Measurements of the absolute branching fractions of the doubly Cabibbo-suppressed decays $D^+\to K^+π^0$, $D^+\to K^+η$ and $D^+\to K^+η^{\prime}$

TL;DR

This BESIII study reports absolute branching fractions for the doubly Cabibbo-suppressed decays $D^+ \to K^+ \pi^0$, $D^+ \to K^+ \eta$, and $D^+ \to K^+ \eta'$ using a double-tag approach on $\psi(3770)$ data, providing significantly improved precision. The analysis leverages a 2D fit to $M_{\rm BC}^{\rm tag}$ and $M_{\rm BC}^{\rm sig}$ to extract DT yields and employs $N_{\rm DT} / \sum_i N^{i}_{\rm ST} (\epsilon^{i}_{\rm DT}/\epsilon^{i}_{\rm ST})$ to determine absolute branching fractions, with results ${\cal B}(D^+\to K^+\pi^0)=(1.45\pm0.06\pm0.08)\times10^{-4}$, ${\cal B}(D^+\to K^+\eta)=(1.17\pm0.10\pm0.03)\times10^{-4}$, and ${\cal B}(D^+\to K^+\eta')=(1.88\pm0.15\pm0.11)\times10^{-4}$. While $K^+\eta$ and $K^+\eta'$ are consistent with world averages, the $K^+\pi^0$ result exceeds the PDG value by about $3\sigma$, contributing valuable input to theoretical models of charm decays. The measurement demonstrates the effectiveness of the DT technique in reducing systematics and refining our understanding of DCS processes.

Abstract

Using $20.3\,\rm fb^{-1}$ of $e^+e^-$ collision data collected at a center-of-mass energy of 3.773\,GeV with the BESIII detector, we present the measurements of the absolute branching fractions of the doubly Cabibbo-suppressed decays $D^+\to K^+π^0$, $D^+\to K^+η$ and $ D^+ \to K^+ η^{\prime}$ with the double-tag method, with significantly improved precision compared to the previous measurements. The statistical significance of each signal decay exceeds $10σ$. The branching fractions are determined to be ${\mathcal B}(D^+\to K^+ π^0) = (1.45 \pm 0.06 \pm 0.08)\times 10^{-4}$, ${\mathcal B}(D^+\to K^+ η) = (1.17 \pm 0.10 \pm 0.03)\times 10^{-4}$ and ${\mathcal B}(D^+\to K^+ η^{\prime}) = (1.88 \pm 0.15 \pm 0.11)\times 10^{-4}$, where the first uncertainties are statistical and the second systematic. The branching fractions of $D^+\to K^+η$ and $ D^+ \to K^+ η^{\prime}$ are consistent with the world average values. The reported branching fraction of $D^+\to K^+π^0$ deviates with the world average value by 3$σ$.

Figures (4)

• Figure 1: Fits to the $M_{\rm BC}$ distributions of the ST $D^-$ candidates. The dots with error bars are data, and the blue solid and red dashed curves are the fit results and the fitted backgrounds, respectively.
• Figure 2: The distributions of $M_{\rm BC}^{\rm tag}$ versus $M_{\rm BC}^{\rm sig}$ and the projections on $M_{\rm BC}^{\rm sig}$ and $M_{\rm BC}^{\rm tag}$ of the 2D fits to the DT candidate events of (a) $D^+\to K^+\pi^0$ and (b) $D^+\to K^+ \eta$ in data sample with three tags. For both sub-figures (a) and (b), in the right two columns, the dots with error bars are data, the blue solid curves are the fit results, the black dashed lines are the signals, and the red dashed lines are the BKG I, II and III. For sub-figure (a), the green dashed line is fixed peaking background.
• Figure 3: The distributions of $M_{\rm BC}^{\rm tag}$ versus $M_{\rm BC}^{\rm sig}$ and the projections on $M_{\rm BC}^{\rm sig}$ and $M_{\rm BC}^{\rm tag}$ of the 2D fits to the DT candidate events of (a) $D^+\to K^+\eta^\prime(\pi^{+}\pi^{-}\eta)$, (b) $D^+\to K^+\eta^\prime(\pi^{+}\pi^{-}\gamma)$ in the $\eta^\prime$ signal region and (c) $D^+\to K^+\eta^\prime(\pi^{+}\pi^{-}\gamma)$ in the $\eta^\prime$ sideband region in data sample with three tags. In the fit of (c), the parameters of the smeared Gaussian function have been fixed to those in the $\eta^\prime$ signal region. For all three sub-figures (a), (b) and (c), in the right two columns, the dots with error bars are data, the blue solid curves are the fit results, the black dashed lines are the signals, and the red dashed lines are the BKG I, II and III. For sub-figure (b), the green dashed line is the normalized sideband events. For sub-figure (a), due to the low backgrounds, the black curves overlap with blue curves.
• Figure 4: Comparisons of experimental measurements and theoretical calculations for (a) $D^+\to K^+\pi^0$, (b) $D^+\to K^+\eta$ and (c) $D^+\to K^+\eta^{\prime}$. The green bands represent the $1\sigma$ PDG values. Results before and after the horizontal black line are theoretical and experimental results, respectively. For experimental results, the first uncertainties are statistical and the second ones are systematic. For theoretical calculations, the uncertainties are systematic only.