Search for FCNC $B_{s(d)} \rightarrow \mu^+ \mu^-$ Decays at CDF

The flavor-changing neutral current decay $B_{s(d)}\rightarrow \mu^+ \mu^-$
is one of the most sensitive probes to physics beyond the
Standard Model. The predicted branching ratio in the
Standard Model is on the order of $10^{-9}$ ($10^{-10}$) for $B_s$ ($B_d$),
which is beyond the sensitivity of the current experiments.
However, in many extensions of the Standard Model, the
branching ratio is naturally enhanced by one to three orders
of magnitude and thus would be observable at the Tevatron.
In a previous study using 780 pb$^{-1}$ of data, the CDF experiment
has already obtained the most stringent limits in the world
for both $B_s$ and $B_d$ decays.  In this study we report on a newly
improved analysis to search for $B_{s(d)} \rightarrow \mu^+ \mu^-$ decays using
1 fb$^{-1}$ of data collected with the CDF II detector at the
Fermilab Tevatron.