Measurements of the Ratios ${\cal B}(D_s^+\to \eta\ell^+\nu)/{\cal B}(D_s^+\to \phi\ell^+\nu)$ and ${\cal B}(D_s^+\to \eta'\ell^+\nu)/{\cal B}(D_s^+\to \phi\ell^+\nu)$

Abstract

Using the CLEO~II detector we measure ${\cal B}(D_s^+\to \eta e^+\nu)/{\cal B}(D_s^+\to \phi e^+\nu) =1.24\pm0.12\pm0.15$, ${\cal B}(D_s^+\to \eta' e^+\nu)/{\cal B}(D_s^+\to \phi e^+\nu) =0.43\pm0.11\pm0.07$ and ${\cal B}(D_s^+\to \eta' e^+\nu)/{\cal B}(D_s^+\to \eta e^+\nu) =0.35\pm0.09\pm0.07$. We find the vector to pseudoscalar ratio, ${\cal B}(D_s^+\to \phi e^+\nu)/{\cal B}(D_s^+\to (\eta+\eta') e^+\nu) =0.60\pm0.06\pm0.06$, which is similar to the ratio found in non strange $D$ decays.