LargeΔI=32Contribution toε′/εin Supersymmetry

We show that in supersymmetric extensions of the standard model gluino box diagrams can yield a large $\mathrm{CP}$-violating $\Delta I=\frac{3}{2}$ contribution to $s\to d\overline{q}q$ flavor-changing neutral current processes, which feeds into the $I=2\mathrm{}$ isospin amplitude in $K\to \pi \pi$ decays. This contribution requires only moderate mass splitting between the right-handed squarks ${\tilde{u}}_R$ and ${\tilde{d}}_R$, and persists for squark masses of order 1 TeV. Taking into account current bounds from $K-\overline{K}$ mixing, the resulting contribution to ${\epsilon }^{\prime }/\epsilon$ could naturally be an order of magnitude larger than the measured value.