K(L) --> pi0 e+ e- and K(L) --> pi0 mu+ mu-: A binary star on the stage of flavor physics

A systematic analysis of New Physics impacts on the rare decays KL→π0ell+ell- is performed. Thanks to their different sensitivities to flavor-changing local effective interactions, these two modes could provide valuable information on the nature of the possible New Physics at play. In particular, a combined measurement of both modes could disentangle scalar/pseudoscalar from vector or axial-vector contributions. For the latter, model-independent bounds are derived. Finally, the KL→π0μ+μ- forward-backward CP-asymmetry is considered, and shown to give interesting complementary information.