Resolving puzzle in ${\Xi }_c^0\to {\Xi }^{-}{e}^{+}{\nu }_e$ with ${\Xi }_c-{\Xi }_c^{\prime }$ mixing

Abstract

We study the ratio of $R=2\Gamma ({\Xi }_c^0\to {\Xi }^{-}{e}^{+}{\nu }_e)/3\Gamma ({\Lambda }_c^{+}\to \Lambda e^{+}{\nu }_e)$, which is found to be $R=1(0.8)$ from the exact (broken) $SU(3)$ flavor symmetry, in sharp contrast to the average value of $R_{av}=0.59\pm 0.10$ from the ALICE collaboration and lattice QCD results. We propose to use the mixing of ${\Xi }_c-{\Xi }_c^{\prime }$ to resolve the puzzle. With the model-independent mass relations, we find that the mixing angle is $|{\theta }_c|=0.137(5)\pi$, which suppresses ${\Xi }_c\to \Xi e^{+}{\nu }_e$ about $20\%$ model-independently, resulting in $R\approx 0.6$ with the $SU(3)$ flavor breaking effect. We explicitly demonstrate that $R=0.70\pm 0.09$ from the bag model, which is also consistent with $R_{av}$. To test the mixing mechanism, we recommend the experiments to measure the decays of ${\Xi }_c\to {\Xi }^{\prime }(1530)e^{+}{\nu }_e$, whose branching fractions are determined to be $(4.4\sim 8.7)\times 10^{-3}$ and $(1.3\sim 2.6)\%$ for ${\Xi }_c^0$ and ${\Xi }_c^{+}$, respectively, but vanish without the mixing. In addition, nonvanishing values of $\mathcal{B}({\Xi }_c^{+}\to {\Xi }^{\prime 0}(1530){\pi }^{+})$ and $\mathcal{B}({\Xi }_c^{+}\to {\Sigma }^{\prime +}(1530){\overline{K}}^0)$ will also be evidences of the mixing based on the Köner-Pati-Woo theorem, which are calculated as $(3.8\sim 7.5)\times 10^{-3}$ and $(6.6\sim 13)\times 10^{-4}$, respectively. We emphasize that ${\theta }_c$ is sizable and should be given serious considerations in future studies on the heavy baryon systems.

Comments: 16 pages, 4 figures, accepted by PLB