Improved measurements of branching fractions for ${\eta }_c\to \varphi \varphi$ and $\omega \varphi$

Using $(223.7\pm 1.4)\times {10}^6$ J/$\psi$ events accumulated with the BESIII detector, we study ${\eta }_c$ decays to $\varphi \varphi$ and $\omega \varphi$ final states. The branching fraction of ${\eta }_c\to \varphi \varphi$ is measured to be $Br({\eta }_c\to \varphi \varphi )=(2.5\pm 0.3_{-0.7}^{+0.3}\pm 0.6)\times {10}^{-3}$, where the first uncertainty is statistical, the second is systematic, and the third is from the uncertainty of $Br(J\mathrm{/}\psi \to \gamma {\eta }_c)$. No significant signal for the double OZI-suppressed decay of ${\eta }_c\to \omega \varphi$ is observed, and the upper limit on the branching fraction is determined to be $Br({\eta }_c\to \omega \varphi )<2.5\times {10}^{-4}$ at the 90% confidence level.