<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>ϕ</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>2170</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math> decaying to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>ϕ</mml:mi><mml:mi>η</mml:mi></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>ϕ</mml:mi><mml:msup><mml:mi>η</mml:mi><mml:mo>′</mml:mo></mml:msup></mml:math>

In this work we calculate the decay widths of $\ensuremath{\phi}(2170)$ to $\ensuremath{\phi}\ensuremath{\eta}$ and $\ensuremath{\phi}{\ensuremath{\eta}}^{\ensuremath{'}}$ by considering as a $\ensuremath{\phi}K\overline{K}$ state, with $K\overline{K}$ clustering ${f}_{0}(980)$. These have been recently determined BESIII, BABAR, Belle collaborations aim unraveling nature $\ensuremath{\phi}(2170)$. By analyzing data on cross sections process ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}\ensuremath{\phi}\ensuremath{\eta}$, two solutions were found BESIII collaboration same ${\ensuremath{\chi}}^{2}$ per number degrees freedom (n.d.f.), mass width for However, different values ${\mathcal{B}}_{\ensuremath{\phi}\ensuremath{\eta}}^{\ensuremath{\phi}(2170)}{\mathrm{\ensuremath{\Gamma}}}_{{e}^{+}{e}^{\ensuremath{-}}}^{\ensuremath{\phi}(2170)}$ obtained, where ${\mathcal{B}}_{\ensuremath{\phi}\ensuremath{\eta}}^{\ensuremath{\phi}(2170)}$ is branching fraction $\ensuremath{\phi}(2170)\ensuremath{\rightarrow}\ensuremath{\phi}\ensuremath{\eta}$ ${\mathrm{\ensuremath{\Gamma}}}_{{e}^{+}{e}^{\ensuremath{-}}}^{\ensuremath{\phi}(2170)}$ $\ensuremath{\phi}(2170)\ensuremath{\rightarrow}{e}^{+}{e}^{\ensuremath{-}}$: ${0.24}_{\ensuremath{-}0.07}^{+0.12}\text{ }\text{ }\mathrm{eV}$ (solution I) ${10.11}_{\ensuremath{-}3.13}^{+3.87}\text{ II). case ${\mathcal{B}}_{\ensuremath{\phi}{\ensuremath{\eta}}^{\ensuremath{'}}}^{\ensuremath{\phi}(2170)}{\mathrm{\ensuremath{\Gamma}}}_{{e}^{+}{e}^{\ensuremath{-}}}^{\ensuremath{\phi}(2170)}$, value $7.1\ifmmode\pm\else\textpm\fi{}0.7\ifmmode\pm\else\textpm\fi{}0.7$ was from fits section ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}\ensuremath{\phi}{\ensuremath{\eta}}^{\ensuremath{'}}$. The has also more recently, although statistical significance related signal in low. We $\ensuremath{\phi}{\ensuremath{\eta}}^{\ensuremath{'}}$, compare their ratio ${\mathrm{\ensuremath{\Gamma}}}_{\ensuremath{\phi}\ensuremath{\eta}}^{\ensuremath{\phi}(2170)}/{\mathrm{\ensuremath{\Gamma}}}_{\ensuremath{\phi}{\ensuremath{\eta}}^{\ensuremath{'}}}^{\ensuremath{\phi}(2170)}$ one using above mentioned experimental data. Considering theoretical uncertainties, lower limit our result ($\ensuremath{\simeq}2.6$) close upper obtained ($\ensuremath{\simeq}2$) solution II ${\mathcal{B}}_{\ensuremath{\phi}\ensuremath{\eta}}^{\ensuremath{\phi}(2170)}{\mathrm{\ensuremath{\Gamma}}}_{{e}^{+}{e}^{\ensuremath{-}}}^{\ensuremath{\phi}(2170)}$, well ($\ensuremath{\simeq}2.8$) when III IV ${\mathcal{B}}_{\ensuremath{\phi}\ensuremath{\eta}}^{\ensuremath{\phi}(2170)}{\mathrm{\ensuremath{\Gamma}}}_{{e}^{+}{e}^{\ensuremath{-}}}^{\ensuremath{\phi}(2170)}$.