<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:mrow><mml:mn/><mml:mo>(</mml:mo><mml:mn>3654</mml:mn><mml:mo>)</mml:mo><mml:mn/></mml:math>and hyperfine splitting in charmonium

The hyperfine splitting for the $2S$ charmonium state is calculated and the predicted number is ${\ensuremath{\Delta}}_{\mathrm{HF}}(2S)=57\ifmmode\pm\else\textpm\fi{}8\mathrm{MeV},$ being by derivation the lower bound of this splitting. It results in $M({\ensuremath{\eta}}_{c}(2S))=3630\ifmmode\pm\else\textpm\fi{}8\mathrm{MeV},$ which is smaller by two standard deviations than found in the Belle experiment, but close to the ${\ensuremath{\eta}}_{c}(2S)$ mass observed by the same group in the experiment ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}J/\ensuremath{\psi}{\ensuremath{\eta}}_{c}$ where $M({\ensuremath{\eta}}_{c}(2S))=3622\ifmmode\pm\else\textpm\fi{}12\mathrm{MeV}$ was found.

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