Lifetime difference measurements of the $B_s$ meson at CDF

Using a data sample of 1 fb$^{-1}$ collected by the displaced
track trigger of the CDF Run II detector, produced in $p\bar{p}$ 
collisions at $\sqrt{s} = 1.96$ TeV, we present the first measurements of
the lifetimes of the $B_s$ and $B_d$ mesons in two-body charmless decays
$B_s \rightarrow K^+ K^-$, $B_d \rightarrow K^+ \pi^-$ and $B_d \rightarrow \pi^+ \pi^-$. 
Using our result of $\tau(B_s \rightarrow K^+ K^-)$ and the latest average of the 
$B_s$ lifetime in flavor specific decays, we determine
$\Delta\Gamma_{CP}/\Gamma_{CP}(B_s \rightarrow K^+ K^-)$. In addition, using a di-muon
triggered sample we update our earlier measurement of
$\Delta\Gamma_s/\Gamma_s$ in $B_s \rightarrow J/\psi \phi$ CP-mixed decays. This
involves extraction of lifetimes and polarization amplitudes from an
angular analysis of these decays.