QED factorization of non-leptonic B decays

We show that the QCD factorization approach for B-meson decays to charmless hadronic two-body final states can be extended to include electromagnetic corrections. The presence of electrically charged final-state particles complicates the framework. Nevertheless, the factorization formula takes the same form as in QCD alone, with appropriate generalizations of the definitions of light-cone distribution amplitudes and form factors to include QED effects. More precisely, we factorize QED effects above the strong interaction scale Lambda (QCD) for the non-radiative matrix elements M1M2QiB of the current-current operators from the effective weak interactions. The rates of the branching fractions for the infrared-finite observables B-> M1M2gamma with photons of maximal energy E << Lambda (QCD) is then obtained by multiplying with the soft-photon exponentiation factors. We provide first estimates for the various electromagnetic corrections, and in particular quantify their impact on the pi K ratios and sum rules that are often used as diagnostics of New Physics.