QED factorization of non-leptonic $B$ decays

TL;DR

This paper extends the QCD factorization approach for non-leptonic B decays to include electromagnetic corrections, enabling more precise predictions of decay rates and ratios relevant for New Physics searches.

Contribution

It introduces a method to incorporate QED effects into the QCD factorization framework for B-meson decays, maintaining the same formula structure with generalized definitions.

Findings

Electromagnetic corrections can be factorized above the QCD scale.

Soft-photon exponentiation accounts for infrared-finite observables.

Electromagnetic effects impact $ ext{π}K$ ratios and sum rules used in New Physics tests.

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 $\Lambda_{\rm QCD}$ for the non-radiative matrix elements $\langle M_1 M_2|Q_i|\bar{B}\rangle$ of the current-current operators from the effective weak interactions. The rates of the branching fractions for the infrared-finite observables $\bar B\to M_1 M_2(\gamma)$ with photons of maximal energy $\Delta E\ll\Lambda_{\rm QCD}$ 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.