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Angular Distributions for Multi-body Semileptonic Charmed Baryon Decays

We perform an analysis of angular distributions in semileptonic decays of charmed baryons $B_1^{(\prime)}\to B_2^{(\prime)}(\to B_3^{(\prime)}B_4^{(\prime)})\ell^+ν_{\ell}$, where the $B_1=(Λ_c^+,Ξ_c^{(0,+)})$ are the SU(3)-antitriplet baryons and $B_1'=Ω_c^-$ is an SU(3) sextet. We will firstly derive analytic expressions for angular distributions using helicity amplitude technique. Based on the lattice QCD results for $Λ_c^+\toΛ$ and $Ξ_c^0\toΞ^-$ form factors and model calculation of the $Ω_c^0\toΩ^-$ transition, we predict branching fractions: $\mathcal{B}(Λ_{c}^{+} \rightarrow p π^{-} e^{+} ν_{e})=2.48(15)\%$, $\mathcal{B}(Λ_{c}^+\rightarrow p π^{-}μ^{+}ν_μ)=2.50(14)\%$, $\mathcal{B}(Ξ_{c}\rightarrow Λπ^{-}e^{+}ν_{e})=2.40(30)\%$, $\mathcal{B}(Ξ_{c}\rightarrow Λπ^{-}μ^{+}ν_ν)=2.41(30)\%$, $\mathcal{B}(Ω_{c}\rightarrow ΛK^{-}e^{+}ν_{e})=0.362(14)\%$, $\mathcal{B}(Ω_{c}\rightarrow ΛK^{-}μ^{+}ν_ν)=0.350(14)\%$. Besides, we also predict the $q^2$-dependence and angular distributions of these processes, in particular the coefficients for the $\cos nθ_{\ell}$ ($\cos nθ_{h}$, $\cos nϕ$) $(n=0, 1, 2, \cdots)$ terms. This work can provide a theoretical basis for the ongoing experiments at BESIII, LHCb and BELLE-II.