Measurements of directCPviolation,CPTsymmetry, and other parameters in the neutral kaon system

We present a series of measurements based on $K_{L,S}\to {\pi }^{+}{\pi }^{-}$ and $K_{L,S}\to {\pi }^0{\pi }^0$ decays collected in 1996–1997 by the $\mathrm{KTeV}$ experiment (E832) at Fermilab. We compare these four $\overrightarrow{K}\pi \pi$ decay rates to measure the direct $\mathrm{CP}$ violation parameter $\mathrm{Re}({\epsilon }^{\prime }/\epsilon )=(20.7\mathrm{}\pm 2.8)\times {10}^{-4}.$ We also test $\mathrm{CPT}$ symmetry by measuring the relative phase between the $\mathrm{CP}$ violating and $\mathrm{CP}$ conserving decay amplitudes for $\overrightarrow{K}{\pi }^{+}{\pi }^{-}$ $\left({\phi }_{+-}\right)$ and for $\overrightarrow{K}{\pi }^0{\pi }^0$ $\left({\phi }_{00}\right).\mathrm{}$ We find the difference between the relative phases to be $\Delta \phi \equiv {\phi }_{00}-{\phi }_{+-}=(+0.39\mathrm{}\pm 0.50)°,$ and the deviation of ${\phi }_{+-}$ from the superweak phase to be ${\phi }_{+-}-{\phi }_{\mathrm{SW}}=(+0.61\mathrm{}\pm 1.19)°;$ both results are consistent with $\mathrm{CPT}$ symmetry. In addition, we present new measurements of the $K_L$-$K_S$ mass difference and $K_S$ lifetime: $\Delta m=(5261\mathrm{}\pm 15)\times {10}^6ħ{\mathrm{s}}^{-1}$ and ${\tau }_S=(89.65\mathrm{}\pm 0.07)\times {10}^{-12}\mathrm{s}.$