Probing for New Physics with Rare Charm Baryon ($\Lambda_c$, $\Xi_c$, $\Omega_c$) Decays

We analyze rare charm baryon decays within the standard model and beyond. We identify all null test observables in unpolarized $\Lambda_c \to p \ell^+ \ell^-$, $\ell=e, \mu$ decays, and study the new physics sensitivities. We find that the longitudinal dilepton polarization fraction $F_L$ is sensitive to electromagnetic dipole couplings $C_{7}^{(\prime)}$, and to the right-handed 4-fermion vector coupling $C_{9}^\prime$. The forward-backward asymmetry, $A_{\rm FB}$, due to the GIM-suppression a standard model null test already, probes the left-handed axialvector 4-fermion coupling $C_{10}$; its CP-asymmetry, $A_{\rm FB}^{\rm CP}$, probes CP-violating phases in $C_{10}$. Physics beyond the standard model can induce branching ratios of dineutrino modes $\Lambda_c \to p \nu \bar \nu $ up to a few times $10^{-5}$, and one order of magnitude smaller if lepton flavor universality is assumed, while standard model rates are negligible. Charged lepton flavor violation allows for striking signals into $e^\pm \mu^\mp$ final states, up to $10^{-6}$ branching ratios model-independently, and up to order $10^{-8}$ in leptoquark models. Related three-body baryon decays $\Xi_c \to \Sigma \ell \ell$, $\Xi_c \to \Lambda \ell \ell$ and $\Omega_c \to \Xi \ell \ell$ offer similar opportunities to test the standard model with $|\Delta c|=|\Delta u|=1$ transitions.