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The damped oscillating structures (OS) were recently revealed in the proton"effective" form factor (FF) data. For the time being they can be neitherconfirmed nor disproved by investigations of timelike data on the individualproton electric and proton magnetic FFs because their precision and reliability(especially of the proton electric FF data) has not achieved required level forthis aim. On the other hand, conjectures that the OS are direct manifestationsof the quark-gluon structure of the proton indicate that they must not bespecific only for the proton and neutron, but that they should be present alsofor other hadrons. This opens a plausibility to find damped oscillatorystructures also from the EM FFs data of such hadrons, for which adequate EM FFsdata exist, by using the same procedure as for the proton. Consequently in thispaper damped oscillatory structures are investigated in the EM FFs data of thecharged and neutral $K$-mesons to be extracted from the correspondingproduction cross sections, $\sigma^{bare}_{tot}(e^+e^-\to K^+ K^-)$ measuredfrom the threshold up to 64 GeV$^2$ and $\sigma^{bare}_{tot}(e^+e^-\to K_sK_L)$ measured from the threshold up to 9.5 GeV$^2$ of the total c.m. energysquared. The following results have been obtained. If the charged and neutralK-meson EM FFs timelike data are described by the three parametric formula bymeans of which OS have been revealed from the "effective" proton FF data thenOS appear. If physically well founded Unitary and Analytic model of the K-mesonEM structure is used for a description of the charged K-meson EM FFs data, noOS are visible. However, in the case of the neutral K-meson EM FF data onecannot make a definite decision. The overall results indicate that OS obtainedfrom the "effective" proton FF data are likely an artefact of the threeparametric formula which does not describe these data well.

Study of damped oscillating structures from charged and neutral K-meson electromagnetic form factors data