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We study the correlation between $\epe$ and $\Delta I=1/2$ rule in theframework of non-linear $\sigma$ model including scalar mesons. The matrixelements of QCD and Electroweak (EW) penguin operators are computed withinfactorization approximation. Using the matrix elements and changing the scalarmeson mass, we find that there is correlation between $\epe$ and $\Delta I=1/2$amplitude. However, it is difficult to explain both $\epe$ and $\Delta I=1/2$amplitude simultaneously. In order to be compatible with $\epe$, typically,about half of $\Delta I=1/2$ amplitude can be explained at most. Our resultsuggests there may be substantial non-factorizable contribution to CPconserving $K \to \pi \pi$ amplitudes.Comment: Title has been changed, 19 pages in RevTex, ps figures included,  psfig.sty and here.sty are require

physical review. d. particles, fields, gravitation, and cosmology/physical review. d. particles and fields

Penguin diagrams in the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>Δ</mml:mi><mml:mi>I</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:mn>2</mml:mn><mml:mn /></mml:math>rule and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi>ε</mml:mi></mml:mrow><mml:mrow><mml:mo>′</mml:mo></mml:mrow></mml:msup></mml:mrow><mml:mo>/</mml:mo><mml:mi>ε</mml:mi></mml:math>with σ models

Penguin diagrams in theΔI=1/2rule andε′/εwith σ models