The $\Delta I=1/2$ Rule in the Chiral Limit

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.

33 pages, 6 figures, uses JHEP.cls, minor changes in presentation, misprints and numerical error corrected, accepted in JHEP

References in corpus (1)

• Weak Hamiltonian, CP Violation and Rare Decays

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• Charged Kaon K \to 3 pi CP Violating Asymmetries at NLO in CHPT
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• The Impact of |Delta I|=5/2 Transitions in K-> pi pi Decays
• SU(3) analysis of four-quark operators: $K\to \pi \pi$ and vacuum matrix elements
• Present and Future CP Measurements
• The Strong Isospin-Breaking Correction for the Gluonic Penguin Contribution to epsilon'/epsilon at Next-to-Leading Order in the Chiral Expansion
• Large N Approach to Kaon Decays and Mixing 28 Years Later: Delta I = 1/2 Rule, \hat B_K and Delta M_K
• Chiral Limit Prediction for epsilon'/epsilon at NLO in 1/N_c
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