The ${\eta }_c(3654)$ and hyperfine splitting in charmonium

Abstract

The hyperfine splitting for the 2S charmonium state is calculated and the predicted number is ${\Delta }_{\mathrm{HF}}(2S)=57\pm 8$ MeV, being by derivation the lower bound of this splitting. It results in $M({\eta }_c(2S))=3630\pm 8$ MeV, which is smaller by two standard deviations than found in the Belle experiment \cite{ref.01}, but close to the ${\eta }_c(2S)$ mass observed by the same group in the experiment $e^{+}{e}^{-}\to J/\psi {\eta }_c$ \cite{ref.06} where $M({\eta }_c(2S))=3622\pm 12$ MeV was found.

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