Analysis of hadronic weak decays of charmed baryons in the topological diagrammatic approach

We present a study of $$ {\Xi}_c^0\to {\Xi}^0{\pi}^0 $$ Ξ c 0 → Ξ 0 π 0 , $$ {\Xi}_c^0\to {\Xi}^0\eta $$ Ξ c 0 → Ξ 0 η , and $$ {\Xi}_c^0\to {\Xi}^0{\eta}^{\prime } $$ Ξ c 0 → Ξ 0 η ′ decays using the Belle and Belle II data samples, which have integrated luminosities of 980 fb−1 and 426 fb−1, respectively. We measure the following relative branching fractions$$ {\displaystyle \begin{array}{c}\mathcal{B}\left({\Xi}_c^0\to {\Xi}^0{\pi}^0\right)/\mathcal{B}\left({\Xi}_c^0\to {\Xi}^{-}{\pi}^{+}\right)=0.48\pm 0.02\left(\textrm{stat}\right)\pm 0.03\left(\textrm{syst}\right),\\ {}\mathcal{B}\left({\Xi}_c^0\to {\Xi}^0\eta \right)/\mathcal{B}\left({\Xi}_c^0\to {\Xi}^{-}{\pi}^{+}\right)=0.11\pm 0.01\left(\textrm{stat}\right)\pm 0.01\left(\textrm{syst}\right),\\ {}\mathcal{B}\left({\Xi}_c^0\to {\Xi}^0{\eta}^{\prime}\right)/\mathcal{B}\left({\Xi}_c^0\to {\Xi}^{-}{\pi}^{+}\right)=0.08\pm 0.02\left(\textrm{stat}\right)\pm 0.01\left(\textrm{syst}\right)\end{array}} $$ B Ξ c 0 → Ξ 0 π 0 / B Ξ c 0 → Ξ − π + = 0.48 ± 0.02 stat ± 0.03 syst , B Ξ c 0 → Ξ 0 η / B Ξ c 0 → Ξ − π + = 0.11 ± 0.01 stat ± 0.01 syst , B Ξ c 0 → Ξ 0 η ′ / B Ξ c 0 → Ξ − π + = 0.08 ± 0.02 stat ± 0.01 syst for the first time, where the uncertainties are statistical (stat) and systematic (syst). By multiplying by the branching fraction of the normalization mode, $$ \mathcal{B}\left({\Xi}_c^0\to {\Xi}^{-}{\pi}^{+}\right) $$ B Ξ c 0 → Ξ − π + , we obtain the following absolute branching fraction results$$ {\displaystyle \begin{array}{c}\mathcal{B}\left({\Xi}_c^0\to {\Xi}^0{\pi}^0\right)=\left(6.9\pm 0.3\left(\textrm{stat}\right)\pm 0.5\left(\textrm{syst}\right)\pm 1.3\left(\operatorname{norm}\right)\right)\times {10}^{-3},\\ {}\mathcal{B}\left({\Xi}_c^0\to {\Xi}^0\eta \right)=\left(1.6\pm 0.2\left(\textrm{stat}\right)\pm 0.2\left(\textrm{syst}\right)\pm 0.3\left(\operatorname{norm}\right)\right)\times {10}^{-3},\\ {}\mathcal{B}\left({\varXi}_c^0\to {\Xi}^0{\eta}^{\prime}\right)=\left(1.2\pm 0.3\left(\textrm{stat}\right)\pm 0.1\left(\textrm{syst}\right)\pm 0.2\left(\operatorname{norm}\right)\right)\times {10}^{-3},\end{array}} $$ B Ξ c 0 → Ξ 0 π 0 = 6.9 ± 0.3 stat ± 0.5 syst ± 1.3 norm × 10 − 3 , B Ξ c 0 → Ξ 0 η = 1.6 ± 0.2 stat ± 0.2 syst ± 0.3 norm × 10 − 3 , B Ξ c 0 → Ξ 0 η ′ = 1.2 ± 0.3 stat ± 0.1 syst ± 0.2 norm × 10 − 3 , where the third uncertainties are from $$ \mathcal{B}\left({\Xi}_c^0\to {\Xi}^{-}{\pi}^{+}\right) $$ B Ξ c 0 → Ξ − π + . The asymmetry parameter for $$ {\Xi}_c^0\to {\Xi}^0{\pi}^0 $$ Ξ c 0 → Ξ 0 π 0 is measured to be $$ \alpha \left({\Xi}_c^0\to {\Xi}^0{\pi}^0\right)=-0.90\pm 0.15\left(\textrm{stat}\right)\pm 0.23\left(\textrm{syst}\right) $$ α Ξ c 0 → Ξ 0 π 0 = − 0.90 ± 0.15 stat ± 0.23 syst .

Measurements of the branching fractions of $$ {\Xi}_c^0\to {\Xi}^0{\pi}^0 $$, $$ {\Xi}_c^0\to {\Xi}^0\eta $$, and $$ {\Xi}_c^0\to {\Xi}^0{\eta}^{\prime } $$ and asymmetry parameter of $$ {\Xi}_c^0\to {\Xi}^0{\pi}^0 $$

Adachi,

Aggarwal,

Aihara

et al. 2024

Final-state rescattering mechanism of charmed baryon decays

Jia,

Jiang,

Wang

et al. 2024

The dynamical studies on the non-leptonic weak decays of charmed baryons are always challenging, due to the large non-perturbative contributions at the charm scale. In this work, we develop the final-state rescattering mechanism to study the two-body non-leptonic decays of charmed baryons. The final-state interaction is a physical picture of long-distance effects. Instead of using the Cutkosky rule to calculate the hadronic triangle diagrams which can only provide the imaginary part of decay amplitudes, we point out that the loop integral is more appropriate, as both the real parts and the imaginary parts of amplitudes can be calculated completely. In this way, it can be obtained for the non-trivial strong phases which are essential to calculate CP violations. With the physical picture of long-distance effects and the reasonable method of calculations, it is amazingly achieved that all the nine existing experimental data of branching fractions for the $$ {\Lambda}_c^{+} $$ Λ c + decays into an octet light baryon and a vector meson can be explained by only one parameter of the model. Besides, the decay asymmetries and CP violations are not sensitive to the model parameter, since the dependence on the parameter is mainly cancelled in the ratios, so that the theoretical uncertainties on these observables are lowered down.

Systematics of U-spin sum rules for systems with direct sums

Gavrilova,

Schacht

2024

A rich mathematical structure underlying flavor sum rules has been discovered recently. In this work, we extend these findings to systems with a direct sum of representations. We prove several results for the general case. We derive an algorithm that enables the determination of all U-spin amplitude sum rules at arbitrary order of the symmetry breaking for any system containing a direct sum of the representations 0 ⨁ 1. Potential applications are numerous and include, for example, higher order sum rules for CP-violating charm decays with an arbitrary number of final states.