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Observation of $CP$ violation in two-body $B_{(\mathrm{s})}^{ 0}$-meson decays to charged pions and kaons

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Abstract

The time-dependent $CP$ asymmetries of $B^0\to \pi^+\pi^-$ and $B^0_\mathrm{s} \to K^+K^-$ decays are measured using a data sample of $pp$ collisions corresponding to an integrated luminosity of 1.9 fb$^{-1}$, collected with the LHCb detector at a centre-of-mass energy of 13 TeV. The results are \begin{eqnarray*} C_{\pi\pi} & = & -0.311 \pm 0.045 \pm 0.015, \\ S_{\pi\pi} & = & -0.706 \pm 0.042 \pm 0.013, \\ C_{KK} & = & \phantom{-}0.164 \pm 0.034 \pm 0.014, \\ S_{KK} & = & \phantom{-}0.123 \pm 0.034 \pm 0.015, \\ \cal {A}^{\mathrm{\Delta\Gamma}}_{\mathit{KK}} & = & -0.83\phantom{0} \pm 0.05\phantom{0} \pm 0.09, \end{eqnarray*} where the first uncertainties are statistical and the second systematic. The same data sample is used to measure the time-integrated $CP$ asymmetries of $B^0\to K^+\pi^-$ and $B^0_\mathrm{s}\to K^-\pi^+$ decays and the results are \begin{eqnarray*} A_{CP}^{B^0} & = & -0.0824 \pm 0.0033 \pm 0.0033, \\ A_{CP}^{B^0_\mathrm{s}} & = & \phantom{-}0.236\phantom{0} \pm 0.013\phantom{0} \pm 0.011. \end{eqnarray*} All results are consistent with earlier measurements. A combination of LHCb measurements provides the first observation of time-dependent $CP$ violation in $B^0_\mathrm{s}$ decays.

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Dependence of the effective decay-time resolution, $\sigma_{\rm eff}$, on the estimated decay-time uncertainty, $\delta_t$, for the background-subtracted data sample of $ { J \mskip -3mu/\mskip -2mu\psi } \rightarrow \mu ^+ \mu ^- $ decays. The result of a linear fit is superimposed.

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Distributions of (top left) $ K ^\pm$ $\pi ^\mp$ invariant mass, (top right) $ B _{( s )}^0$ decay time, mistag fractions (bottom left) $\eta_{\rm OS}$ and (bottom right) $\eta_{\rm SSc}$ for $ K ^\pm$ $\pi ^\mp$ candidates. The result of the simultaneous fit is overlaid. The various components contributing to the fit model are drawn as stacked histograms.

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Distributions of (top left) $\pi ^+$ $\pi ^-$ invariant mass, (top right) $ B _{( s )}^0$ decay time, mistag fractions (bottom left) $\eta_{\rm OS}$ and (bottom) $\eta_{\rm SSc}$ for $\pi ^+$ $\pi ^-$ candidates. The result of the simultaneous fit is overlaid. The various components contributing to the fit model are drawn as stacked histograms.

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Distributions of (top left) $ K ^+ K ^- $ invariant mass, (top right) $ B _{( s )}^0$ decay time, mistag fractions (bottom left) $\eta_{\rm OS}$ and (bottom right) $\eta_{{\rm SS} K }$ for $ K ^+ K ^- $ candidates. The result of the simultaneous fit is overlaid. The various components contributing to the fit model are drawn as stacked histograms.

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Time-dependent asymmetries for $ K ^\pm$ $\pi ^\mp$ candidates with $5.20 < m( K ^\pm \pi ^\mp ) < 5.32\text{ Ge V /}c^2 $: (left) using the OS-tagging decision and (right) the SSc-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 $5.20 < m(\pi ^+ \pi ^- ) < 5.35\text{ Ge V /}c^2 $ and $5.30 < m( K ^+ K ^- ) < 5.44\text{ 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. The asymmetry for the $ K ^+ K ^- $ candidates is folded into one mixing period $2\pi/\Delta m_{ s } $ and the parameter $t_0 = 0.2\text{ ps} $ corresponds to the minimum value of the decay-time used in the fit.

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Distributions of the (top left) $\pi ^+$ $\pi ^-$ invariant mass, (top right) decay time for tagged $ B ^0$ mesons, (bottom left) decay time for untagged $ B ^0$ mesons and (bottom right) asymmetry for the $ B ^0 \rightarrow \pi ^+ \pi ^- $ decays. The individual components are shown for the invariant-mass spectrum while only tagged background-subtracted candidates are shown in the decay-time spectrum. The fit results to the different distributions are overlaid. The various components contributing to the invariant mass model are drawn as stacked histograms.

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Distributions of the $ K ^+$ $ K ^-$ invariant mass (top left), decay time for tagged $ B ^0_ s $ mesons (top right), decay time for untagged $ B ^0_ s $ candidates (bottom left) and asymmetry (bottom right) for the $ B ^0_ s \rightarrow K ^+ K ^- $ decays. The individual components are shown for the invariant mass spectrum while only background-subtracted candidates are shown in the decay time spectrum. The fit results to the different distributions are overlaid. The various components contributing to the invariant mass model are drawn as stacked histograms. The asymmetry for the $ K ^+ K ^- $ candidates is folded into one mixing period $2\pi/\Delta m_{ s } $ and the parameter $t_0 = 0.2\text{ ps} $ corresponds to the minimum value of the decay-time used in the fit.

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Two-dimensional 68% and 95% confidence-level regions for the measured $ C P$ -violating parameters of the $ B ^0 \rightarrow \pi ^+ \pi ^- $ (left) and $ B ^0_ s \rightarrow K ^+ K ^- $ (right) decays from the two methods. The simultaneous method is shown in purple while the per-candidate method in green. Previous measurements of these parameters are also shown, with the LHCb Run 1 result in blue, the Belle result in yellow and the BaBar result in red. The confidence-level regions are calculated using only the statistical uncertainties of all the measurements. The correlation is found to be approximately 84% for all $ C P$ -violating parameters between the simultaneous and per-event methods.

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Tables and captions

Values of the parameters $\Delta m_{ d }$ , $\Delta m_{ s }$ , $\Gamma_{ d }$ [25], $\Gamma_{ s }$ and $\Delta\Gamma_{ s }$ [60] used in the two methods. For $\Gamma_{ s }$ and $\Delta\Gamma_{ s }$ the correlation factor, $\rho$, between the two quantities is also reported. The decay width difference $\Delta\Gamma_{ d }$ is fixed to zero.

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Systematic uncertainties on the $C P$-violating parameters. The values given for each individual contribution to the systematic uncertainty are those for the simultaneous method. The total systematic uncertainties are given both for the simultaneous and the per-candidate methods. The dash indicates that the uncertainty is not applicable.

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Correlations of statistical uncertainties among the $ C P$ -violating parameters.

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Correlations of systematic uncertainties among the $ C P$ -violating parameters.

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Correlation matrix for the $ C P$ violation parameters obtained from the combination with Run-1 results.

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Created on 06 March 2021.