Perturbative approach to the penguin-induced $B \to πϕ$

Using a modified perturbative approach that includes the Sudakov resummation and transverse degrees of freedom we analyze the penguin-induced $B^{-} \to π^{-}ϕ$ decay by applying the next-to-leading order effective weak Hamiltonian. The modified perturbative method enables us to include nonfactorizable contributions and to control virtual momenta appearing in the process. Besides, we apply the three-scale factorization theorem for nonleptonic processes that offers the possibility of having the scale-independent product of short- and long-distance parts in the amplitude of the weak Hamiltonian. The calculation supports the results obtained in the BSW factorization approach, illustrating the electroweak penguin dominance and the branching ratio of order ${\cal O}(10^{-8})$. However, the estimated prediction of 16% for the CP asymmetry is much larger than that obtained in the factorization approach.

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