Improved measurements of branching fractions for $eta_ctophiphi$ and $omegaphi$

Using $(223.7pm1.4)times10^6$ J/$psi$ events accumulated with the BESIII detector, we study $eta_c$ decays to $phiphi$ and $omegaphi$ final states. The branching fraction of $eta_ctophiphi$ is measured to be $Br(eta_ctophiphi)=(2.5pm0.3^{+0.3}_{-0.7}pm0.6)times10^{-3}$, where the first uncertainty is statistical, the second is systematic, and the third is from the uncertainty of $Br(J/psitogammaeta_c)$. No significant signal for the double OZI-suppressed decay of $eta_ctoomegaphi$ is observed, and the upper limit on the branching fraction is determined to be $Br(eta_ctoomegaphi)<2.5times 10^{-4}$ at the 90% confidence level.