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arXiv · hep-ph/9811472

The $ΔI=1/2$ Rule in the Chiral Limit

Johan Bijnens·Joaquim Prades
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Abstract

We discuss the matching between long-distance and short-distance at next-to-leading in $1/N_c$ and show how the scheme-dependence from the two-loop renormalization group running can be treated. We then use this method to study the three $O(p^2)$ terms contributing to non-leptonic kaon decays, namely the usual octet and 27-plet derivative terms as well as the weak mass term using the Extended Nambu--Jona-Lasinio model as the low energy approximation. We also discuss subtleties in the momentum routing in the low energy theory and a problem in separating factorizable and non-factorizable contributions from the $Q_6$ operator in the chiral limit. We update our earlier results on the $B_K$ parameter as well.

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Johan Bijnens, Joaquim Prades. 1999-02-02. The $ΔI=1/2$ Rule in the Chiral Limit. https://doi.org/10.1088/1126-6708%2F1999%2F01%2F023

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