QED factorization of non-leptonic B decays

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 $$ \left\langle {M}_1{M}_2\left|{Q}_i\right|\overline{B}\right\rangle $$ M 1 M 2 Q i B ¯ of the current-current operators from the effective weak interactions. The rates of the branching fractions for the infrared-finite observables $$ \overline{B}\to {M}_1{M}_2\left(\gamma \right) $$ B ¯ → M 1 M 2 γ 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.

QED corrections in $$ \overline{B}\to \overline{K}{\mathrm{\ell}}^{+}{\mathrm{\ell}}^{-} $$ at the double-differential level

“…An example of which is provided by B s → µ + µ − , where it was found that the chirality suppression of the non radiative decay m µ /m b is lifted to m µ /Λ QCD ("enhanced power corrections") when QED corrections are taken into account [33]. These authors develop QED corrections to B decays within the soft collinear effective theory (SCET) framework, recently extended to B → Kπ [34]. It allows for the resummation of different types of logarithms [35] Another approach is lattice QCD, where the precision in Kaon physics per se demands the inclusion of QED corrections [36,37] with first results in leptonic decays [38][39][40].…”

Light-cone distribution amplitudes of light mesons with QED effects

“…The study of QED effects in B-meson decays has become an active field of research in recent years [1][2][3][4][5][6][7], as such effects will become increasingly more important when higher experimental precision is reached. The standard treatment of QED effects assumes the mesons to be point-like to very small distances of order 1/m B .…”

“…This allows for a clear separation of very lowenergetic photons with a point-like coupling to mesons from photons with energy of order Λ QCD up to m B , at which scale one can use the 1/m B expansion. First studies following this path were made in [1][2][3][4]. In particular, in [3] we have shown that the QCD factorization formula [8,9] for non-leptonic charmless B decays into two light mesons, B → M 1 M 2 , can be extended to include QED corrections to all orders in α em .…”

“…First studies following this path were made in [1][2][3][4]. In particular, in [3] we have shown that the QCD factorization formula [8,9] for non-leptonic charmless B decays into two light mesons, B → M 1 M 2 , can be extended to include QED corrections to all orders in α em . Similar to the well-known QCD case, the relevant hadronic matrix elements can then be expressed as [3] 1…”

Disentangling observable dependence in SCETI and SCETII anomalous dimensions: angularities at two loops

“…This refactorization is similar in spirit to that performed in section 4.2 of refs [42,43],. albeit in a different physical context.…”