# 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). Fig1.pdf [24 KiB] HiDef png [205 KiB] Thumbnail [171 KiB] *.C file 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. Fig2.pdf [14 KiB] HiDef png [127 KiB] Thumbnail [115 KiB] *.C file 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. Fig3a.pdf [13 KiB] HiDef png [101 KiB] Thumbnail [99 KiB] *.C file Fig3b.pdf [13 KiB] HiDef png [118 KiB] Thumbnail [112 KiB] *.C file 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). Fig4.pdf [14 KiB] HiDef png [110 KiB] Thumbnail [109 KiB] *.C file Animated gif made out of all figures. PAPER-2011-028.gif Thumbnail

## 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 $m_{KK}$.\\ Table_1.pdf [46 KiB] HiDef png [71 KiB] Thumbnail [35 KiB] tex code 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.\\ Table_2.pdf [54 KiB] HiDef png [191 KiB] Thumbnail [87 KiB] tex code

Created on 18 January 2020.