QED factorization of non-leptonic B decays
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Springer
Received: September 2, 2020 Accepted: October 4, 2020 Published: November 17, 2020
Martin Beneke,a Philipp Böer,a Jan-Niklas Toelstedea,b and K. Keri Vosa a
Physik Department T31, Technische Universität München, James-Franck-Straße 1, D-85748 Garching, Germany b Max-Planck-Institute for Physics, Föhringer Ring 6, D-80805 Munich, Germany
E-mail: [email protected], [email protected], [email protected] 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 ¯ of the current-current opscale ΛQCD for the non-radiative matrix elements hM1 M2 |Qi |Bi erators from the effective weak interactions. The rates of the branching fractions for the ¯ → M1 M2 (γ) with photons of maximal energy ∆E ΛQCD infrared-finite observables B 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. Keywords: QCD Phenomenology ArXiv ePrint: 2008.10615
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP11(2020)081
JHEP11(2020)081
QED factorization of non-leptonic B decays
Contents 1 Introduction
1
2 Factorization formulas
3
3.4
IIγ Hard-scattering kernels Hi,Q 2
5 5 7 9 10 11 11 13
4 SCETI factorization 4.1 Soft rearrangement 4.2 The soft form factor and the semi-leptonic amplitude 4.2.1 Semi-leptonic QED factorization 1 4.2.2 Introducing Asl,M red
15 15 17 18 19
5 SCETII factorization 5.1 Generalized B-meson LCDA 5.2 Spectator scattering and complete factorization
21 21 22
6 Ultrasoft photons and decay rates
24
7 Estimates for πK observables 7.1 Electroweak corrections to the Wilson coefficients 7.2 QED contributions from the hard-scattering kernels 7.2.1 Penguin-dominated B → πK decays 7.3 Ultrasoft factors 7.4 Ratios, isospin sum rule, and CP asymmetries
27 28 29 30 32 32
8 Conclusion
35
¯ 0 → M + M − spectator scattering A Photon polarization and B 1 2 q
36
1
Introduction
In this paper we generalize the QCD factorization formula [1, 2] D
E
¯ = FB→M × TiI ∗ φM + TiII ∗ φM ∗ φM ∗ φB M1 M2 |Qi |B 1 2 1 2
(1.1)
for non-leptonic B decays into two light mesons to include QED. The formula is valid in the heavy-quark limit and expresses the matrix elements of operators Qi from the effective
–1–
JHEP11(2020)081
3 Matching onto SCETI , renormalization and hard-scattering kernels 3.1 SCETI operators 3.2 Matching equation and renormalization 3.2.1 Anti-collinear kernel 3.2.2 Generalize
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