CP VIOLATION IN K DECAY FROM LATTICE QCD, RIKEN BNL RESEARCH CENTER, RBRC AND PARTICLE PHYSICS SEMINAR, BROOKHAVEN NATIONAL LABORATORY, UPTON, N.Y., JULY 26, 2001.

The entire history of the discoveries of K{sub L}{sup o} and violations of T and CP began at Brookhaven. It is most appropriate for us to hold today's special seminar on CP Violation in K decay in this laboratory. Forty-five years ago, in the same paper on parity nonconservation, it was also pointed out that there is no proof of T symmetry in the weak interaction, nor of C invariance. That paper was submitted to the Physical Review (then, also located at BNL) on June 22, 1956. A month later, Lederman and his collaborators discovered a long-lived neutral V particle (now called K{sub L}{sup o}) at the Cosmotron using the cloud chamber. This discovery was presented as a rigorous proof of C symmetry. In the same summer at Brookhaven, in collaboration with Oehme and Yang, I did the analysis on the neutral kaon system, assuming T, C and CP violations (but based on CPT symmetry). In that work, the two non-orthogonal eigen-states {psi}{sub +} and {psi}{sub -} (now K{sub S}{sup o} and K{sub L}{sup o}) were characterized by a non-orthogonality parameter {alpha} ({approx_equal} 2 Re{epsilon} in today's notation), which was shown to be small, because of unitarity. We then went on to discuss the various decay modes of the long-lived and short-lived neutral kaons as tests of possible T and CP violations. The paper was completed in December 1956, before parity-nonconservation was experimentally established. Eight years later, the important discovery of CP violation was made by Christenson, Cronin, Fitch and Turlay at BNL