Lepton pair decays of the $K_L$ meson in the light-front model

Abstract

We analyze $K_L$ lepton pair decays of $K_L \to l^+\l^-\gamma$ and $K_L \to l^+l^-l'^+l'^-$ $(l, l'=e, \mu)$ 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 out 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 on $K_L\to e^+e^-$ is about 20% smaller than that in the ChPT. We also discuss whether one could extract the short-distance physics from $K_L\to \mu^+\mu^-$.