CONSISTENTLY COMPUTING THE K → π LONG DISTANCE WEAK TRANSITION

Abstract

First we extract the long-distance (LD) weak matrix element <π|HW|K> from K → 2π, K → 3π, KL→ 2γ, K+→ π+e+e-, K+→ π+μ+μ-and KL→ μ+μ-data and give compatible theoretical estimates. We also link this LD scale to the single-quark-line (SQL) transition scale βWand then test the latter SQL scale against the decuplet weak decay amplitude ratio <π-Ξ0| HW|Ω->/<Ξ-|HW|Ω->. Finally, we study LD KS→ 2γ decay. All of these experimental and theoretical values for <π|HW|K> are in good agreement. We deduce an average value from 11 experimental determinations of <π|HW|K> = (3.59 ± 0.05) × 10-8GeV2, while the theoretical SQL values average to (3.577 ± 0.004) × 10-8GeV2.