K to ππ Decay amplitudes from Lattice QCD
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by
T. Blum, P.A. Boyle, N.H. Christ, N. Garron, E. Goode, T. Izubuchi, C.
Lehner, Q. Liu, R.D. Mawhinney, C.T. Sachrajda, A. Soni, C. Sturm (+2 others)
2011
Abstract
We report a direct lattice calculation of the K to ππ decay matrix
elements for both the Δ I=1/2 and 3/2 amplitudes A_0 and A_2 on 2+1
flavor, domain wall fermion, 16^3×32×16 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→ππ 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
computing the complete, complex amplitude A_0, a calculation central to
understanding the Δ =1/2 rule and testing the standard model of CP
violation in the kaon system.
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1106.2714v1
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