Non-perturbative Renormalization of Four-Fermion Operators Relevant to $B_K$ with Staggered Quarks

We present preliminary results of matching factors of the four-fermion operators relevant to $B_K$, which are obtained using the non-perturbative renormalization (NPR) method in the RI-MOM scheme with HYP-smeared improved staggered fermions. We use the MILC asqtad coarse ($a\cong 0.12$fm) ensembles with ${20}^3\times 64$ geometry and $a{m}_{\mathrm{\ell }}\mathrm{/}a{m}_s=0.01\mathrm{/}0.05$. We compare NPR results with those of one-loop perturbative matching.