Preliminary results of $ÎI=1/2$ and $3/2$, $K$ to $ÏÏ$ Decay Amplitudes from Lattice QCD
arXiv:1010.3768
Abstract
We report a direct lattice calculation of the $K$ to $ÏÏ$ decay matrix elements for both $ÎI=1/2$ and $3/2$ channels on 2+1 flavor, domain wall fermion, $16^3\times32$ lattices with zero $ÏÏ$ relative momentum and $m_Ï=420$ MeV. All $K^0$ to $ÏÏ$ contractions are carefully listed and calculated. The decay into the isospin zero $ÏÏ$ final state, which receives contributions from the disconnected graphs, is very difficult to calculate, but a clear signal in the similar disconnected $ÏÏ$ 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 $ÎI=1/2$ rule in the $420$ MeV pion system.
7 pages, proceedings for the 28th International Symposium on Lattice Field Theory, Lattice2010, June 14-19, 2010, Villasimius, Italy