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

TL;DR

This paper reports preliminary non-perturbative renormalization results for four-fermion operators relevant to $B_K$ using RI-MOM scheme with improved staggered fermions, comparing with perturbative methods.

Contribution

It introduces a non-perturbative renormalization approach for four-fermion operators in lattice QCD with staggered quarks, providing a comparison with perturbative matching.

Findings

NPR results obtained for $B_K$ operators.

Comparison shows differences between NPR and perturbative matching.

Preliminary results on MILC coarse ensembles.

Abstract

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 $am_{\ell}/am_s = 0.01/0.05$. We compare NPR results with those of one-loop perturbative matching.