TY - JOUR
T1 - $K$ to $ππ$ Decay amplitudes from Lattice QCD
AU - Blum, T.
AU - A. Boyle, P.
AU - H. Christ, N.
AU - Garron, N.
AU - Goode, E.
AU - Izubuchi, T.
AU - Lehner, C.
AU - Liu, Q.
AU - D. Mawhinney, R.
AU - T. Sachrajda, C.
AU - Soni, A.
AU - Sturm, C.
AU - Yin, H.
AU - Zhou, R.
N1 - 40 pages, 12 figures
PY - 2011/6/14
Y1 - 2011/6/14
N2 - We report a direct lattice calculation of the $K$ to $\pi\pi$ decay matrix elements for both the $\Delta I=1/2$ and 3/2 amplitudes $A_0$ and $A_2$ on 2+1 flavor, domain wall fermion, $16^3\times32\times16$ lattices. This is a complete calculation in which all contractions for the required ten, four-quark operators are evaluated, including the disconnected graphs in which no quark line connects the initial kaon and final two-pion states. These lattice operators are non-perturbatively renormalized using the Rome-Southampton method and the quadratic divergences are studied and removed. This is an important but notoriously difficult calculation, requiring high statistics on a large volume. In this paper we take a major step towards the computation of the physical $K\to\pi\pi$ amplitudes by performing a complete calculation at unphysical kinematics with pions of mass 422\,MeV at rest in the kaon rest frame. With this simplification we are able to resolve Re$(A_0)$ from zero for the first time, with a 25% statistical error and can develop and evaluate methods for computing the complete, complex amplitude $A_0$, a calculation central to understanding the $\Delta =1/2$ rule and testing the standard model of CP violation in the kaon system.
AB - We report a direct lattice calculation of the $K$ to $\pi\pi$ decay matrix elements for both the $\Delta I=1/2$ and 3/2 amplitudes $A_0$ and $A_2$ on 2+1 flavor, domain wall fermion, $16^3\times32\times16$ lattices. This is a complete calculation in which all contractions for the required ten, four-quark operators are evaluated, including the disconnected graphs in which no quark line connects the initial kaon and final two-pion states. These lattice operators are non-perturbatively renormalized using the Rome-Southampton method and the quadratic divergences are studied and removed. This is an important but notoriously difficult calculation, requiring high statistics on a large volume. In this paper we take a major step towards the computation of the physical $K\to\pi\pi$ amplitudes by performing a complete calculation at unphysical kinematics with pions of mass 422\,MeV at rest in the kaon rest frame. With this simplification we are able to resolve Re$(A_0)$ from zero for the first time, with a 25% statistical error and can develop and evaluate methods for computing the complete, complex amplitude $A_0$, a calculation central to understanding the $\Delta =1/2$ rule and testing the standard model of CP violation in the kaon system.
U2 - 10.1103/PhysRevD.84.114503
DO - 10.1103/PhysRevD.84.114503
M3 - Article
VL - 84
SP - 114503
JO - Physical Review D, particles, fields, gravitation, and cosmology
JF - Physical Review D, particles, fields, gravitation, and cosmology
ER -