The timedependent 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 CPviolating 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.
Feynman diagrams for $ B ^0_ s $  $\overline{ B }{} ^0_ s $ mixing, within the SM. 
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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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Definition of helicity angles as discussed in the text. 
helAng[..].pdf [27 KiB] HiDef png [22 KiB] Thumbnail [10 KiB] *.C file 

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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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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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. 
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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 longlived 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 triggeracceptance 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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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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angEff[..].pdf [6 KiB] HiDef png [130 KiB] Thumbnail [111 KiB] *.C file 

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Average measured wrongtag probability ($\omega$) versus estimated wrongtag 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 wrongtag probability calibration, corresponding to the parameters of Table 3. 
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Distributions of the estimated wrongtag 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) OSonly and (b) SSKonly tagging categories are shown. 
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Decaytime and helicityangle distributions for $ B ^0_ s \rightarrow { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} K ^+ K ^ $ decays (data points) with the onedimensional 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 (longdashed red), $ C P$ odd (shortdashed green) and Swave (dotteddashed purple) contributions. 
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helcos[..].pdf [7 KiB] HiDef png [188 KiB] Thumbnail [143 KiB] *.C file 

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Twodimensional 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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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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Profile likelihood for $\Delta m_{ s } $ from a fit where $\Delta m_{ s } $ is unconstrained. 
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Backgroundsubtracted (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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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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Definition of angular and timedependent functions. 
Table_2.pdf [60 KiB] HiDef png [74 KiB] Thumbnail [33 KiB] tex code 

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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Bins of $m( K ^+ K ^ )$ used in the analysis and the $C_{\rm SP}$ correction factors for the Swave interference term, assuming a uniform distribution of nonresonant $K^{+}K^{}$ contribution and a nonrelativistic BreitWigner 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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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 Swave 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 Swave fractions in bins of $m(K^{+}K^{})$. 
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Statistical and systematic uncertainties for Swave 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. 
Table_13.pdf [49 KiB] HiDef png [47 KiB] Thumbnail [24 KiB] tex code 
Created on 06 March 2021.