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. 
box_di[..].pdf [40 KiB] HiDef png [36 KiB] Thumbnail [16 KiB] *.C file 

Feynman diagrams contributing to the decay $ B ^0_ s \rightarrow J/\psi h^{+}h^{}$ within the SM, where $h = \pi, K$. 
tree_p[..].pdf [17 KiB] HiDef png [67 KiB] Thumbnail [30 KiB] *.C file 

Definition of helicity angles as discussed in the text. 
helAng[..].pdf [27 KiB] HiDef png [29 KiB] Thumbnail [14 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. 
BMassLin.pdf [8 KiB] HiDef png [223 KiB] Thumbnail [175 KiB] *.C file 

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. 
mumuMa[..].pdf [9 KiB] HiDef png [165 KiB] Thumbnail [133 KiB] *.C file 

KKMassLin.pdf [9 KiB] HiDef png [160 KiB] Thumbnail [128 KiB] *.C file 

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] HiDef png [163 KiB] Thumbnail [124 KiB] *.C file 

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. 
presca[..].pdf [35 KiB] HiDef png [165 KiB] Thumbnail [137 KiB] *.C file 

presca[..].pdf [38 KiB] HiDef png [178 KiB] Thumbnail [149 KiB] *.C file 

$ 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. 
Bs_Hlt[..].pdf [22 KiB] HiDef png [86 KiB] Thumbnail [87 KiB] *.C file 

Bs_Hlt[..].pdf [23 KiB] HiDef png [102 KiB] Thumbnail [107 KiB] *.C file 

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. 
angEff[..].pdf [6 KiB] HiDef png [119 KiB] Thumbnail [104 KiB] *.C file 

angEff[..].pdf [6 KiB] HiDef png [131 KiB] Thumbnail [110 KiB] *.C file 

angEff[..].pdf [5 KiB] HiDef png [98 KiB] Thumbnail [96 KiB] *.C file 

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. 
calibr[..].pdf [15 KiB] HiDef png [127 KiB] Thumbnail [112 KiB] *.C file 

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. 
eta_OS.pdf [15 KiB] HiDef png [126 KiB] Thumbnail [135 KiB] *.C file 

eta_SSK.pdf [14 KiB] HiDef png [120 KiB] Thumbnail [123 KiB] *.C file 

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. 
time_sFit.pdf [11 KiB] HiDef png [199 KiB] Thumbnail [148 KiB] *.C file 

helcos[..].pdf [7 KiB] HiDef png [200 KiB] Thumbnail [144 KiB] *.C file 

helcos[..].pdf [7 KiB] HiDef png [200 KiB] Thumbnail [148 KiB] *.C file 

helphi[..].pdf [8 KiB] HiDef png [193 KiB] Thumbnail [143 KiB] *.C file 

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]. 
2DLLscan.pdf [16 KiB] HiDef png [448 KiB] Thumbnail [163 KiB] *.C file 

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. 
SWaveP[..].pdf [5 KiB] HiDef png [99 KiB] Thumbnail [84 KiB] *.C file 

Profile likelihood for $\Delta m_{ s } $ from a fit where $\Delta m_{ s } $ is unconstrained. 
LLscan[..].pdf [13 KiB] HiDef png [214 KiB] Thumbnail [119 KiB] *.C file 

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. 
pk_paper.pdf [15 KiB] HiDef png [223 KiB] Thumbnail [217 KiB] *.C file 

pmu_paper.pdf [16 KiB] HiDef png [207 KiB] Thumbnail [196 KiB] *.C file 

Animated gif made out of all figures. 
PAPER2013002.gif Thumbnail 
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 $\phi_{ s }$ . 
Table_1.pdf [55 KiB] HiDef png [63 KiB] Thumbnail [30 KiB] tex code 

Definition of angular and timedependent functions. 
Table_2.pdf [60 KiB] HiDef png [87 KiB] Thumbnail [41 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. 
Table_3.pdf [34 KiB] HiDef png [32 KiB] Thumbnail [15 KiB] tex code 

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. 
Table_4.pdf [36 KiB] HiDef png [117 KiB] Thumbnail [50 KiB] tex code 

Parameters of the common signal fit to the $m( J / \psi K^{+}K^{})$ distribution in data. 
Table_5.pdf [58 KiB] HiDef png [80 KiB] Thumbnail [35 KiB] tex code 

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. 
Table_6.pdf [52 KiB] HiDef png [59 KiB] Thumbnail [29 KiB] tex code 

Correlation matrix for the principal physics parameters. 
Table_7.pdf [49 KiB] HiDef png [61 KiB] Thumbnail [31 KiB] tex code 

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. 
Table_8.pdf [48 KiB] HiDef png [112 KiB] Thumbnail [60 KiB] tex code 

Statistical and systematic uncertainties. 
Table_9.pdf [57 KiB] HiDef png [123 KiB] Thumbnail [59 KiB] tex code 

Statistical and systematic uncertainties for Swave fractions in bins of $m(K^{+}K^{})$. 
Table_10.pdf [54 KiB] HiDef png [117 KiB] Thumbnail [55 KiB] tex code 

Statistical and systematic uncertainties for Swave phases in bins of $m(K^{+}K^{})$. 
Table_11.pdf [55 KiB] HiDef png [103 KiB] Thumbnail [45 KiB] tex code 

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. 
Table_12.pdf [51 KiB] HiDef png [154 KiB] Thumbnail [63 KiB] tex code 

Correlation matrix for statistical uncertainties on combined results. 
Table_13.pdf [49 KiB] HiDef png [59 KiB] Thumbnail [30 KiB] tex code 
Created on 18 January 2020.