Infrared Fixed Point in the Strong Running Coupling: Unravelling the ΔI=1/2 Puzzle in K-Decays

Abstract

<jats:p> 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 α<jats:sub> IR </jats:sub> in the running coupling α<jats:sub>s</jats:sub> of quantum chromodynamics (QCD) for three light quarks u, d, s. At the fixed point, the quark condensate [Formula: see text] spontaneously breaks scale and chiral SU (3)<jats:sub>L</jats:sub>× SU (3)<jats:sub>R</jats:sub> symmetry. Consequently, the low-lying spectrum contains nine Nambu–Goldstone bosons: π, K, η and a QCD dilaton σ. We identify σ as the f<jats:sub>0</jats:sub>(500) resonance and construct a chiral-scale perturbation theory χPT<jats:sub>σ</jats:sub> for low-energy amplitudes expanded in α<jats:sub>s</jats:sub> about α<jats:sub> IR </jats:sub>. The ΔI = 1/2 rule emerges in the leading order of χPT<jats:sub>σ</jats:sub> through a σ-pole term K<jats:sub>S</jats:sub>→σ→ππ, with a g<jats:sub>K<jats:sub>S</jats:sub>σ</jats:sub> coupling fixed by data on γγ→π<jats:sup>0</jats:sup>π<jats:sup>0</jats:sup> and K<jats:sub>S</jats:sub>→γγ. We also determine R<jats:sub> IR </jats:sub> ≈5 for the nonperturbative Drell–Yan ratio at α<jats:sub> IR </jats:sub>. </jats:p>