First measurements of the branching fractions for the decay modes $Ξ_c^{0} \to Λη$ and $Ξ_c^0 \to Λη'$ and search for the decay $Ξ_c^{0} \to Λπ^0$ using Belle and Belle II data

TL;DR

This work reports the first measurements of the branching fractions for the singly Cabibbo-suppressed decays Xi_c^0 -> Lambda eta and Xi_c^0 -> Lambda eta' and a search for Xi_c^0 -> Lambda pi^0 using combined Belle and Belle II data. Using unbinned extended likelihood fits to multiple final states and a luminosity-weighted, simultaneous fit across datasets, the analysis yields the first observation of Xi_c^0 -> Lambda eta and evidence for Xi_c^0 -> Lambda eta', with absolute branching fractions of order 10^-4; the Lambda pi^0 mode is not observed and an upper limit is set. The results agree with most theoretical predictions and help clarify the role of topological diagrams in charmed-baryon decays, providing important inputs for models of factorizable and non-factorizable contributions. The study demonstrates the power of combining Belle and Belle II data to improve precision in rare charm-baryon decays and tests of flavor symmetry predictions.

Abstract

Using data samples of 988.4 fb$^{-1}$ and 427.9 fb$^{-1}$ collected with the Belle and Belle II detectors, we present a study of the singly Cabibbo-suppressed decays $Ξ_c^{0} \to Λη$, $Λη'$, and $Λπ^0$. We observe the decay $Ξ_c^0 \to Λη$ and find evidence for the decay $Ξ_c^0 \to Λη'$, with corresponding branching ratios determined to be ${\mathcal{B}(Ξ_c^0 \to Λη)}/{\mathcal{B}(Ξ_c^0 \to Ξ^- π^+)}= (4.16 \pm 0.91 \pm {0.23})\%$ and ${\mathcal{B}(Ξ_c^0 \to Λη')}/{\mathcal{B}(Ξ_c^0 \to Ξ^- π^+)}= (2.48 \pm 0.82 \pm {0.12})\%$, respectively. We find no significant signal in the $Ξ_c^0 \to Λπ^0$ decay mode and set an upper limit at the 90% credibility level of ${\mathcal{B}(Ξ_c^0 \to Λπ^0)}/{\mathcal{B}(Ξ_c^0 \to Ξ^- π^+)}< {3.5\%}$. Multiplying these ratios by the world-average branching fraction of the normalization channel, $\mathcal{B}(Ξ_c^0 \to Ξ^- π^+)=(1.43 \pm 0.27)\%$, we obtain the absolute branching fractions of $\mathcal{B}(Ξ_c^0 \to Λη)= (5.95 \pm 1.30 \pm {0.32} \pm 1.13) \times 10^{-4}$, $\mathcal{B}(Ξ_c^0 \to Λη')= (3.55 \pm 1.17 \pm {0.17} \pm 0.68) \times 10^{-4}$, and an upper limit at the 90% credibility level on the absolute branching fraction of $\mathcal{B}(Ξ_c^0 \to Λπ^0)< {5.2} \times 10^{-4}$. The quoted first and second uncertainties are statistical and systematic, respectively, while the third uncertainties arise from the branching fraction of the normalization mode. These results are consistent with most theoretical predictions and further the understanding of the underlying decay mechanisms.

Figures (4)

• Figure 1: Topological diagrams contributing to $\Xi_c^0 \rightarrow\xspace \Lambda h^0$ decays: internal $W$-emission $C$, inner $W$-emission $C'$, and $W$-exchange diagrams $E_1$ and $E_2$Cheng:2021_charm_rev.
• Figure 2: The invariant mass spectra of $\Xi^- \pi^+$ candidates in (a) Belle and (b) Belle II data. Dots with error bars represent the data; solid red curves indicate the signal fit functions; dashed red lines denote the fitted combinatorial backgrounds; solid blue curves illustrate the best fit results. The gray bars show the pull distributions of the best fit results.
• Figure 3: The invariant mass spectra of (a) $\Lambda \eta$, (b) $\Lambda \eta'$, and (c) $\Lambda \pi^0$ candidates overlaid with the fit results obtained using Belle and Belle II data samples. Dots with error bars represent the number of events in data; solid red curves indicate the signal PDFs; dashed red lines denote the fitted combinatorial backgrounds; solid blue curves illustrate the fit results. The gray bars show the pull distributions of the fit results.
• Figure 4: Comparison of the branching fractions $\mathcal{B}(\Xi_c^0 \rightarrow\xspace \Lambda \eta)$, $\mathcal{B}(\Xi_c^0 \rightarrow\xspace \Lambda \eta')$, and of the measured 90% C.L. upper limit on $\mathcal{B}(\Xi_c^0 \rightarrow\xspace \Lambda \pi^0)$ with their respective theoretical predictions Zhao:2018movGeng:2018plkZou:2019kzqGeng:2019xboHsiao:2021nscZhong:2022expGeng:2023pkrZhong:2024zmeXing:2024nvg. Dots with error bars represent central values and their uncertainties; those without indicate a lack of theoretical uncertainty. Missing dots signify the absence of theoretical predictions for that decay mode. Some predictions exhibit large errors that are not fully captured within the present scale. The black dots with error bars denote the measured absolute branching fractions of decays $\Xi_c^0 \rightarrow\xspace \Lambda \eta$ and $\Xi_c^0 \rightarrow\xspace \Lambda \eta'$. The red vertical bands indicate the $\pm1\sigma$ intervals which are dominated by the systematic uncertainty of $\mathcal{B}(\Xi_c^0 \rightarrow\xspace \Xi^- \pi^+)$. The red dashed line and the black arrow indicate the measured 90% C.L. upper limits of the $\mathcal{B}(\Xi_c^0 \rightarrow\xspace \Lambda \pi^0)$. For refs. Hsiao:2021nscZhong:2022exp, (I) indicates the predicted value based on the SU(3)$_{F}$ symmetry, while (II) takes into account the breaking SU(3)$_{F}$ symmetry. For the Ref. Xing:2024nvg, (I) and (II) denote the predicted values based on real form factors alone and those incorporating complex form factors, respectively.