The effect of higher-dimensional operators in $K \to \pi\pi$ decays

Abstract

We reexamine the weak ΔS = 1 sector by including higher-dimensional four-quark operators in the lowenergy effective Lagrangian ℒeffΔS=1. The introduction of a physical cut-off Λ ∼- 1 GeV as an effective mass scale in QCD allows for a systematic expansion in powers of p/Λ where p denotes some external quark momentum. Within this framework analytical expressions for the higher-dimensional operators are obtainable. By means of the chiral quark model we evaluate K → ππ matrix elements of LeffΔS=1 and identify the corrections to the isospin decay channels g(1/2) and g(3/2). While little affecting ΔI = 1/2 transitions the effect is substantial in the ΔI = 3/2 case where it amounts to a 40% enhancement numerically.