INFRARED FIXED POINT IN THE STRONG RUNNING COUPLING: UNRAVELING THE ΔI = 1/2 PUZZLE IN K-DECAYS

In this paper, we present an explanation for the ΔI = 1/2 rule in K-decays based on the premise of an infrared fixed point αIR in the running coupling αs of quantum chromodynamics (QCD) for three light quarks u, d, s. At the fixed point, the quark condensate spontaneously breaks scale and chiral SU(3)L×SU(3)R symmetry. Consequently, the low-lying spectrum contains nine Nambu–Goldstone bosons: π, K, η and a QCD dilaton σ. We identify σ as the f0(500) resonance and construct a chiral-scale perturbation theory χPTσ for low-energy amplitudes expanded in αs about αIR. The ΔI = 1/2 rule emerges in the leading order of χPTσ through a σ-pole term KS→σ→ππ, with a gKSσ coupling fixed by data on γγ→π0π0 and KS→γγ. We also determine RIR ≈5 for the nonperturbative Drell–Yan ratio at αIR.