Precision measurement of $CP$ violation in $B_s^0\to J/\ddot{I}ˆK^{+}{K}^{-}$ decays

Abstract

The time-dependent $CP$ asymmetry in $B_s^0\to J/\ddot{I}ˆK^{+}{K}^{-}$ decays is measured using $pp$ collision data, corresponding to an integrated luminosity of $3.0$fb${}^{-1}$, collected with the LHCb detector at centre-of-mass energies of $7$ and $8$TeV. In a sample of 96 000 $B_s^0\to J/\ddot{I}ˆK^{+}{K}^{-}$ decays, the $CP$-violating phase $\ddot{I}{•}_s$ is measured, as well as the decay widths $\hat{I}{“}_L$ and $\hat{I}{“}_H$ of the light and heavy mass eigenstates of the $B_s^0-{\bar{B}}_s^0$ system. The values obtained are $\ddot{I}{•}_s=-0.058\pm 0.049\pm 0.006$ rad, $\hat{I}{“}_s\equiv (\hat{I}{“}_L+\hat{I}{“}_H)/2=0.6603\pm 0.0027\pm 0.0015$ps${}^{-1}$, and$\hat{I}”\hat{I}{“}_s\equiv \hat{I}{“}_L-\hat{I}{“}_H=0.0805\pm 0.0091\pm 0.0032$ps${}^{-1}$, where the first uncertainty is statistical and the second systematic. These are the most precise single measurements of those quantities to date. A combined analysis with $B_s^0\to J/\ddot{I}ˆ\ddot{I}{€}^{+}\ddot{I}{€}^{-}$ decays gives $\ddot{I}{•}_s=-0.010\pm 0.039$rad. All measurements are in agreement with the Standard Model predictions. For the first time the phase $\ddot{I}{•}_s$ is measured independently for each polarisation state of the $K^{+}{K}^{-}$ system and shows no evidence for polarisation dependence.

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