An analysis of $K^0$ regeneration data from Fermilab in the energy range 30-110 GeV has been carried out to determine the $K_L-K_S$ mass difference $\Delta m$, the $K_S$ lifetime ${\tau }_S$, and the $\mathrm{CP}$-violation parameter ${\eta }_{+-}$. We find that the average values of $\Delta m$, ${\tau }_S$, ${tan\phi }_{+-}$, and $\left|{\eta }_{+-}\right|$ at Fermilab energies differ from the accepted low-energy (∼5 GeV) values by approximately 4, 2, 3, and 9 standard deviations, respectively. As a consequence of the discrepancy between low-energy and high-energy values, an investigation of a possible energy dependence of the parameters was carried out. Using two different methods, the parameters were fitted to a form $x=x_0(1+b_x^{\mathrm{}\left(N\right)\mathrm{}}{\gamma }^N)$ where $x$ is any of the parameters $\Delta m$, ${\tau }_S$, $\left|{\eta }_{+-}\right|$, and ${tan\phi }_{+-}$, $\gamma =\frac{E_K}{m_K}$ is the usual relativistic factor, and $N=1\mathrm{} or 2$. The resulting slope parameters $b_x^{\mathrm{}\left(N\right)\mathrm{}}$ differ from zero by 0-4 standard deviations depending on the parameter and on whether the low-energy value is included. The details of the fits are presented here, and a discussion is also given of new experiments which could check and extend the present results.

• Received 2 December 1982

DOI:https://doi.org/10.1103/PhysRevD.28.476