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# 36th Annual International Symposium on Lattice Field Theory

22-28 July 2018
Kellogg Hotel and Conference Center
EST timezone

## Towards non-perturbative renormalization of $\Delta S = 1$ four-quark operators with a position-space procedure

Jul 26, 2018, 9:30 AM
20m
104 (Kellogg Hotel and Conference Center)

### 104

#### Kellogg Hotel and Conference Center

219 S Harrison Rd, East Lansing, MI 48824
Standard Model Parameters and Renormalization

### Speaker

Dr Masaaki Tomii (Columbia University)

### Description

We construct a concrete strategy to implement the non-perturbative renormalization of the $\Delta S = 1$ four-quark operators, which are associated with $K \to \pi\pi$ matrix elements. These non-perturbative methods can be used to determine the Wilson coefficients for the 3-flavor theory, avoiding a significant source of systematic uncertainty that arises from perturbative matching through the charm threshold. The use of an on-shell, gauge-invariant, position-space scheme is important below the charm threshold to avoid any mixing with irrelevant operators which becomes a serious problem when the RI/MOM scheme is used at low energies. In this talk, we provide a renormalization condition in the position-space procedure which is applicable even if operators mix with each other. A new treatment of discretization errors based on the idea of averaging correlators over spheres is introduced with an example of quark mass renormalization, which can be compared with our previous result from the RI/SMOM scheme.

### Primary author

Dr Masaaki Tomii (Columbia University)

 Slides