Measurements of the inclusive Branching fractions of the $D_s^{+}\to \eta ({\eta }^{\mathrm{\prime }})X$ decays

Using $e^{+}{e}^{-}$ collision data collected with the BESIII detector at center-of-mass energies between $4.128$ and $4.226$ GeV, corresponding to an integrated luminosity of $7.33{\mathrm{f}\mathrm{b}}^{-1}$, the inclusive branching fractions of the decays $D_s^{+}\to \eta X$ and $D_s^{+}\to {\eta }^{\mathrm{\prime }}X$ ($X$ denotes any possible particles) are measured to be $(30.72\pm 0.90\pm 0.46)\mathrm{\%}$ and $(12.30\pm 0.94\pm 0.37)\mathrm{\%}$, where the first uncertainties are statistical and the second systematic. The results are consistent with the previous CLEO measurements, with precision improved by factors of 2.8 and 1.9 for $D_s^{+}\to \eta X$ and $D_s^{+}\to {\eta }^{\mathrm{\prime }}X$, respectively.