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

Abstract

We analyze $K_L$ lepton pair decays of $K_L\to l^{+}{\text{l}}^{-}\gamma$ 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 $K_L\to {\gamma }^{\ast }{\gamma }^{\ast }$ 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 $K_L\to {\mu }^{+}{\mu }^{-}$.

Comments: LaTex, 16 pages, 3 figures; version to appear in PRD