Abstract
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 ΛQCD for the non-radiative matrix elements leftlangle {M}_1{M}_2left|{Q}_iright|overline{B}rightrangle of the current-current operators from the effective weak interactions. The rates of the branching fractions for the infrared-finite observables overline{B}to {M}_1{M}_2left(gamma right) with photons of maximal energy ∆E ≪ ΛQCD 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 πK ratios and sum rules that are often used as diagnostics of New Physics.
Highlights
Weak interactions below the electroweak scale in terms of B → M1 transition form factors, light-cone distribution amplitudes (LCDAs) of the B meson and final mesons M1,2, and their convolution with short-distance kernels
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
We considered the soft-inclusive decay rates Γ[B → M1M2] U (M1M2) + Xs] EXs≤∆E, where the final state Xs consists of photons and possibly electron-positron pairs with total energy less than ∆E ΛQCD in the B-meson rest frame
Summary
The “right” insertion, where the “emitted meson” M2 carries flavour (Du) and is formed from the [Du] quark bilinear in Q1,2 with spinor indices contracted in the bracket This contributes to the colour-allowed tree-amplitude α1(M1M2).. Process-dependent B → M1 transition “form factor” FQB2M1(0) that knows about the electric charge and direction of flight of M2 This generalized SCETI B → M1 form factor will contain soft spectator-scattering contributions, which would otherwise result in endpointsingular convolution integrals. We derive the factorization formulas within the framework of SCET [16,17,18,19] This can be done in a two-step matching procedure QCD×QED → SCETI → SCETII (see [20] for a review of this approach for QCD factorization of nonleptonic decays).
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