Second-Order Weak Processes and Weak-Interaction Cutoff

The problem of the weak-interaction cutoff $\Lambda$ has been studied with the universal current-current theory (UFI) and the intermediate-vector-boson (IVB) model, using the Bjorken technique to treat the high-energy behavior and the "hard meson" technique of Weinberg and Schnitzer. With these methods, the most divergent contributions to the second-order weak decay ${K_L}^0\to \mu \overline{\mu }$ and ${K_L}^0-{K_S}^0$ mass difference $\Delta m$ are essentially independent of strong interaction. From ${K_L}^0\to \mu \overline{\mu }$ decay, $\Lambda \lesssim 35-100$ BeV, and from $\Delta m$, $\Lambda \simeq 3-4$ BeV. With this latter value of $\Lambda$, the predicted rate of ${K_L}^0\to \mu \overline{\mu }$ is reduced to a value obtained by Bég treating this process as first-order in weak and second-order in electromagnetic interaction. The Bég calculation is redone with the algebra of currents, and the soft-kaon contribution to ${K_L}^0\to \mu \overline{\mu }$ is calculated with both the UFI and IVB models. A possible origin of the low value of $\Lambda$ deduced from $\Delta m$ is discussed.