Revisiting B->phi pi Decays in the Standard Model

In the standard model (SM), we re-investigate the rare decay $B\to \varphi \pi$, which has been viewed as an ideal probe to detect the new physics signals beyond the SM. Contributions in the naive factorization method, the radiative corrections, the long-distance contributions, and the contributions due to the $\omega$-$\varphi$ mixing are taken into account. 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 $\gamma =(58.6\pm 10{)}^{\circ }$ and the mixing angle $\theta= -(3.0\pm 1.0)^\circ$,weobtainthebranchingratiosof$B\to \phi\pi$as$ {\rm Br}(B^\pm\to \phi \pi^\pm)= (3.2 ^{+0.8-1.2}{-0.7+1.8}) \times 10^{-8}$and$ {\rm Br}(B^0 \to \phi \pi^0) = (6.8 ^{+0.3-0.7}{-0.3+1.0}) \times 10^{-9}$. If the future experiment reports a branching ratio of order ${10}^{-7}$ for $B^-\to \phi \pi^-$ decay, it may not be a clear signal for any new physics scenario. In order to discriminate the large new physics contributions and 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, and the results are about $(-8.0_{-1.0-0.1}^{+0.9+1.5})$ 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.