We analyze $K_L$ lepton pair decays of $K_L\to l^{+}{l}^{-}\gamma$ and $K_L\to l^{+}{l}^{-}{l}^{\prime +}{l}^{\prime -}(l,l^{\prime }=e,\mu )$ within the framework of the light-front QCD approach (LFQA). With the $K_L\to {\gamma }^{*}{\gamma }^{*}$ form factors evaluated in a model with the LFQA, we calculate the decay branching ratios and find that our results are all consistent with the experimental data. In addition, we study $K_L\to l^{+}{l}^{-}$ decays. We point out that our prediction for $K_L\to e^{+}{e}^{-}$ is about $20\%$ smaller than that in chiral perturbation theory. We also discuss whether one could extract the short-distance physics from $K_L\to {\mu }^{+}{\mu }^{-}.$

• Received 21 March 2002

DOI:https://doi.org/10.1103/PhysRevD.66.034005