Study of $φ\to K\bar{K}$ and $K_{S}^{0}-K_{L}^{0}$ Asymmetry in the Amplitude Analysis of $D_{s}^{+} \to K_{S}^{0}K_{L}^{0}π^{+}$ Decays

Abstract

Using $e^+e^-$ annihilation data corresponding to a total integrated luminosity of 7.33 $\rm fb^{-1}$ collected at center-of-mass energies between 4.128 and 4.226~GeV with the BESIII detector, we provide the first amplitude analysis and absolute branching fraction measurement of the hadronic decay $D_{s}^{+} \to K_{S}^{0}K_{L}^{0}π^{+}$. The branching fraction of $D_{s}^{+} \to K_{S}^{0}K_{L}^{0}π^{+}$ is determined to be $(1.86\pm0.06_{\rm stat}\pm0.03_{\rm syst})\%$. Combining the $\mathcal{B}[D_{s}^{+} \to φ(\to K_{S}^0K_{L}^0) π^+]$ obtained in this work and the world average of $\mathcal{B}[D_{s}^{+} \to φ(\to K^+K^-) π^+]$, we measure the relative branching fraction $\mathcal{B}(φ\to K_S^0K_L^0)/\mathcal{B}(φ\to K^+K^-)$=($0.593 \pm 0.023_{\rm stat} \pm 0.014_{\rm syst} \pm 0.016_{φπ}$), where the third error is due to the uncertainty of the $\mathcal{B}(D_s^+ \to φπ^+,φ\to K^+K^-)$. Our result deviates from the Particle Data Group value by more than 3$σ$. Furthermore, the asymmetry of the branching fractions of $D^+_s\to K_{S}^0K^{*}(892)^{+}$ and $D^+_s\to K_{L}^0K^{*}(892)^{+}$, $\frac{\mathcal{B}[D_{s}^{+} \to K_{S}^0K^{*}(892)^{+}]-\mathcal{B}[D_{s}^{+} \to K_{L}^0K^{*}(892)^{+}]}{\mathcal{B}[D_{s}^{+} \to K_{S}^0K^{*}(892)^{+}]+\mathcal{B}[D_{s}^{+} \to K_{L}^0K^{*}(892)^{+}]}$, is determined to be $(-14.5\pm 5.1_{\rm stat}\pm 1.8_{\rm syst})\%$.

Figures (4)

• Figure 1: Dalitz plots of $M^{2}_{K_L^0\pi^+}$ versus $M^{2}_{K_S^0\pi^+}$ for $D^+_s\to K^0_SK^0_L\pi^+$, of (a) the sum of all data samples and (b) the signal MC samples generated based on the amplitude analysis. The black curve indicates the kinematic boundary.
• Figure 2: Distributions of (a) $M_{K_S^0K_L^0}^{2}$ less than 1.1 GeV$^{2}$/$c^4$, (b) $M_{K_S^0K_L^0}^{2}$ greater than 1.1 GeV$^{2}$/$c^4$, (c) $M_{K_L^0\pi^+}^{2}$ and (d) $M_{K_S^0\pi^+}^{2}$ from the nominal fit. The data samples are represented by points with error bars, the fit results by blue lines, and the backgrounds by gray dashed lines. Colored dashed lines show the individual components of the fit model. The numbers in the upper right corner represent the goodness of fit, $\chi^2$/$N_{\rm bin}$, where $N_{\rm bin}$ denotes the number of bins for each projection. In the calculation, adjacent bins are merged to ensure that each bin has no fewer than 10 entries.
• Figure 3: Fit to the $M_{\rm miss}^{2}$ distribution of the DT signal candidates. The data samples are represented by points with error bars, the signal contributions by the red dashed line, the total fit results by the solid blue line, and the background contributions by the dashed black line.
• Figure 4: Comparison of the results for $R_{\phi}$ measured in this analysis and the HBC, OLYA, CMD2, and CMD3 experiments. Above the dotted line are the theoretical calculations, below are the experimental results. The green band present the total uncertainty obtained in this work.