Mixing effects of ${\Sigma }^0-{\Lambda }^0$ in ${\Lambda }_c^{+}$ decays

Abstract

We analyze the mixing between ${\Sigma }^0$ and ${\Lambda }^0$ based on the baryon masses. We distinguish the contributions from QCD and QED in the baryon mass splittings. We find that the mixing angle between ${\Sigma }^0$ and ${\Lambda }^0$ is $(2.07\pm 0.03)\times 10^{-2}$, which leads to the decay branching fraction and up-down asymmetry of ${\Lambda }_c^{+}\to {\Sigma }^0{e}^{+}{\nu }_e$ to be $\mathcal{B}({\Lambda }_c^{+}\to {\Sigma }^0{e}^{+}{\nu }_e)=(1.5\pm 0.2)\times 10^{-5}$ and $\alpha ({\Lambda }_c^{+}\to {\Sigma }^0{e}^{+}{\nu }_e)=-0.86\pm 0.04$, respectively. Moreover, we obtain that $\Delta \mathcal{B}\equiv \mathcal{B}({\Lambda }_c^{+}\to {\Sigma }^0{\pi }^{+})-\mathcal{B}({\Lambda }_c^{+}\to {\Sigma }^{+}{\pi }^0)=(3.8\pm 0.5)\times 10^{-4}$ and $\Delta \alpha \equiv \alpha ({\Lambda }_c^{+}\to {\Sigma }^0{\pi }^{+})-\alpha ({\Lambda }_c^{+}\to {\Sigma }^{+}{\pi }^0)=(-1.6\pm 0.7)\times 10^{-2}$, which should vanish without the mixing.

Comments: 11 pages, no figure, version accepted by PRD