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

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.

8 pages, 3 figures. Contribution to the proceedings of the workshop "Determination of the Fundamental Parameters of QCD", Nanyang Technological University, Singapore, 18-22 March 2013, to be published in Mod. Phys. Lett. A