Revisiting B->phi pi Decays in the Standard Model

TL;DR

This paper re-examines the rare B to phi pi decay within the Standard Model, accounting for various corrections, and predicts branching ratios that could help distinguish between Standard Model effects and new physics in future experiments.

Contribution

It provides a detailed Standard Model prediction for B to phi pi decay rates, including radiative, long-distance, and mixing effects, clarifying the potential for new physics signals.

Findings

Branching ratio for B±→φπ± is approximately 3.2×10⁻⁸.

Branching ratio for B⁰→φπ⁰ is approximately 6.8×10⁻⁹.

Predicted direct CP asymmetries are around -8% and -6% for charged and neutral channels.

Abstract

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.