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 \( \left\langle {M}_1{M}_2\left|{Q}_i\right|\overline{B}\right\rangle \) of the current-current operators from the effective weak interactions. The rates of the branching fractions for the infrared-finite observables \( \overline{B}\to {M}_1{M}_2\left(\gamma \right) \) 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.
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References
M. Beneke, G. Buchalla, M. Neubert and C.T. Sachrajda, QCD factorization for B → ππ decays: strong phases and CP-violation in the heavy quark limit, Phys. Rev. Lett. 83 (1999) 1914 [hep-ph/9905312] [INSPIRE].
M. Beneke, G. Buchalla, M. Neubert and C.T. Sachrajda, QCD factorization for exclusive, nonleptonic B meson decays: General arguments and the case of heavy light final states, Nucl. Phys. B 591 (2000) 313 [hep-ph/0006124] [INSPIRE].
M. Beneke and S. Jager, Spectator scattering at NLO in non-leptonic b decays: tree amplitudes, Nucl. Phys. B 751 (2006) 160 [hep-ph/0512351] [INSPIRE].
M. Beneke and S. Jager, Spectator scattering at NLO in non-leptonic B decays: Leading penguin amplitudes, Nucl. Phys. B 768 (2007) 51 [hep-ph/0610322] [INSPIRE].
G. Bell, NNLO vertex corrections in charmless hadronic B decays: Imaginary part, Nucl. Phys. B 795 (2008) 1 [arXiv:0705.3127] [INSPIRE].
G. Bell, NNLO vertex corrections in charmless hadronic B decays: real part, Nucl. Phys. B 822 (2009) 172 [arXiv:0902.1915] [INSPIRE].
M. Beneke, T. Huber and X.-Q. Li, NNLO vertex corrections to non-leptonic B decays: tree amplitudes, Nucl. Phys. B 832 (2010) 109 [arXiv:0911.3655] [INSPIRE].
C.S. Kim and Y.W. Yoon, Order \( {\alpha}_s^2 \) magnetic penguin correction for B decay to light mesons, JHEP 11 (2011) 003 [arXiv:1107.1601] [INSPIRE].
G. Bell, M. Beneke, T. Huber and X.-Q. Li, Two-loop current-current operator contribution to the non-leptonic QCD penguin amplitude, Phys. Lett. B 750 (2015) 348 [arXiv:1507.03700] [INSPIRE].
G. Bell, M. Beneke, T. Huber and X.-Q. Li, Two-loop non-leptonic penguin amplitude in QCD factorization, JHEP 04 (2020) 055 [arXiv:2002.03262] [INSPIRE].
M. Beneke, C. Bobeth and R. Szafron, Enhanced electromagnetic correction to the rare B-meson decay Bs,d → μ+ μ−, Phys. Rev. Lett. 120 (2018) 011801 [arXiv:1708.09152] [INSPIRE].
M. Beneke, C. Bobeth and R. Szafron, Power-enhanced leading-logarithmic QED corrections to Bq → μ+ μ−, JHEP 10 (2019) 232 [arXiv:1908.07011] [INSPIRE].
M. Beneke, P. Böer, J.N. Toelstede and K.K. Vos, in preparation.
K.G. Chetyrkin, M. Misiak and M. Münz, |∆F| = 1 nonleptonic effective Hamiltonian in a simpler scheme, Nucl. Phys. B 520 (1998) 279 [hep-ph/9711280] [INSPIRE].
M. Beneke and M. Neubert, QCD factorization for B → PP and B → PV decays, Nucl. Phys. B 675 (2003) 333 [hep-ph/0308039] [INSPIRE].
C.W. Bauer, S. Fleming, D. Pirjol and I.W. Stewart, An effective field theory for collinear and soft gluons: Heavy to light decays, Phys. Rev. D 63 (2001) 114020 [hep-ph/0011336] [INSPIRE].
C.W. Bauer, D. Pirjol and I.W. Stewart, Soft collinear factorization in effective field theory, Phys. Rev. D 65 (2002) 054022 [hep-ph/0109045] [INSPIRE].
M. Beneke, A.P. Chapovsky, M. Diehl and T. Feldmann, Soft collinear effective theory and heavy to light currents beyond leading power, Nucl. Phys. B 643 (2002) 431 [hep-ph/0206152] [INSPIRE].
M. Beneke and T. Feldmann, Multipole expanded soft collinear effective theory with non-Abelian gauge symmetry, Phys. Lett. B 553 (2003) 267 [hep-ph/0211358] [INSPIRE].
M. Beneke, Soft-collinear factorization in B decays, Nucl. Part. Phys. Proc. 261-262 (2015) 311 [arXiv:1501.07374] [INSPIRE].
M. Beneke and T. Feldmann, Factorization of heavy to light form-factors in soft collinear effective theory, Nucl. Phys. B 685 (2004) 249 [hep-ph/0311335] [INSPIRE].
G. Lepage and S.J. Brodsky, Exclusive processes in quantum chromodynamics: evolution equations for hadronic wave functions and the form-factors of mesons, Phys. Lett. B 87 (1979) 359 [INSPIRE].
G. Lepage and S.J. Brodsky, Exclusive processes in perturbative quantum chromodynamics, Phys. Rev. D 22 (1980) 2157 [INSPIRE].
A.V. Efremov and A.V. Radyushkin, Factorization and asymptotical behavior of pion form-factor in QCD, Phys. Lett. B 94 (1980) 245 [INSPIRE].
M. Beneke, Y. Kiyo and D. Yang, Loop corrections to subleading heavy quark currents in SCET, Nucl. Phys. B 692 (2004) 232 [hep-ph/0402241] [INSPIRE].
M. Beneke and T. Feldmann, Symmetry breaking corrections to heavy to light B meson form-factors at large recoil, Nucl. Phys. B 592 (2001) 3 [hep-ph/0008255] [INSPIRE].
M. Beneke, P. Böer and K.K. Vos, in preparation.
A. Sirlin, Large mW, mZ behavior of the O(α) corrections to semileptonic processes mediated by W , Nucl. Phys. B 196 (1982) 83 [INSPIRE].
M. Beneke and D. Yang, Heavy-to-light B meson form-factors at large recoil energy: spectator-scattering corrections, Nucl. Phys. B 736 (2006) 34 [hep-ph/0508250] [INSPIRE].
A. von Manteuffel, R.M. Schabinger and H.X. Zhu, The two-loop soft function for heavy quark pair production at future linear colliders, Phys. Rev. D 92 (2015) 045034 [arXiv:1408.5134] [INSPIRE].
E. Baracchini and G. Isidori, Electromagnetic corrections to non-leptonic two-body B and D decays, Phys. Lett. B 633 (2006) 309 [hep-ph/0508071] [INSPIRE].
T. Huber, E. Lunghi, M. Misiak and D. Wyler, Electromagnetic logarithms in \( \overline{B} \) → Xsl+l−, Nucl. Phys. B 740 (2006) 105 [hep-ph/0512066] [INSPIRE].
C. Bobeth, P. Gambino, M. Gorbahn and U. Haisch, Complete NNLO QCD analysis of \( \overline{B} \) → Xsℓ+ ℓ− and higher order electroweak effects, JHEP 04 (2004) 071 [hep-ph/0312090] [INSPIRE].
G.S. Bali et al., Light-cone distribution amplitudes of pseudoscalar mesons from lattice QCD, JHEP 08 (2019) 065 [arXiv:1903.08038] [INSPIRE].
A. Carbone et al., Invariant mass line shape of B → PP decays at LHCb, CERN-LHCb-PUB-2009-031 (2010).
LHCb collaboration, Measurement of CP asymmetries in two-body \( {B}_{(s)}^0 \)-meson decays to charged pions and kaons, Phys. Rev. D 98 (2018) 032004 [arXiv:1805.06759] [INSPIRE].
M. Gronau and J.L. Rosner, Rate and CP-asymmetry sum rules in B → Kπ, Phys. Rev. D 74 (2006) 057503 [hep-ph/0608040] [INSPIRE].
M. Gronau, A Precise sum rule among four B → Kπ CP asymmetries, Phys. Lett. B 627 (2005) 82 [hep-ph/0508047] [INSPIRE].
D. Giusti et al., First lattice calculation of the QED corrections to leptonic decay rates, Phys. Rev. Lett. 120 (2018) 072001 [arXiv:1711.06537] [INSPIRE].
C.T. Sachrajda et al., Radiative corrections to semileptonic decay rates, PoS(LATTICE2019)162 [arXiv:1910.07342] [INSPIRE].
G.M. de Divitiis et al., Real photon emissions in leptonic decays, arXiv:1908.10160 [INSPIRE].
C. Kane, C. Lehner, S. Meinel and A. Soni, Radiative leptonic decays on the lattice, PoS(LATTICE2019)134 [arXiv:1907.00279] [INSPIRE].
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Beneke, M., Böer, P., Toelstede, JN. et al. QED factorization of non-leptonic B decays. J. High Energ. Phys. 2020, 81 (2020). https://doi.org/10.1007/JHEP11(2020)081
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DOI: https://doi.org/10.1007/JHEP11(2020)081