ΔI=1/2 rule for kaon decays derived from QCD infrared fixed point

This article gives details of our proposal to replace ordinary chiral SU(3)(L) x SU(3)(R) perturbation theory chi PT3 by three-flavor chiral-scale perturbation theory chi PT sigma. In chi PT sigma, amplitudes are expanded at low energies and small u, d, s quark masses about an infrared fixed point a(IR) of three-flavor QCD. At alpha(IR), the quark condensate <(q) over barq >(vac) not equal 0 induces nine Nambu-Goldstone bosons: pi, K, eta, and a 0(++) QCD dilaton sigma. Physically, sigma appears as the f(0)(500) resonance, a pole at a complex mass with real part less than or similar to m(K). The Delta I = 1/2 rule for nonleptonic K decays is then a consequence of chi PT sigma, with a K-S sigma coupling fixed by data for gamma gamma -> pi pi and K-S -> gamma gamma. We estimate R-IR approximate to 5 for the nonperturbative Drell-Yan ratio R = sigma(e(+)e(-) -> hadrons)/sigma(e(+)e(-) -> mu(+)mu(-)) at alpha(IR) and show that, in the many-color limit, sigma/f(0) becomes a narrow q (q) over bar state with planar-gluon corrections. Rules for the order of terms in chi PT sigma loop expansions are derived in Appendix A and extended in Appendix B to include inverse-power Li-Pagels singularities due to external operators. This relates to an observation that, for gamma gamma channels, partial conservation of the dilatation current is not equivalent to sigma-pole dominance.