Bd \to \pi^- K^{(*)+} and Bs \to \pi^+(\rho^+) K^- decays with QCD factorization and flavor symmetry

Understand

The QCD factorization (QCDF) method usually contains infrared divergences which introduce large model dependence to its predictions on charmless B decays.

• The amplitudes of charmless B decays can be decomposed into "tree" and "penguin" parts which are conventionally defined, not from the topology of the dominant diagrams, but through their associated CKM factors V_{ub}^* V_{uq} and V_{tb}^* V_{tq}, respectively, with q=d,s.
• We find that for B_{d,s} \to \pi^+ K^- decays, the "tree" amplitude can be well estimated in QCDF with small errors, as the endpoint singularities have been canceled to a large extent.
• With this as the only input from QCDF and combined with flavor symmetry, the branching ratio of B_s \to \pi^+ K^- are estimated to be significantly larger than the CDF measurement.