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Measurement of $CP$ violation and the $B_s^0$ meson decay width difference with $B_s^0 \to J/\psi K^+K^-$ and $B_s^0\to J/\psi\pi^+\pi^-$ decays

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Abstract

The time-dependent CP asymmetry in B_s^0\to J/\psi K^+K^- decays is measured using $pp$ collision data at \sqrt{s}=7TeV, corresponding to an integrated luminosity of 1.0fb^-1, collected with the LHCb detector. The decay time distribution is characterised by the decay widths \Gamma_L and \Gamma_H of the light and heavy mass eigenstates of the B_s^0--\bar{B}_s^0 system and by a CP-violating phase \phi_s. In a sample of 27 617 B_s^0\to J/\psi K^+K^- decays, where the dominant contribution comes from B_s^0\to J/\psi\phi decays, these parameters are measured to be \phi_s = 0.07 \pm 0.09 (stat) \pm 0.01 (syst) rad, \Gamma_s \equiv (\Gamma_L+\Gamma_H)/2 = 0.663 \pm 0.005 (stat) \pm 0.006 (syst) ps^-1, \Delta\Gamma_s \equiv \Gamma_L -\Gamma_H = 0.100 \pm 0.016 (stat) \pm 0.003 (syst) & ps^-1, corresponding to the single most precise determination of \phi_s, \Delta\Gamma_s and \Gamma_s. The result of performing a combined analysis with B_s^{0} \to J/\psi \pi^+\pi^- decays gives \phi_s = 0.01 \pm 0.07 (stat) \pm 0.01 (syst) rad, \Gamma_s = 0.661 \pm 0.004 (stat) \pm 0.006 (syst) ps^-1, \Delta\Gamma_s = 0.106 \pm 0.011 (stat) \pm 0.007 (syst) & ps^-1. All measurements are in agreement with the Standard Model predictions.

Figures and captions

Feynman diagrams for $ B ^0_ s $ -- $\overline{ B }{} ^0_ s $ mixing, within the SM.

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box_diagram.pdf

Feynman diagrams contributing to the decay $ B ^0_ s \rightarrow J/\psi h^{+}h^{-}$ within the SM, where $h = \pi, K$.

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tree_penguin.pdf

Definition of helicity angles as discussed in the text.

helAng[..].pdf [27 KiB]
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helAngles_compiled.pdf

Invariant mass distribution of the selected $ B ^0_ s \rightarrow J\!/\!\psi K^{+}K^{-}$ candidates. The mass of the $\mu^{+}\mu^{-}$ pair is constrained to the $ J\!/\!\psi$ mass [8]. Curves for the fitted contributions from signal (dotted red), background (dotted green) and their combination (solid blue) are overlaid.

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BMassLin.pdf

Background subtracted invariant mass distributions of the (a) $\mu^{+}\mu^{-}$ and (b) $K^{+}K^{-}$ systems in the selected sample of $ B ^0_ s \rightarrow J\!/\!\psi K^{+}K^{-}$ candidates. The solid blue line represents the fit to the data points described in the text.

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mumuMassLin.pdf
KKMassLin.pdf [9 KiB]
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KKMassLin.pdf

Decay time resolution, $\sigma_{t}$, for selected $ B ^0_ s \rightarrow J\!/\!\psi K^{+}K^{-}$ signal events. The curve shows a fit to the data of the sum of two gamma distributions with a common mean.

Bs2Jps[..].pdf [17 KiB]
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Bs2JpsiKK_sigmat_signal_only.pdf

Decay time distribution of prompt $ { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} K ^+ K ^- $ candidates. The curve (solid blue) is the decay time model convolved with a Gaussian resolution model. The decay time model consists of a delta function for the prompt component and two exponential functions with different decay constants, which represent the $ B ^0_ s \rightarrow J\!/\!\psi K^{+}K^{-}$ signal and long-lived background, respectively. The decay constants are determined from the fit. The same dataset is shown in both plots, on different scales.

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$ B ^0_ s $ decay time trigger-acceptance functions obtained from data. The unbiased trigger category is shown on (a) an absolute scale and (b) the biased trigger category on an arbitrary scale.

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Bs_HltPropertimeAcceptance_PhiMassWindow30MeV_NextBestPVCut_Data_40bins_AlmostUnbiased.pdf
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Bs_HltPropertimeAcceptance_PhiMassWindow30MeV_NextBestPVCut_Data_40bins_ExclusivelyBiased.pdf

Angular acceptance function evaluated with simulated $ B ^0_ s \!\rightarrow J\!/\!\psi\phi$ events, scaled by the mean acceptance. The acceptance is shown as a function of (a) $\cos\theta_{K} $, (b) $\cos\theta_{\mu} $ and (c) $\varphi_{h} $, where in all cases the acceptance is integrated over the other two angles. The points are obtained by summing the inverse values of the underlying physics PDF for simulated events and the curves represent a polynomial parameterisation of the acceptance.

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Average measured wrong-tag probability ($\omega$) versus estimated wrong-tag probability ($\eta$) calibrated on $ B ^+ \!\rightarrow { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} K ^+ $ signal events for the OS tagging combinations for the background subtracted events in the signal mass window. Points with errors are data, the red curve represents the result of the wrong-tag probability calibration, corresponding to the parameters of Table 3.

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calibrationOS.pdf

Distributions of the estimated wrong-tag probability, $\eta$, of the $ B ^0_ s \rightarrow J/\psi K^{+}K^{-}$ signal events obtained using the sPlot method on the $ J\!/\!\psi K^{+}K^{-}$ invariant mass distribution. Both the (a) OS-only and (b) SSK-only tagging categories are shown.

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eta_OS.pdf
eta_SSK.pdf [14 KiB]
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eta_SSK.pdf

Decay-time and helicity-angle distributions for $ B ^0_ s \rightarrow { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} K ^+ K ^- $ decays (data points) with the one-dimensional projections of the PDF at the maximal likelihood point. The solid blue line shows the total signal contribution, which is composed of $ C\!P$ -even (long-dashed red), $ C\!P$ -odd (short-dashed green) and S-wave (dotted-dashed purple) contributions.

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time_sFit.pdf
helcos[..].pdf [7 KiB]
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helcosthetaK_sFit.pdf
helphi[..].pdf [8 KiB]
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helphi_sFit.pdf

Two-dimensional profile likelihood in the ($\Delta\Gamma_{ s } $, $\phi_{ s } $) plane for the $ B ^0_ s \rightarrow { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} K ^+ K ^- $ dataset. Only the statistical uncertainty is included. The SM expectation of $\Delta\Gamma_{ s } =0.087 \pm 0.021 {\rm \,ps^{-1}} $ and $\phi_{ s } = -0.036 \pm 0.002\rm \,rad $ is shown as the black point with error bar [3,43].

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2DLLscan.pdf

Variation of $\delta_{\rm S}-\delta_\perp$ with $m( K ^+ K ^- )$ where the uncertainties are the quadrature sum of the statistical and systematic uncertainties in each bin. The decreasing phase trend (blue circles) corresponds to the physical solution with $\phi_{ s }$ close to zero and $\Delta\Gamma_{s}>0$. The ambiguous solution is also shown.

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SWavePhases.pdf

Profile likelihood for $\Delta m_{ s } $ from a fit where $\Delta m_{ s } $ is unconstrained.

LLscan[..].pdf [13 KiB]
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LLscan_deltaM_narrow.pdf

Background-subtracted (a) kaon and (b) muon momentum distributions for $B_{s}^{0}\rightarrow { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} K ^+ K ^- $ signal events in data compared to simulated $B_{s}^{0}\rightarrow { J \mskip -3mu/\mskip -2mu\psi \mskip 2mu} \phi$ signal events. The distributions are normalised to the same area. A larger deviation is visible for kaons.

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Animated gif made out of all figures.

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Tables and captions

Results for $\phi_{ s } $ and $\Delta\Gamma_{s}$ from different experiments. The first uncertainty is statistical and the second is systematic (apart from the D0 result, for which the uncertainties are combined). The CDF confidence level (CL) range quoted is that consistent with other experimental measurements of $\phi_{ s }$ .

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Table_1.pdf

Definition of angular and time-dependent functions.

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Table_2.pdf

Calibration parameters ($p_0$, $p_1$,$\langle\eta\rangle$ and $\Delta p_0$) corresponding to the OS and SSK taggers. The uncertainties are statistical and systematic, respectively, except for $\Delta p_0$ where they have been added in quadrature.

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Table_3.pdf

Bins of $m( K ^+ K ^- )$ used in the analysis and the $C_{\rm SP}$ correction factors for the S-wave interference term, assuming a uniform distribution of non-resonant $K^{+}K^{-}$ contribution and a non-relativistic Breit-Wigner shape for the decays via the $\phi$ resonance.

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Parameters of the common signal fit to the $m( J\!/\!\psi K^{+}K^{-})$ distribution in data.

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Table_5.pdf

Results of the maximum likelihood fit for the principal physics parameters. The first uncertainty is statistical and the second is systematic. The value of $\Delta m_{ s } $ was constrained to the measurement reported in Ref. [40]. The evaluation of the systematic uncertainties is described in Sect. 10.

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Correlation matrix for the principal physics parameters.

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Results of the maximum likelihood fit for the S-wave parameters, with asymmetric statistical and symmetric systematic uncertainties. The evaluation of the systematic uncertainties is described in Sect. 10.

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Statistical and systematic uncertainties.

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Statistical and systematic uncertainties for S-wave fractions in bins of $m(K^{+}K^{-})$.

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Statistical and systematic uncertainties for S-wave phases in bins of $m(K^{+}K^{-})$.

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Results of combined fit to the $B_s^0 \rightarrow J/\psi K^+K^-$ and $B_s^0 \rightarrow J/\psi \pi^+\pi^-$ datasets. The first uncertainty is statistical and the second is systematic.

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Correlation matrix for statistical uncertainties on combined results.

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Created on 09 December 2018.Citation count from INSPIRE on 18 December 2018.