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 ${\Lambda }_{\mathrm{QCD}}$ for the non-radiative matrix elements $⟨M_1{M}_2|Q_i|\bar{B}⟩$ 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 $\Delta E\ll {\Lambda }_{\mathrm{QCD}}$ 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.

arXiv comment44 pages, 6 figures

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• Muon-electron backward scattering: a prime example for endpoint singularities in SCET
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• Light-cone distribution amplitudes of light mesons with QED effects
• Structure-Dependent QED Effects in Exclusive B Decays at Subleading Power
• On the contribution of the electromagnetic dipole operator ${\mathcal{O}}_7$ to the ${\bar{B}}_s\to {\mu }^{+}{\mu }^{-}$ decay amplitude
• Renormalization of the next-to-leading-power $\gamma \gamma \to h$ and $gg\to h$ soft quark functions
• Notes on QED Corrections in Weak Decays
• Disentangling observable dependence in SCETI and SCETII anomalous dimensions: angularities at two loops
• Structure-dependent QED effects in exclusive $B$-meson decays
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• QED factorization of two-body non-leptonic and semi-leptonic $B$ to charm decays
• The QED nonfactorizable correction to the semileptonic charmed three-body $B$ decays
• Estimating QCD-factorization amplitudes through $SU(3)$ symmetry in $B\to PP$ decays
• The Simplest B Decay, Precisely
• Standard Model predictions for Lepton Flavour Universality ratios of inclusive semileptonic $B$ decays