| Summary: | Abstract We study the full angular distribution of semileptonic rare charm baryon decays in which the secondary baryon undergoes weak decay with sizable polarization parameter, $$\Xi _c^+\rightarrow \Sigma ^+\,(\rightarrow p\pi ^0)\ell ^+\ell ^-$$ Ξ c + → Σ + ( → p π 0 ) ℓ + ℓ - , $$\Xi _c^0\rightarrow \Lambda ^0\,(\rightarrow p \pi ^-)\ell ^+\ell ^-$$ Ξ c 0 → Λ 0 ( → p π - ) ℓ + ℓ - and $$\Omega _c^0\rightarrow \Xi ^0\,(\rightarrow \Lambda ^{0} \pi ^0)\ell ^+\ell ^-$$ Ω c 0 → Ξ 0 ( → Λ 0 π 0 ) ℓ + ℓ - . Such self-analyzing decay chains allow for seven additional observables compared to three-body decays such as $$\Lambda _c \rightarrow p \ell ^+ \ell ^-$$ Λ c → p ℓ + ℓ - , with different sensitivities to the $$|\Delta c|=|\Delta u|=1$$ | Δ c | = | Δ u | = 1 weak couplings. Opportunities to test the standard model in $$c \rightarrow u$$ 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 $$A_{\text {FB}}^\ell $$ A FB ℓ , hadronic $$A_{\text {FB}}^{\text {H}}$$ A FB H , and combined forward–backward asymmetry $$A_{\text {FB}}^{\ell \text {H}}$$ A FB ℓ H together with the fraction of longitudinally produced leptons, $$F_L$$ F L , is able to pin down the dipole couplings $$C_{7},C^\prime _{7}$$ C 7 , C 7 ′ and the semileptonic (axial-) vector ones $$C_{10},C^\prime _{9},C^\prime _{10}$$ C 10 , C 9 ′ , C 10 ′ . $$A_{\text {FB}}^{\text {H}}$$ A FB H is also accessible with dineutrino $$c \rightarrow u \nu {\bar{\nu }}$$ c → u ν ν ¯ modes and probes right-handed currents.
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