Likelihood analysis of the newly observed $f_0(2020)$, $f_0(2330)$, and $f_0(2470)$ in $J\mathrm{/}\psi \to \gamma {\eta }^{\mathrm{\prime }}{\eta }^{\mathrm{\prime }}$ as high-lying unflavored scalar mesons

Light mesons have always been an important part of the whole hadron family, once inspiring the SU(3) classification of hadrons as a typical example~\cite{Gell-Mann:1964ewy}. Until now, the search for light mesons has been an ongoing task in hadron physics. In particular, with the accumulation of experimental data, more and more light flavor mesons with the masses around 2.2 GeV were found, including the $Y(2175)$ observed in $J\mathrm{/}\psi \to \eta \phi f_0(980)$~\cite{BES:2007sqy} and the $X(2370)$ reported in the decay of $J\mathrm{/}\psi \to \gamma {\eta }^{\mathrm{\prime }}{\pi }^{+}{\pi }^{-}$~\cite{BESIII:2010gmv,BESIII:2019wkp}. These progresses show that there is a chance to construct the light meson family, which is also an effective approach to deepen our understanding of non-perturbative behavior of the strong interaction.