Studies of $D^{+}\to \{{\eta }^{\prime },\eta ,\varphi \}{e}^{+}{\nu }_e$

We report the first observation of the decay $D^{+}\to {\eta }^{\prime }{e}^{+}{\nu }_e$ in two analyses, which combined provide a branching fraction of $\mathcal{B}(D^{+}\to {\eta }^{\prime }{e}^{+}{\nu }_e)=(2.16\pm 0.53\pm 0.07)\times {10}^{-4}$. We also provide an improved measurement of $\mathcal{B}(D^{+}\to \eta e^{+}{\nu }_e)=(11.4\pm 0.9\pm 0.4)\times {10}^{-4}$, provide the first form factor measurement, and set the improved upper limit $\mathcal{B}(D^{+}\to \varphi e^{+}{\nu }_e)<0.9\times {10}^{-4}$ (90%C.L.).

Figure 1

Tagged analysis $U$ distributions in data (points) for $D^{+}\to {\eta }^{\prime }{e}^{+}{\nu }_e$ (a), (b), $D^{+}\to \varphi e^{+}{\nu }_e$ with $\varphi \to K^{+}{K}^{-}$ (c), and $D^{+}\to \eta e^{+}{\nu }_e$ with $\eta \to \gamma \gamma$ (d)–(f) and $\eta \to {\pi }^{+}{\pi }^{-}{\pi }^0$ (g)–(i), in the three $q^2$ intervals. The total (solid line) and background (dashed line) distributions from the fits are also shown.

Figure 2

$M_{\mathrm{BC}}$ distributions (GR analysis) for data (points) and signal (unshaded), $D\overline{D}$ (cross-hatch), continuum (grey), and fake $e^{\pm }$ (45° hatch) fit components. (a) $D^{+}\to {\eta }^{\prime }{e}^{+}{\nu }_e$ summed over all submodes. (b)–(d) $D^{+}\to \eta e^{+}{\nu }_e$ in the indicated $q^2$ (${\mathrm{GeV}}^2/c^4$) ranges, also summed over all submodes.

Figure 3

$M_{\mathrm{BC}}$ distributions (GR analysis) for data (points) and signal (unshaded), $D\overline{D}$ (cross-hatch), continuum (grey), and fake $e^{\pm }$ (45° hatch) fit components for both the HQ (left) and non-HQ (right) subsamples in the ${\eta }^{\prime }\to \rho \gamma$ (top), ${\eta }^{\prime }\to {\pi }^{+}{\pi }^{-}{\eta }_{\gamma \gamma }$ (middle), and ${\eta }^{\prime }\to {\pi }^0{\pi }^0{\eta }_{\gamma \gamma }$ (bottom) submodes.

Figure 4

Comparison of data and MC components scaled by nominal GR fit results in the $D^{+}\to \eta e^{+}{\nu }_e$ mode for (a) signal side $\Delta E$, (b) $\cos {\theta }_{We}$, (c) electron momentum spectrum, (d) missing momentum spectrum, (e) ${\pi }^{\pm }$ momentum spectrum for the nonsignal $D$ side, and (f) $K^{\pm }$ momentum spectrum for the nonsignal $D$ side. Shown are data (points) and signal (unshaded), $D\overline{D}$ (cross-hatch), continuum (grey), and fake $e^{\pm }$ (45° hatch) fit components.

Figure 5

Comparison of data and MC components scaled by nominal GR fit results in the $D^{+}\to {\eta }^{\prime }{e}^{+}{\nu }_e$ mode for (a) signal side $\Delta E$, (b) $\cos {\theta }_{We}$, (c) electron momentum spectrum, (d) missing momentum spectrum, (e) ${\pi }^{\pm }$ momentum spectrum for the nonsignal $D$ side, and (f) $K^{\pm }$ momentum spectrum for the nonsignal $D$ side. Shown are data (points) and signal (unshaded), $D\overline{D}$ (cross-hatch), continuum (grey), and fake $e^{\pm }$ (45° hatch) fit components.

Figure 6

The partial rates from the tagged (circles) and GR (squares) analyses, and the form factor (FF) fit (histogram). The dashed lines indicate the total uncertainty on the fit rates.