Measurements of the absolute branching fractions for $D_s^{+}\to \eta e^{+}{\nu }_e$ and $D_s^{+}\to {\eta }^{\prime }{e}^{+}{\nu }_e$

By analyzing $482{\mathrm{pb}}^{-1}$ of $e^{+}{e}^{-}$ collision data collected at $\sqrt{s}=4.009\mathrm{GeV}$ with the BESIII detector at the BEPCII collider, we measure the absolute branching fractions for the semileptonic decays $D_s^{+}\to \eta e^{+}{\nu }_e$ and $D_s^{+}\to {\eta }^{\prime }{e}^{+}{\nu }_e$ to be $B(D_s^{+}\to \eta e^{+}{\nu }_e)=(2.30\pm 0.31\pm 0.08)\%$ and $B(D_s^{+}\to {\eta }^{\prime }{e}^{+}{\nu }_e)=(0.93\pm 0.30\pm 0.05)\%$, respectively, and their ratio $\frac{B(D_s^{+}\to {\eta }^{\prime }{e}^{+}{\nu }_e)}{B(D_s^{+}\to \eta e^{+}{\nu }_e)}=0.40\pm 0.14\pm 0.02$, 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 $\eta -{\eta }^{\prime }$ mixing angle and improve upon the $D_s^{+}$ semileptonic branching ratio precision.

Figure 1

Results of the fits to the $M_{\mathrm{BC}}$ distributions of the ST $D_s^{-}$ modes (a) $K^{+}{K}^{-}{\pi }^{-}$, (b) $\varphi {\rho }^{-}$, $\varphi \to K^{+}{K}^{-}$, (c) $K_S^0{K}^{+}{\pi }^{-}{\pi }^{-}$, (d) $K_S^0{K}^{-}{\pi }^{+}{\pi }^{-}$, (e) $K_S^0{K}^{-}$, (f) ${\pi }^{+}{\pi }^{-}{\pi }^{-}$, (g) $\eta {\pi }^{-}$, $\eta \to \gamma \gamma$, (h) ${\eta }^{\prime }{\pi }^{-}$, ${\eta }^{\prime }\to \eta {\pi }^{+}{\pi }^{-}$, (i) ${\eta }^{\prime }{\pi }^{-}$, ${\eta }^{\prime }\to \gamma {\rho }^0$, (j) $\eta {\rho }^{-}$, $\eta \to \gamma \gamma$. In each plot, the dots with error bars are from data, the red solid curve represents the total fit to the data, the blue dashed curve describes the ARGUS background, and the green dotted curve denotes the signal shape.

Figure 2

Distributions of $U_{\mathrm{miss}}$ of the candidates for (a) $D_s^{+}\to \eta e^{+}{\nu }_e$, (b) $D_s^{+}\to {\eta }^{\prime }(\eta {\pi }^{+}{\pi }^{-})e^{+}{\nu }_e$ and (c) $D_s^{+}\to {\eta }^{\prime }(\gamma {\rho }^0)e^{+}{\nu }_e$. The pair of arrows indicates the signal region, points with error bars show the events from data, the solid histograms show the scaled events from inclusive MC, the hatched and dashed histograms show the peaking background (“Peak Bkg”) and sideband backgrounds (“Side Bkg”), respectively.