Pinning down $\mathrm{\mid }\mathrm{\Delta }c\mathrm{\mid }=\mathrm{\mid }\mathrm{\Delta }u\mathrm{\mid }=1$ 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, ${\mathrm{\Xi }}_c^{+}\to {\mathrm{\Sigma }}^{+}(\to p{\pi }^0){\mathrm{\ell }}^{+}{\mathrm{\ell }}^{-}$, ${\mathrm{\Xi }}_c^0\to {\mathrm{\Lambda }}^0(\to p{\pi }^{-}){\mathrm{\ell }}^{+}{\mathrm{\ell }}^{-}$ and $\Omega_c^0\to\Xi^0,(\to \Lambda^{0} \pi^0)\ell^+\ell^-$. Such self-analyzing decay chains allow for seven additional observables compared to three-body decays such as $\Lambda_c \to p \ell^+ \ell^-$,withdifferentsensitivitiestothe$|\Delta c|=|\Delta u|=1$weakcouplings\mathrm{.}Opportunitiestotestthestandardmodelin$c \to u$ transitions with standard model null tests and other angular observables are worked out. We show that a joint model-independent analysis of the leptonic $A_{\text{FB}}^{\mathrm{\ell }}$, hadronic $A_{\text{FB}}^{\text{H}}$, and combined forward-backward asymmetry $A_{\text{FB}}^{\mathrm{\ell }\text{H}}$ together with the fraction of longitudinally produced leptons, $F_L$, is able to pin down the dipole couplings $C_7,C_7^{\mathrm{\prime }}$ and the semileptonic (axial-) vector ones $C_{10},C_9^{\mathrm{\prime }},C_{10}^{\mathrm{\prime }}$. $A_{\text{FB}}^{\text{H}}$ is also accessible with dineutrino $c\to u\nu \bar{\nu }$ modes and probes right-handed currents.