Pinning down $$|\Delta c|=|\Delta u|=1$$ couplings with rare charm baryon decays

We study the full angular distribution of semileptonic rare charm baryon decays in which secondary undergoes weak decay with sizable polarization parameter, $\Xi_c^+\to\Sigma^+\,(\to p\pi^0)\ell^+\ell^-$, $\Xi_c^0\to\Lambda^0\,(\to p \pi^-)\ell^+\ell^-$ and $\Omega_c^0\to\Xi^0\,(\to \Lambda^{0} \pi^0)\ell^+\ell^-$. Such self-analyzing chains allow for seven additional observables compared to three-body such as $\Lambda_c \to \ell^+ \ell^-$, different sensitivities $|\Delta c|=|\Delta u|=1$ couplings. Opportunities test standard model $c u$ transitions null tests other are worked out. show that a joint model-independent analysis leptonic $A_{\text{FB}}^\ell$, hadronic $A_{\text{FB}}^{\text{H}}$, combined forward-backward asymmetry $A_{\text{FB}}^{\ell\text{H}}$ together fraction longitudinally produced leptons, $F_L$, is able pin down dipole couplings $C_{7},C^\prime_{7}$ (axial-) vector ones $C_{10},C^\prime_{9},C^\prime_{10}$. $A_{\text{FB}}^{\text{H}}$ also accessible dineutrino u \nu \bar \nu$ modes probes right-handed currents.