Positronium is an ideal system for the research of the QED, especially for the QED in bound state. The discrepancy of 3.9sigma is found recently between the measured HFS values and the QED prediction ($O(alpha^3)$). It might be due to the contributio
n of the unknown new physics or the systematic problems in the previous all measurements. We propose new method to measure HFS precisely and directly. A gyrotron, a novel sub-THz light source is used with a high-finesse Fabry-Perot cavity to obtain enough radiation power at 203 GHz. The present status of the optimization studies and current design of the experiment are described.
We present our results for the on-shell Delta I = 3/2 kaon decay matrix elements using domain wall fermions and the DBW2 gauge action at one coarse lattice spacing corresponding to 1/a = 1.31 GeV in the quenched approximation. The on-shell matrix ele
ments are evaluated in two different frames: the center-of-mass frame and non-zero total-momentum frame. We employ the formula proposed by Lellouch and Luscher in the center-of-mass frame, and its extension for non-zero total momentum frame to extract the infinite volume, on-shell, center-of-mass frame decay amplitudes. We determine the decay amplitude at the physical pion mass and momentum from the chiral extrapolation and an interpolation of the relative momentum using the results calculated in the two frames. We have obtained Re(A_2) = 1.66(23)(^{+48}_{-03})(^{+53}_{-0}) x 10^{-8} GeV and Im(A_2) = -1.181(26)(^{+141}_{-014})(^{+44}_{-0}) x 10^{-12} GeV at the physical point, using the data at the relatively large pion mass, m_pi > 0.35 GeV. The first error is statistic, and the second and third are systematic. The second error is estimated with several fits of the chiral extrapolation including (quenched) chiral perturbation formula at next to leading order using only lighter pion masses. The third one is estimated with an analysis using the lattice dispersion relation. The result of Re(A_2) is reasonably consistent with experiment.
