Revisiting B->phi pi Decays in the Standard Model

In the standard model (SM), we re-investigate the rare decay $B\to \phi\pi$, 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 $\omega$-$\phi$ 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 $\omega$-$\phi$ 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 $\theta= -(3.0\pm 1.0)^\circ$, we obtain the branching ratios of $B\to \phi\pi$ 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 $\omega$-$\phi$ 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 $(-8.0^{+0.9+1.5}_{-1.0-0.1})$ and $(-6.3^{-0.5+2.5}_{+0.7-2.5})$ for $B^\pm\to \phi \pi^\pm$ and $B^0 \to \phi \pi^0$, respectively.