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

Abstract

We study the pure penguin decays $B\to \varphi \pi$ and $B^0\to \varphi \varphi$. Using QCD factorization, we find $\mathcal{B}(B^{\pm }\to \varphi {\pi }^{\pm })=2.0_{-0.1}^{+0.3}\times 10^{-8}$. For the pure penguin annihilation process $B^0\to \varphi \varphi$, analyzed here for the first time, $\mathcal{B}(B^0\to \varphi \varphi )=2.1_{-0.3}^{+1.6}\times 10^{-9}$. 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, $|\lambda {{}^{\prime \prime }}_{i23}\lambda {{}^{\prime \prime }}_{i21}|<6\times 10^{-5}$, $|{\lambda }_{i23}^{\prime }{\lambda }_{i21}^{\prime }|<4\times 10^{-4}$ and $|{\lambda }_{i32}^{\prime }{\lambda }_{i12}^{\prime }|<4\times 10^{-4}$ for $i=1,2,3$. Our new bounds on $|\lambda {{}^{\prime \prime }}_{i23}\lambda {{}^{\prime \prime }}_{i21}|$ are one order of magnitude stronger than before. Within the available upper bounds for $|\lambda {{}^{\prime \prime }}_{i23}\lambda {{}^{\prime \prime }}_{i21}|$, $|{\lambda }_{i23}^{\prime }{\lambda }_{i21}^{\prime }|$ and $|{\lambda }_{i32}^{\prime }{\lambda }_{i12}^{\prime }|$, we find that $\mathcal{B}(B\to \varphi \varphi )$ could be enhanced to $10^{-8}\sim 10^{-7}$. Experimental searches for these decays are strongly urged.

5 pages, 3 figures embeded

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