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arXiv · 0710.1926

Eradication of singularities in the next-to-leading order RG evolution for the ΔS = 1 effective Hamiltonian with 3 quark flavours

David H. Adams·Weonjong Lee
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Abstract

We consider the renormalization group evolution for the operators in the $ΔS=1$ effective Hamiltonian with 3 active quark flavors, which is needed in the numerical analysis of data sets for $ε'/ε$ calculated in lattice QCD. Singularities are present in the original solution of Buras et al. at next-to-leading order. We show how these can be eradicated through a method of analytic continuation to obtain the correct finite solution in this case. Furthermore, we trace the origin of the singularities to a breakdown of the approach of Buras et al. in the 3 flavour case, and show how it can be rectified so that singularitites are absent from the beginning.

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David H. Adams, Weonjong Lee. 2007-10-10. Eradication of singularities in the next-to-leading order RG evolution for the ΔS = 1 effective Hamiltonian with 3 quark flavours. https://arxiv.org/abs/0710.1926

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