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Search for the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>X</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>2370</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math> and observation of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>η</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">→</mml:mo><mml:mi>η</mml:mi><mml:mi>η</mml:mi><mml:mi>η</mml:…

Search for the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>X</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>2370</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math> and observation of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>η</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">→</mml:mo><mml:mi>η</mml:mi><mml:mi>η</mml:mi><mml:mi>η</mml:…

Using a sample of $1.31\ifmmode\times\else\texttimes\fi{}{10}^{9}\text{ }\text{ }J/\ensuremath{\psi}$ events collected with the BESIII detector, we perform a study of $J/\ensuremath{\psi}\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\eta}\ensuremath{\eta}{\ensuremath{\eta}}^{\ensuremath{'}}$ to search for the $X(2370)$ and ${\ensuremath{\eta}}_{c}$ in the $\ensuremath{\eta}\ensuremath{\eta}{\ensuremath{\eta}}^{\ensuremath{'}}$ invariant mass distribution. No significant signal for the $X(2370)$ is observed, and we set an upper limit for the product branching …