A Measurement of the $B^0_s \to K^+K^-$ Lifetime at the LHCb Experiment

The LHCb experiment was constructed to search for new physical phenomena not predicted by the Standard Model of particle physics in high energy proton-proton collisions at the Large Hadron Collider (LHC). In 2010 LHCb accumulated an integrated luminosity of 37.66 pb$^{-1}$ at a centre-of-mass energy of 7 TeV. The $B^0_s \to K^+K^-$ decay mode is sensitive to the existence of beyond the Standard Model physics and the presence of such new physics may be detected through a precise measurement of its mean lifetime. The effective $B^0_s \to K^+K^-$ lifetime $\tau_{K^{+}K^{-}}$ is measured relative to the $B^0 \to K^{+}\pi^{-}$ lifetime $\tau_{B \to K_\pi}$ in order to control the effect of proper time bias due to selection acceptance. The difference of inverse lifetimes $\Delta\Gamma_{K^{+}K^{-}} \equiv$ 1/$\tau_{K^{+}K^{-}} - 1/\tau_{B\to K\pi}$ is measured as $\Delta\Gamma_ {K^{+}K^{-}} $ = 0.013 $\pm$ 0.045(stat)$\pm$ 0.005(syst) $\pm$ 0.001(model) ps$^{-1}$. Using the world average of the mean $B^0$ lifetime the effective $B^0_s \to K^+K^-$ lifetime is measured as $\tau_{K^{+}K^{-}} $ = 1.490$\pm$0.100(stat)$\pm$0.012(syst)$\pm$0.002(model)$\pm$0.007(input) ps, consistent with the Standard Model prediction. In addition, a Bayesian method to correct for proper time acceptance bias in relative lifetime measurements is presented and studies are performed using the decay modes $D^0 \to K^+K^-$ and $D^0 \to \pi^{+}K^{-}$. A study of the quantity $y_{CP}$, which is sensitive to new sources of CP violation in the $D^0$ system, is presented in the context of this acceptance correction method.