Towards non-perturbative matching of three/four-flavor Wilson coefficients with a position-space procedure

Abstract

We propose a strategy to non-perturbatively match the Wilson coefficients in the three- and four-flavor theories, which uses two-point Green's functions of the corresponding four-quark operators at long distances. The idea is refined by combining with the spherical averaging technique, which enables us to convert two-point functions calculated on the lattice into continuous functions of the distance $|x-y|$ between two operators. We also show the result for an exploratory calculation of two-point functions of the $\Delta S=1$ operators $Q_7$ and $Q_8$ that are in the $(8_L,8_R)$ representation of ${\mathrm{SU}(3)}_L\times {\mathrm{SU}(3)}_R$ and mix with each other.

Comments: 7 pages, 2 figures, Proceedings of the 36th International Symposium on Lattice Field Theory (Lattice 2018), July 22-28, 2018, East Lancing, USA