$B\to \varphi \pi$ and $B^0\to \varphi \varphi$ in the Standard Model and new bounds on R parity violation

We study the pure penguin decays $B\to \varphi \pi$ and $B^0\to \varphi \varphi$. Using QCD factorization, we find ${\cal B}(B^\pm \to\phi\pi^{\pm} )=2.0^{+0.3}{-0.1}\times 10^{-8}$\mathrm{.}Forthepurepenguinannihilationprocess$B^0 \to \phi\phi$,analyzedhereforthefirsttime,${\cal B}(B^0 \to\phi\phi)=2.1^{+1.6}{-0.3}\times 10^{-9}$. The smallness of these decays in the Standard Model makes them sensitive probes for new physics. From the upper limit of $B\to \varphi \pi$,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$i=1,2,3$\mathrm{.}Ournewboundson$|\lambda{‘’}{i23}\lambda{‘’}{i21}|$ are one order of magnitude stronger than before. Within the available upper bounds for $| \lambda{‘’}{i23}\lambda{‘’}{i21}|$,$|\lambda’{i23}\lambda’{i21}|$and$|\lambda’{i32}\lambda’{i12}|$,wefindthat${\cal B}(B\to\phi\phi)$ could be enhanced to ${10}^{-8}\sim {10}^{-7}$. Experimental searches for these decays are strongly urged.