Measurement of the branching fractions of $D_{s}^{+}\rightarrow \eta'X$ and $D_{s}^{+}\rightarrow \eta'\rho^{+}$ in $e^+e^-\to D^+_{s}D^-_{s}$

We study Ds+ decays to final states involving the η′ with a 482 pb−1 data sample collected at s=4.009 GeV with the BESIII detector at the BEPCII collider. We measure the branching fractions B(Ds+→η′X)=(8.8±1.8±0.5)% and B(Ds+→η′ρ+)=(5.8±1.4±0.4)% where the first uncertainty is statistical and the second is systematic. In addition, we estimate an upper limit on the non-resonant branching ratio B(Ds+→η′π+π0)<5.1% at the 90% confidence level. Our results are consistent with CLEO's recent measurements and help to resolve the disagreement between the theoretical prediction and CLEO's previous measurement of B(Ds+→η′ρ+) .