In the standard model, we reinvestigate the rare decay $B\to \varphi \pi$, which is viewed as an ideal probe to detect the new physics signals. We find that the tiny branching ratio in the naive factorization can be dramatically enhanced by the radiative corrections and the $\omega -\varphi$ mixing effect, while the long-distance contributions are negligibly small. Assuming the Cabibbo-Kobayashi-Maskawa angle $\gamma =(58.6\pm 10)°$ and the mixing angle $\theta =-(3.0\pm 1.0)°$, we obtain the branching ratios of $B\to \varphi \pi$ as $\mathrm{Br}(B^{\pm }\to \varphi {\pi }^{\pm })=({3.2}_{-0.7+1.8}^{+0.8-1.2})\times {10}^{-8}$ and $\mathrm{Br}(B^0\to \varphi {\pi }^0)=({6.8}_{-0.3+1.0}^{+0.3-0.7})\times {10}^{-9}$. If the future experiment reports a branching ratio of $(0.2–0.5)\times {10}^{-7}$ for $B^{-}\to \varphi {\pi }^{-}$ decay, it may not be a clear signal for any new physics scenario. In order to discriminate the large new physics contributions from those due to the $\omega -\varphi$ mixing, we propose to measure the ratio of branching fractions of the charged and neutral $B$ decay channel. We also study the direct $CP$ asymmetries of these two channels: $(-{8.0}_{-1.0-0.1}^{+0.9+1.5})\%$ and $(-{6.3}_{+0.7-2.5}^{-0.5+2.5})\%$ for $B^{\pm }\to \varphi {\pi }^{\pm }$ and $B^0\to \varphi {\pi }^0$, respectively. These asymmetries are dominated by the mixing effect.

• Received 13 May 2009

DOI:https://doi.org/10.1103/PhysRevD.80.014024