Measurements of the absolute branching fractions for $D_s^{+}\to \hat{I}\cdot e^{+}\hat{I}{½}_e$ and $D_s^{+}\to \hat{I}{\cdot }^{\prime }{e}^{+}\hat{I}{½}_e$

Abstract

By analyzing 482 pb${}^{-1}$ of $e^{+}{e}^{-}$ collision data collected at $\sqrt{s}=4.009$ GeV with the BESIII detector at the BEPCII collider, we measure the absolute branching fractions for the semileptonic decays $D_s^{+}\to \hat{I}\cdot e^{+}\hat{I}{½}_e$ and $D_s^{+}\to \hat{I}{\cdot }^{\prime }{e}^{+}\hat{I}{½}_e$ to be $B(D_s^{+}\to \hat{I}\cdot e^{+}\hat{I}{½}_e)=(2.30\pm 0.31\pm 0.08)$\% and $B(D_s^{+}\to \hat{I}{\cdot }^{\prime }{e}^{+}\hat{I}{½}_e)=(0.93\pm 0.30\pm 0.05)$\%, respectively, and their ratio $\frac{B(D_s^{+}\to \hat{I}{\cdot }^{\prime }{e}^{+}\hat{I}{½}_e)}{B(D_s^{+}\to \hat{I}\cdot e^{+}\hat{I}{½}_e)}=0.40\pm 0.14\pm 0.02$, where the first uncertainties are statistical and the second ones are systematic. The results are in good agreement with previous measurements within uncertainties; they can be used to determine the $\hat{I}\cdot -\hat{I}{\cdot }^{\prime }$ mixing angle and improve upon the $D_s^{+}$ semileptonic branching ratio precision.

9 pages, 2 figures