Preliminary results of $ΔI=1/2$ and $3/2$, $K$ to $ππ$ Decay Amplitudes from Lattice QCD

Details Preliminary results of $ΔI=1/2$ and $3/2$, $K$ to $ππ$ Decay Amplitudes from Lattice QCD Preliminary results of $ΔI=1/2$ and $3/2$, $K$ to $ππ$ Decay Amplitudes from Lattice QCD

2010-10-19

arxiv.org/abs/1010.3768v1

PoS Lattice2010:314,2010

Physics

High Energy Physics

High Energy Physics - Lattice

7 pages, proceedings for the 28th International Symposium on Lattice Field Theory, Lattice2010, June 14-19, 2010, Villasimius,

Scientific paper

We report a direct lattice calculation of the $K$ to $\pi\pi$ decay matrix elements for both $\Delta I=1/2$ and $3/2$ channels on 2+1 flavor, domain wall fermion, $16^3\times32$ lattices with zero $\pi\pi$ relative momentum and $m_\pi=420$ MeV. All $K^0$ to $\pi\pi$ contractions are carefully listed and calculated. The decay into the isospin zero $\pi\pi$ final state, which receives contributions from the disconnected graphs, is very difficult to calculate, but a clear signal in the similar disconnected $\pi\pi$ correlator can be seen. Preliminary results, some with large errors, will be presented for the various contributions to the renormalized weak matrix elements $A_0$ and $A_2$. We obtain Re$(A_0)$ with $25%$ error in the case of zero momentum on shell decay, and find a factor of 6 enhancement for the $\Delta I=1/2$ rule in the $420$ MeV pion system.

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