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Determination of the sign of the decay width difference in the $B^0_s$ system

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Abstract

The interference between the K+K- S-wave and P-wave 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.

Figures and captions

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 ^- $ S-wave signal events, and (b) $ K ^+ K ^- $ P-wave 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 P-wave events is also shown (dashed lines). Note the interference between the $ K ^+ K ^- $ S-wave and P-wave amplitudes integrated over the angular variables has vanishing contribution in these distributions.

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Measured phase differences between S-wave and perpendicular P-wave 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 $\Delta\ln L =-2$ (dash-dotted lines).

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Animated gif made out of all figures.

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Tables and captions

Numbers of signal and background events in the $m_{J/\psi KK}$ range of 5200--5550 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 09 December 2018.Citation count from INSPIRE on 18 December 2018.