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