Recently, the KOTO experiment reported their new preliminary result of searching for the decay K L → π 0 νν. Three candidate events were observed in the signal region, which exceed significantly the expectation based on the standard model. On the other hand, the new NA62 and previous BNL-E949 experiments yielded a consistent result and confirmed the standard model prediction in the charged meson decay K þ → π þ νν. Furthermore, the two decays are bound by a well-motivated relation from an analysis of isospin symmetry that is hard to break by the new physics of heavy particles. In this work, we study the issue by a systematic effective field theory approach with three of the simplest scenarios, in which the K L may decay into a new light neutral particle X, i.e., K L → π 0 X, K L → γγX, or K L → π 0 XX. We assess the feasibility of the scenarios by simulations and by incorporating constraints coming from NA62 and other relevant experiments. Our main conclusion is that the scenario K → πXX for a long-lived scalar X seems more credible than the other two when combining distributions and other experimental constraints while the region below the KOTO's blind box provides a good detection environment to search for all three scenarios for a relatively heavy X.