The interference between the K+K Swave and Pwave amplitudes in B_s > J/psi K+K decays with the K+K pairs in the region around the phi(1020) resonance is used to determine the variation of the difference of the strong phase between these amplitudes as a function of K+K invariant mass. Combined with the results from our CP asymmetry measurements in B_s > J/psi phi decays, we conclude that the B_s mass eigenstate that is almost CP =+1 is lighter and decays faster than the mass eigenstate that is almost CP =1. This determines the sign of the decay width difference DeltaGamma_s == Gamma_L Gamma_H to be positive. Our result also resolves the ambiguity in the past measurements of the CP violating phase phi_s to be close to zero rather than pi. These conclusions are in agreement with the Standard Model expectations.
Invariant mass distribution for $ B ^0_s \rightarrow \mu ^+\mu ^ K^+K^$ candidates, with the mass of the $\mu^+\mu^$ pair constrained to the nominal $J/\psi$ mass. The result of the fit is shown with signal (dashed curve) and combinatorial background (dotted curve) components and their sum (solid curve). 
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Background subtracted $ K ^+ K ^ $ invariant mass distribution for $ B ^0_s \rightarrow { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} K ^+ K ^ $ candidates. The vertical dotted lines separate the four intervals. 
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Distribution of (a) $ K ^+ K ^ $ Swave signal events, and (b) $ K ^+ K ^ $ Pwave signal events, both in four invariant mass intervals. In (b), the distribution of simulated $ B ^0_s \rightarrow { J \mskip 3mu/\mskip 2mu\psi \mskip 2mu} \phi$ events in the four intervals assuming the same total number of Pwave events is also shown (dashed lines). Note the interference between the $ K ^+ K ^ $ Swave and Pwave amplitudes integrated over the angular variables has vanishing contribution in these distributions. 
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Measured phase differences between Swave and perpendicular Pwave amplitudes in four intervals of $m_{KK}$ for solution I (full blue circles) and solution II (full black squares). The asymmetric error bars correspond to $\Delta\ln L =0.5$ (solid lines) and $\Delta\ln L =2$ (dashdotted lines). 
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Animated gif made out of all figures. 
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Numbers of signal and background events in the $m_{J/\psi KK}$ range of 52005550 MeV and statistical power per signal event in four intervals of $m_{KK}$.\\ 
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Results from a simultaneous fit of the four intervals of $m_{KK}$, where the uncertainties are statistical only. Only parameters which are needed for the ambiguity resolution are shown.\\ 
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Created on 21 October 2019.