Abstract
Under the assumption that the sign and magnitude of ${{K}_{1}}^{0}\ensuremath{-}{{K}_{2}}^{0}$ mass difference is due to the contribution of the two-pion intermediate state in the self-energy dispersion integral, it is found that the $I=0$ $S$-wave pion-pion interaction is strong near the $K$ mass. The possibility of a di-pion resonance above 500 MeV is suggested.
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