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

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Abstract

We present precise tests of $CP$ and $CPT$ symmetry based on the full data set of $K\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\pi}$ decays collected by the KTeV experiment at Fermi National Accelerator Laboratory during 1996, 1997, and 1999. This data set contains $16\ifmmode\times\else\texttimes\fi{}{10}^{6}$ $K\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}{\ensuremath{\pi}}^{0}$ and $69\ifmmode\times\else\texttimes\fi{}{10}^{6}$ $K\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ decays. We measure the direct $CP$ violation parameter $\mathrm{Re}({ϵ}^{\ensuremath{'}}/ϵ)=(19.2\ifmmode\pm\else\textpm\fi{}2.1)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$. We find the ${K}_{L}\ensuremath{-}{K}_{S}$ mass difference $\ensuremath{\Delta}m=(5270\ifmmode\pm\else\textpm\fi{}12)\ifmmode\times\else\texttimes\fi{}{10}^{6}\ensuremath{\hbar}\text{ }\text{ }{\mathrm{s}}^{\ensuremath{-}1}$ and the ${K}_{S}$ lifetime ${\ensuremath{\tau}}_{S}=(89.62\ifmmode\pm\else\textpm\fi{}0.05)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}\text{ }\text{ }\mathrm{s}$. We also measure several parameters that test $CPT$ invariance. We find the difference between the phase of the indirect $CP$ violation parameter $ϵ$ and the superweak phase: ${\ensuremath{\phi}}_{ϵ}\ensuremath{-}{\ensuremath{\phi}}_{\mathrm{SW}}=(0.40\ifmmode\pm\else\textpm\fi{}0.56)\ifmmode^\circ\else\textdegree\fi{}$. We measure the difference of the relative phases between the $CP$ violating and $CP$ conserving decay amplitudes for $K\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ (${\ensuremath{\phi}}_{+\ensuremath{-}}$) and for $K\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}{\ensuremath{\pi}}^{0}$ (${\ensuremath{\phi}}_{00}$): $\ensuremath{\Delta}\ensuremath{\phi}=(0.30\ifmmode\pm\else\textpm\fi{}0.35)\ifmmode^\circ\else\textdegree\fi{}$. From these phase measurements, we place a limit on the mass difference between ${K}^{0}$ and ${\overline{K}}^{0}$: $\ensuremath{\Delta}M<4.8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}19}\text{ }\text{ }\mathrm{GeV}/{c}^{2}$ at 95% C.L. These results are consistent with those of other experiments, our own earlier measurements, and $CPT$ symmetry.

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