Perturbative matching of the staggered four-fermion operators forε′/ε

Using staggered fermions, we calculate the perturbative corrections to the bilinear and four-fermion operators that are used in the numerical study of weak matrix elements for ${\epsilon }^{\prime }/\epsilon .$ We present results for one-loop matching coefficients between continuum operators, calculated in the naive dimensional regularization (NDR) scheme, and gauge invariant staggered fermion operators. In particular, we concentrate on Feynman diagrams of the current-current insertion type. We also present results for the tadpole improved operators. These results, combined with existing results for penguin diagrams, provide a complete one-loop renormalization of the staggered four-fermion operators. Therefore, using our results, it is possible to match a lattice calculation of $K^0-K^0$ mixing and $\overrightarrow{K}\pi \pi$ decays to the continuum NDR results with all corrections of $\mathcal{O}{(g}^2)$ included.