Tests of discrete symmetries in the semileptonic decays of neutral kaons at CPLEAR

The semileptonic decays of neutral kaon beams, $K^0 \rightarrow \pi e\nu $ and $\overline{K}^0\rightarrow \pi e\nu$, were measured in the CPLEAR experiment, and the parameters $ \Delta m $, Re($x$), Im($x$), and Re($\varepsilon _S$) were extracted using the time-dependent asymmetries in the rates of these two decay channels. Here, $ \Delta m $ is the mass difference between the long and short lived components of the neutral kaons, Re($x$) and Im($x$) are proportional to the real and imaginary parts, repectively, of the $ \Delta S $ = -$ \Delta Q$ amplitude in semileptonic decays, and Re($\varepsilon _S$) is the real part of the CP violating mixing parameter for the short lived neutral kaon.