The $\Delta I=1/2$ Selection Rule

Abstract

We compute the isospin $I=0$ and 2 amplitudes for the decay of a kaon into two pions by estimating the relevant hadronic matrix elements in the chiral quark model. The results are parametrized in terms of the quark and gluon condensates and of the constituent quark mass $M$. The latter is a parameter characteristic of the model, that we restrict by matching the results in the two ${\gamma }_5$-schemes (HV and NDR) of dimensional regularization. We find that, for values of these parameters within the current determinations, the $\Delta I=1/2$ selection rule is well reproduced by means of the cumulative effects of short-distance NLO Wilson coefficients, penguin diagrams, non-factorizable soft-gluon corrections and meson-loop renormalization.

Revised version to be published in Nuclear Physics B

References in corpus (7)

• Chiral Lagrangians and Nambu-Jona-Lasinio like models
• QCD tests from $e^+e^- \rar I=1~$ hadrons data and implication on the value of ${\alpha }_s$ from $\tau$-decays
• Light Quark Masses from QCD
• Studying ${\epsilon }^{\prime }/\epsilon$ in the Chiral Quark Model: ${\gamma }_5$-Scheme Independence and NLO Hadronic Matrix Elements
• The $\Delta S=1$ Weak Chiral Lagrangian as the Effective Theory of the Chiral Quark Model
• QCD corrections to inclusive $\Delta S=1,2$ transitions at the next-to-leading order
• Chiral Lagrangians and Kaon CP-Violation

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