# The 39th International Symposium on Lattice Field Theory (Lattice 2022)

Aug 8 – 13, 2022
Hörsaalzentrum Poppelsdorf
Europe/Berlin timezone

## Direct CP violation in $K \to \pi\pi$ decay at the physical point with periodic boundary conditions

Aug 10, 2022, 5:30 PM
20m
CP1-HSZ/1st-1.002 - HS6 (CP1-HSZ)

### CP1-HSZ/1st-1.002 - HS6

#### CP1-HSZ

50
Oral Presentation Weak Decays and Matrix Elements

Masaaki Tomii

### Description

Since our recent publication on direct CP violation and the Delta I = 1/2 rule in $K \to \pi\pi$ decay which was made with G-parity boundary conditions, we have revisited this problem with a conventional lattice setup employing periodic boundary conditions and two lattice spacings to check our previous result and to improve the precision. We show that the physical amplitude, which corresponds to an excited state in this case, can be obtained reliably with the Generalized Eigenvalue Problem (GEVP) method. Not only are periodic boundary conditions cheaper and allow the use of existing ensembles, but they provide a straightforward path to introduce electromagnetism and strong isospin symmetry breaking, which will be needed in the near future. In this talk, we show our preliminary results on $24^3$ and $32^3$ lattices with domain-wall fermions at physical masses and discuss the prospect of the high-precision calculation of $K \to \pi\pi$ decay with periodic boundary conditions.

### Primary authors

Masaaki Tomii Thomas Blum (UConn) Daniel Hoying (UConn/BNL) Taku Izubuchi (BNL) Luchang Jin (University of Conneticut, Brookhaven National Laboratory) Chulwoo Jung (BNL) Amarjit Soni