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The standard analytic solution of the renormalization group (RG) evolution for the $\Delta S = 1$ Wilson coefficients involves several singularities, which complicate analytic solutions.
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A. J. Buras, M. Jamin, M. E. Lautenbacher and P. H. Weisz, “Effective Hamiltonians for Δ S = 1 \Delta S=1 and Δ B = 1 \Delta B=1 nonleptonic decays beyond the leading logarithmic approximation,” Nucl. Phys. B 370
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A. J. Buras, M. Jamin, M. E. Lautenbacher and P. H. Weisz, “Two loop anomalous dimension matrix for Δ S = 1 \Delta S=1 weak nonleptonic decays. 1. 𝒪 ( α s 2 ) \mathcal{O}(\alpha_{s}^{2}) ,” Nucl. Phys. B 400
1993
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A. J. Buras, M. Jamin and M. E. Lautenbacher, “Two loop anomalous dimension matrix for Δ S = 1 \Delta S=1 weak nonleptonic decays. 2. 𝒪 ( α α s ) \mathcal{O}(\alpha\alpha_{s}) ,” Nucl. Phys. B 400
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N. G. Deshpande, X. G. He and S. Pakvasa, “Gluon dipole penguin contributions to ϵ K ′ / ϵ K \epsilon^{\prime}_{K}/\epsilon_{K} and C P CP violation in hyperon decays in the Standard Model,” Phys. Lett. B 326
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1995
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G. Buchalla, A. J. Buras and M. E. Lautenbacher, “Weak decays beyond leading logarithms,” Rev. Mod. Phys. 68
1996
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A. Lenz, U. Nierste and G. Ostermaier, “Penguin diagrams, charmless B B decays and the missing charm puzzle,” Phys. Rev. D 56
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K. G. Chetyrkin, J. H. Kuhn and M. Steinhauser, “RunDec: A Mathematica package for running and decoupling of the strong coupling and quark masses,” Comput. Phys. Commun. 133
2000
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S. Gardner and G. Valencia, “The Impact of | Δ I | = 5 / 2 |\Delta I|=5/2 transitions in K → π π K\to\pi\pi decays,” Phys. Rev. D 62
2000
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V. Cirigliano, J. F. Donoghue and E. Golowich, “ K → π π K\to\pi\pi phenomenology in the presence of electromagnetism,” Eur. Phys. J. C 18
2000
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2012
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2012
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2014
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2014
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2014
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2015
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2015
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2015
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2015
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2015
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A. J. Buras, “New physics patterns in ϵ K ′ / ϵ K \epsilon^{\prime}_{K}/\epsilon_{K} and ϵ K \epsilon_{K} with implications for rare kaon decays and Δ M K \Delta M_{K} ,” JHEP 1604
2016
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