Measurement of the Branching Fractions D_s⁺ → η′Χ and D_s^+ → η′ρ⁺ in e⁺e⁻ → D_s^+D_s^-

We study D_s⁺ 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(D_s⁺ → η'Χ) = (8.8 ± 1.8 ± 0.5)% and ℬ(D_s⁺ → 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(D_s⁺ → 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(D_s⁺ → η'ρ⁺).