Matrix elements of left-right four-fermion operators and the electropenguin contribution to ε′/ε in lattice QCD with Wilson fermions

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We compute theK−π andK−π−π matrix elements of left-right four-fermion operators with Δ I = 3 2 in quenched lattice QCD andβ = 6.0, with Wilson fermions. This enables us to compute the electropenguin contributions toe′/e. We estimate:(e′/e) EMP = (0.74 ± 0.27) × 10 −3 sin φ , with φ theCP violating C-K-M phase, assuming standard values for the other C-K-M angles. Alternatively, we quoteΩ EMP ≊ 0.40 for the ratio of(ImA 2 /A 2 ) EMP to(−ImA 0 /A 0 ), the latter quantity being estimated from vacuum saturation in the continuum theory. By comparing K −π and K −π−π matrix elements, we check, within 50% errors, the soft-pion relations derived from the chiral structure of the operators. We observe a large enhancement of the matrix element 〈 π − K ¯ 0 | O | π − 〉 , which we interpret as the effect of a scalar octet pole in the π − K ¯ 0 channel. This observation has interesting implications for the related calculation of Δ I = 1 2 , K → ππweak matrix elements.