Measurements of direct<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>CP</mml:mi></mml:math>violation,<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>CPT</mml:mi></mml:math>symmetry, and other parameters in the neutral kaon system

We present a series of measurements based on ${K}_{L,S}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ and ${K}_{L,S}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}{\ensuremath{\pi}}^{0}$ decays collected in 1996--1997 by the $\mathrm{KTeV}$ experiment (E832) at Fermilab. We compare these four $\stackrel{\ensuremath{\rightarrow}}{K}\ensuremath{\pi}\ensuremath{\pi}$ decay rates to measure the direct $\mathrm{CP}$ violation parameter $\mathrm{Re}({\ensuremath{\epsilon}}^{\ensuremath{'}}/\ensuremath{\epsilon})=(20.7\ifmmode\pm\else\textpm\fi{}2.8)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}.$ We also test $\mathrm{CPT}$ symmetry by measuring the relative phase between the $\mathrm{CP}$ violating and $\mathrm{CP}$ conserving decay amplitudes for $\stackrel{\ensuremath{\rightarrow}}{K}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ $({\ensuremath{\varphi}}_{+\ensuremath{-}})$ and for $\stackrel{\ensuremath{\rightarrow}}{K}{\ensuremath{\pi}}^{0}{\ensuremath{\pi}}^{0}$ $({\ensuremath{\varphi}}_{00}).$ We find the difference between the relative phases to be $\ensuremath{\Delta}\ensuremath{\varphi}\ensuremath{\equiv}{\ensuremath{\varphi}}_{00}\ensuremath{-}{\ensuremath{\varphi}}_{+\ensuremath{-}}=(+0.39\ifmmode\pm\else\textpm\fi{}0.50)\ifmmode^\circ\else\textdegree\fi{},$ and the deviation of ${\ensuremath{\varphi}}_{+\ensuremath{-}}$ from the superweak phase to be ${\ensuremath{\varphi}}_{+\ensuremath{-}}\ensuremath{-}{\ensuremath{\varphi}}_{\mathrm{SW}}=(+0.61\ifmmode\pm\else\textpm\fi{}1.19)\ifmmode^\circ\else\textdegree\fi{};$ 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: $\ensuremath{\Delta}m=(5261\ifmmode\pm\else\textpm\fi{}15)\ifmmode\times\else\texttimes\fi{}{10}^{6}\ensuremath{\Elzxh}{\mathrm{s}}^{\ensuremath{-}1}$ and ${\ensuremath{\tau}}_{S}=(89.65\ifmmode\pm\else\textpm\fi{}0.07)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}\mathrm{s}.$