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 α IR in the running coupling αs 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)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 α IR . 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 R IR ≈5 for the nonperturbative Drell–Yan ratio at α IR .

Threshold pion photoproduction in the Skyrme model

Threshold photoproduction of pions on the nucleon is studied in the Skyrme model. Both the rotational and translational degrees of freedom of the Skyrmion are included in the calculations. It is found that in the case of neutral pion production there is a sizeable cancellation between the nucleon pole term and the anomalous contact term. This cancellation is a unique feature of the model and provides an important test of the validity of the model. A definitive conclusion must await a resolution of the existing controversies about the experimental data.