$B^0_s$ Meson Lifetime and $\Delta\Gamma_s$ in the $B^0_s\rightarrow K^+K^-$ Decay Mode

The measurement of the $B^0_s\rightarrow K^+K^-$ lifetime allows a determination of the decay width difference $\Delta\Gamma_s$ that is sensitive to possible new physics effects in penguin dominated $B_s^0$~decays. In Run\,II of the Fermilab Tevatron, the ability to trigger on hadronic decays, has allowed the CDF experiment to collect a large sample of $B^0_s\rightarrow K^+K^-$ events from $p\bar{p}$ collisions at $\sqrt{s}=1.96$~TeV. We report on the progress toward an updated measurement of the lifetime of $B^0_s$ mesons in this decay mode using a larger dataset than previous preliminary results.