Measurement of the Regeneration Phase in Carbon from 4 to 10 GeV/c

A regeneration experiment exploring $K_S-K_L$ interference in the decay modes $K_{S,L}\to {\pi }^{+}{\pi }^{-}$ and $K_{S,L}\to {\pi }^{\pm }{l}^{\mp }\nu$ ($l=\mu or e$) has been performed at the Brookhaven National Laboratory alternating-gradient synchrotron. The regeneration phases in carbon obtained from the time-dependent charge asymmetry of the $K_{e3\mathrm{}}$ and $K_{\mu 3}$ modes are in good agreement and yield a combined result ${\varphi }_f\equiv \arg i\left[f\right(0\mathrm{})-f(0\left)\right]=-40.9\mathrm{}°\pm 2.6°$ at the average $K^0$ momentum of 7.5 GeV/c.