s^0} = 0.213 \pm 0.015 \pm 0.007$, where the first uncertainties are statistical and the second systematic. Evidence for $C P$ violation is found in the $B_s^0\to K^+ K^-$ decay for the first time.

Figures and captions

Efficiencies as a function of decay time for (top left) $ B ^0 \rightarrow K ^+ \pi ^- $ , (top right) $ B ^0_ s \rightarrow \pi ^+ K ^- $ , (bottom left) $ B ^0 \rightarrow \pi ^+ \pi ^- $ and (bottom right) $ B ^0_ s \rightarrow K ^+ K ^- $ decays. The black line is the result of the best fit of Eq. 13 to the histograms, obtained as described in the text. The dark and bright areas correspond to the 68% and 95% confidence intervals, respectively.

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The triangles represent the standard deviation of the difference between the reconstructed ($t$) and true decay ($t_{\rm true}$) time versus $\delta_t$ for simulated (left) $ B ^0_ s \rightarrow \pi ^+ K ^- $ and (right) $ B ^0_ s \rightarrow D ^-_ s \pi ^+ $ decays. The dotted lines are the results of linear-function fits. The histograms represent the corresponding $\delta_t$ distributions with arbitrary normalisations.

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Time-dependent asymmetries of (left) $ B ^0 \rightarrow D ^- \pi ^+ $ and (right) $ B ^0_ s \rightarrow D ^-_ s \pi ^+ $ decays obtained from data. The results of the best fits are superimposed. The time-dependent asymmetry of the $ B ^0_ s \rightarrow D ^-_ s \pi ^+ $ decays is folded into one mixing period $2\pi/\Delta m_{ s } $ of the $ B ^0_ s $ meson. The parameter $t_0 = 0.3 {\mathrm{ ps}} $ corresponds to the minimum value allowed by the selection.

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Distributions of (top left) invariant mass, (top right) decay time, (middle left) decay-time uncertainty, (middle right) $\eta_{\rm OS}$, and (bottom) $\eta_{\rm SSc}$ for candidates in the $ K ^\pm$ $\pi ^\mp$ sample. The result of the simultaneous fit is overlaid. The individual components are also shown.

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Distributions of (top left) invariant mass, (top right) decay time, (middle left) decay-time uncertainty, (middle right) $\eta_{\rm OS}$, and (bottom) $\eta_{\rm SSc}$ for candidates in the $\pi ^+$ $\pi ^-$ sample. The result of the simultaneous fit is overlaid. The individual components are also shown.

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Distributions of (top left) invariant mass, (top right) decay time, (middle left) decay-time uncertainty, (middle right) $\eta_{\rm OS}$, and (bottom) $\eta_{{\rm SS} K }$ for candidates in the $ K ^+ K ^- $ sample. The result of the simultaneous fit is overlaid. The individual components are also shown.

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Time-dependent asymmetries for $ K ^\pm$ $\pi ^\mp$ candidates with invariant-mass values in the interval $5.20 < m < 5.32 {\mathrm{ Ge V /}c^2} $: (left) using the OS-tagging decision and (right) the SS-tagging decision. The result of the simultaneous fit is overlaid.

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Time-dependent asymmetries for (top) $\pi ^+$ $\pi ^-$ and (bottom) $ K ^+ K ^- $ candidates with mass values in the intervals $5.20 < m < 5.35 {\mathrm{ Ge V /}c^2} $ and $5.30 < m < 5.44 {\mathrm{ Ge V /}c^2} $, respectively: (left) using the OS-tagging decision and (right) using either the SSc-tagging decision (for the $\pi ^+$ $\pi ^-$ candidates) or the SS $ K $ -tagging decision (for the $ K ^+ K ^- $ candidates). The result of the simultaneous fit is overlaid.

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Relation between $\omega_{\rm tag}$ on $\eta_{\rm tag}$ for (top left) SS $\pi $ , (top right) SS $ p $ , (bottom left) SSc and (bottom right) SS $ K $ taggers. The black dots represent the average value of $\omega_{\rm tag}$ in bins of $\eta_{\rm tag}$, as described in the text. The black straight line represents the linear relation between $\omega_{\rm tag}$ and $\eta_{\rm tag}$ obtained from the calibration procedure. The darker and brighter areas are the corresponding 68% and 95% confidence intervals, respectively. The distributions of $\eta_{\rm tag}$ are also reported as histograms with arbitrary normalisations.

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Tables and captions

Current experimental knowledge on $ C_{\pi ^+ \pi ^- } $ , $ S_{\pi ^+ \pi ^- } $ , $ C_{ K ^+ K ^- } $ and $ S_{ K ^+ K ^- } $ . For the experimental measurements, the first uncertainties are statistical and the second systematic, whereas for the averages the uncertainties include both contributions. The correlation factors, denoted as $\rho$, are also reported.

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Current experimental knowledge on $A_{ C P }$ for $ B ^0 \rightarrow K ^+ \pi ^- $ and $ B ^0_ s \rightarrow \pi ^+ K ^- $ decays. For the experimental measurements, the first uncertainties are statistical and the second systematic, whereas for the averages the uncertainties include both contributions.

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Values of the parameters $\Delta m_{ d }$ , $\Delta m_{ s }$ , $\Gamma_{ d }$ , $\Gamma_{ s }$ and $\Delta\Gamma_{ s }$ [19], fixed to their central values in the fit to the data. For $\Gamma_{ s }$ and $\Delta\Gamma_{ s }$ the correlation factor between the two quantities is also reported. The decay width difference $\Delta\Gamma_{ d }$ is fixed to zero.

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Tagging powers for the $ B ^0 \rightarrow \pi ^+ \pi ^- $ and $ B ^0_ s \rightarrow K ^+ K ^- $ decays (last two rows), with a breakdown of the OS and SS contributions.

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Systematic uncertainties on the various $ C P$ -violating parameters. When present, the dash indicates that the uncertainty is not applicable to the given case.

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Statistical correlations among the $ C P$ -violating parameters.

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Values for the calibration parameters of the flavour tagging obtained from the fits. The values of $\hat{\eta}_{\rm OS}$ and $\hat{\eta}_{\rm SS}$ are fixed in the fit to $0.37$ and $0.44$, respectively.

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Calibration parameters for the SS $ K $ tagger.

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Created on 11 July 2020.