Amplitude analysis of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msubsup><mml:mrow><mml:mi>K</mml:mi></mml:mrow><mml:mrow><mml:mi>S</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msubsup></mml:mrow><mml:mrow><mml:msubsup><mml:mrow><mml:mi>K</mml:mi></mml:mrow><mml:mrow><mml:mi>S</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msubsup></mml:mrow></mml:math>system produced in the reaction<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi>π</mml:mi></mml:mrow><mml:mrow><mml:mo>−</mml:mo></mml:mrow></mml:msup></mml:mrow><mml:mi>p</mml:mi><mml:mo>→</mml:mo><mml:mrow><mml:msubsup><mml:mrow><mml:mi>K</mml:mi></mml:mrow><mml:mrow><mml:mi>S</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msubsup></mml:mrow><mml:mrow><mml:msubsup><mml:mrow><mml:mi>K</mml:mi></mml:mrow><mml:mrow><mml:mi>S</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msubsup></mml:mrow><mml:mi>n</mml:mi></mml:math>at 23 GeV/<i>c</i>

We have carried out an amplitude analysis of the ${K}_{S}^{0}{K}_{S}^{0}$ system produced in the reaction ${\ensuremath{\pi}}^{\ensuremath{-}}p\ensuremath{\rightarrow}{K}_{S}^{0}{K}_{S}^{0}n$ at 23 GeV/c, based on about 15 000 events in the low-$t$ region ($|t\ensuremath{-}{t}_{min}|&lt;0.1$ Ge${\mathrm{V}}^{2}$). Below 1.6 GeV/${\mathit{c}}^{2}$, our favored solution is very similar to those from previous analyses. For higher masses, we observe the ${K}_{S}^{0}{K}_{S}^{0}$ decay of the $h(2040)$ meson. In addition, the $l=0$ partial wave contains a new state, strongly coupled to ${K}_{S}^{0}{K}_{S}^{0}$, with parameters $M={1.771}_{\ensuremath{-}0.053}^{+0.077}$ GeV/${\mathit{c}}^{2}$ and $\ensuremath{\Gamma}={0.200}_{\ensuremath{-}0.009}^{+0.156}$ GeV/${\mathit{c}}^{2}$. Since this state is most probably $I=0$, we call it the ${S}^{*\ensuremath{'}}(1770)$. We find an $\frac{{f}^{\ensuremath{'}}}{f}$ production ratio of ${0.23}_{\ensuremath{-}0.13}^{+0.14}$, and branching ratios for $f$-meson and $h(2040)$-meson decays into $K\overline{K}$ of (${3.1}_{\ensuremath{-}1.7}^{+0.7}$)% and (${0.67}_{\ensuremath{-}0.15}^{+0.41}$)%, respectively. We find, in a detailed comparison of our results with those from other experiments, that our solution is compatible with all known features of both charged and neutral $K\overline{K}$ systems.