Mixing effects of $Σ^0-Λ^0$ in $Λ_c^+$ decays

We analyze the mixing between $Σ^0$ and $Λ^0$ 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 $Σ^0$ and $Λ^0$ is $(2.07\pm 0.03)\times 10^{-2}$, which leads to the decay branching fraction and up-down asymmetry of $Λ_c^+ \to Σ^0 e^+ ν_e$ to be ${\cal B}(Λ_c^+ \to Σ^0 e^+ ν_e)=(1.5\pm 0.2)\times 10^{-5}$ and $α(Λ_c^+ \to Σ^0 e^+ ν_e)=-0.86\pm 0.04$, respectively. Moreover, we obtain that $Δ{\cal B}\equiv {\cal B}(Λ_c^+\to Σ^0 π^+) - {\cal B}(Λ_c^+\to Σ^+π^0)=(3.8\pm 0.5)\times 10^{-4}$ and $Δα\equivα(Λ_c^+\to Σ^0 π^+) -α(Λ_c^+\to Σ^+π^0)=(-1.6\pm 0.7)\times10^{-2}$, which should vanish without the mixing.

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