Determination of the T- and CPT-violation parameters in the neutral-kaon system using the Bell–Steinberger relation and data from CPLEAR

Data from the CPLEAR experiment, together with the most recent world averages for some of the neutral-kaon parameters, were constrained with the Bell--Steinberger (or unitarity) relation, allowing the T-violation parameter $\ree$ and the CPT-violation parameter $\imd$ of the neutral-kaon mixing matrix to be determined with an increased accuracy: $\ree = (164.9 \pm 2.5)\times 10^{-5}$, $\imd = ( 2.4 \pm 5.0)\times 10^{-5}$. Moreover, the constraint allows the CPT-violation parameter for the neutral-kaon semileptonic decays, $\rey$, to be determined for the first time. The $\Delta S \neq \Delta Q$ parameters $\rexm$ and $\imxp$ are given with an increased accuracy. The quantity $\mathrm{Re}(y~+~x_-)$, which enters the T-violation CPLEAR asymmetry previously published, is determined to be $(0.2 \pm 0.3)\times 10^{-3}$. The value obtained for $\red$ is in agreement with the one resulting from a previous unconstrained fit and has a slightly smaller error.