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First Measurement of the Electromagnetic Form Factor of the Neutral Kaon at a Large Momentum Transfer and the Effect of $SU(3)$ Breaking

At large momentum transfers the photon interacts with the charges and spins of the constituent partons in a hadron. It is expected that the neutral kaon can acquire finite electromagnetic form factors because its wave function is affected by the order of magnitude difference between the mass of the strange quark and that of the down quark, or flavor $SU(3)$ breaking. We report on the first measurement of the form factor of neutral kaons at the large timelike momentum transfer of $|Q^2|=17.4$ GeV$^2$ by measuring the cross section for $e^+e^-\to K_SK_L$ at $\sqrt{s}=4.17$ GeV using CLEO-c data with an integrated luminosity of 586 pb$^{-1}$. We obtain $F_{K_SK_L}(17.4~\textrm{GeV}^2)=5.3\times10^{-3}$, with a 90% C.L. interval of $(2.9-8.2)\times10^{-3}$. This is nearly an order of magnitude smaller than $F_{K^+K^-}(17.4~\textrm{GeV}^2)=(44\pm1)\times10^{-3}$, and indicates that the effect of $SU(3)$ breaking is small. In turn, this makes it unlikely that the recently observed strong violation of the pQCD prediction, $F_{π^+π^-}(|Q^2|)/F_{K^+K^-}(|Q^2|)=f_π^2/f_K^2$, which is based on the assumption of similar wave functions for the pions and kaons, can be attributed to $SU(3)$ breaking alone.