Speaker
Description
The resent status of RBC/UKQCD's long-time project on $K\to\pi\pi$ decay will be presented. A central focus of this talk will be a study of possible systematic effects in interpolating finite-volume matrix elements, computed for the ground and first excited two-pion states obtained with periodic boundary conditions, to the physical kinematics. As a sensitive diagnostic of this interpolation procedure, we examine the matrix element of the pseudoscalar density $\bar s\gamma_5 d$, which should vanish for on-shell transitions by the equations of motion. We also compare multiple prescriptions for determining subtraction coefficients associated with $1/a^2$ power-divergent mixings and discuss their impact on the interpolated on-shell matrix elements. We then present our first attempt at the continuum limit using a series of coarser lattice ensembles (1.0 GeV and 1.4 GeV) and estimates of the associated systematic uncertainties. Finally, we will report the current status of calculations on a newer series of ensembles with smaller lattice spacings, including first results from the $48^3\times96$ ensemble, as a step toward reducing continuum-extrapolation uncertainties in future determinations.