Infrared Fixed Point in the Strong Running Coupling: Unraveling the \Delta I=1/2 puzzle in K-Decays

TL;DR

This paper proposes that an infrared fixed point in QCD explains the Delta I=1/2 rule in K-decays, linking scale symmetry breaking, the spectrum of Nambu-Goldstone bosons, and low-energy amplitudes through a novel chiral-scale perturbation theory.

Contribution

It introduces a new explanation for the Delta I=1/2 rule based on an infrared fixed point and develops a chiral-scale perturbation theory incorporating a QCD dilaton.

Findings

Identification of sigma as the f_0(500) resonance.

Derivation of the Delta I=1/2 rule from sigma-pole dominance.

Estimate of the nonperturbative Drell-Yan ratio R_IR ~ 5.

Abstract

In this talk, we present an explanation for the Delta I = 1/2 rule in K-decays based on the premise of an infrared fixed point alpha_IR in the running coupling alpha_s 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 x SU(3)_R symmetry. Consequently, the low-lying spectrum contains nine Nambu-Goldstone bosons: pi,K,eta and a QCD dilaton sigma. We identify sigma as the f_0(500) resonance and construct a chiral-scale perturbation theory CHPT_sigma for low-energy amplitudes expanded in alpha_s about alpha_IR. The Delta I = 1/2 rule emerges in the leading order of CHPT_sigma through a sigma-pole term K_S --> sigma --> 2 pi, with a K_S-sigma coupling fixed by data on 2 gamma --> 2 pi^0 and K_S --> 2 gamma. We also determine R_IR ~ 5 for the nonperturbative Drell-Yan ratio at alpha_IR.