  We study the pure penguin decays $B \to \phi\pi$ and $B^0 \to \phi\phi$.
Using QCD factorization, we find ${\cal B}(B^\pm \to\phi\pi^{\pm}
)=2.0^{+0.3}_{-0.1}\times 10^{-8}$. For the pure penguin annihilation process
$B^0 \to \phi\phi$, analyzed here for the first time, ${\cal B}(B^0
\to\phi\phi)=2.1^{+1.6}_{-0.3}\times 10^{-9}$. The smallness of these decays in
the Standard Model makes them sensitive probes for new physics. From the upper
limit of $B\to \phi\pi$,we find constraints on R parity violating couplings, $|
\lambda{''}_{i23}\lambda{''}_{i21}|<6\times10^{-5}$, $|
\lambda'_{i23}\lambda'_{i21}|<4\times10^{-4}$ and $|
\lambda'_{i32}\lambda'_{i12}|<4\times10^{-4}$ for $i=1,2,3$. Our new bounds on
$|\lambda{''}_{i23}\lambda{''}_{i21}|$ are one order of magnitude stronger than
before. Within the available upper bounds for $|
\lambda{''}_{i23}\lambda{''}_{i21}|$, $|\lambda'_{i23}\lambda'_{i21}|$ and
$|\lambda'_{i32}\lambda'_{i12}|$, we find that ${\cal B}(B\to\phi\phi)$ could
be enhanced to $10^{-8}\sim 10^{-7}$. Experimental searches for these decays
are strongly urged.
