Pinning down |Δ c |=|Δ u |=1 couplings with rare charm baryon decays

We study the full angular distribution of semileptonic rare charm baryon decays in which the secondary baryon undergoes weak decay with sizable polarization parameter, Ξ_c⁺→Σ⁺(→p π⁰) ℓ⁺ℓ^- , Ξ_c⁰→Λ⁰(→p π^-) ℓ⁺ℓ^- and Ω_c⁰→Ξ⁰(→Λ⁰π⁰) ℓ⁺ℓ^- . Such self-analyzing decay chains allow for seven additional observables compared to three-body decays such as Λ_c→p ℓ⁺ℓ^- , with different sensitivities to the |Δ c |=|Δ u |=1 weak couplings. Opportunities to test the standard model in c →u transitions with standard model null tests and other angular observables are worked out. We show that a joint model-independent analysis of the leptonic A_FB^ℓ, hadronic A_FB^H, and combined forward-backward asymmetry A_FB^{ℓ H} together with the fraction of longitudinally produced leptons, F_L, is able to pin down the dipole couplings C₇,C₇^' and the semileptonic (axial-) vector ones C₁₀,C₉^',C₁₀^' . A_FB^H is also accessible with dineutrino c →u ν ν ¯ modes and probes right-handed currents.