Effective field theory analysis of rare $|\Delta c|=|\Delta u|=1$ charm decays

We perform a global analysis of $|\Delta c| = |\Delta u| = 1$ transitions using recent data on $D^0 \to \mu^+\mu^-$, $D^+ \to \pi ^+\,\mu^+\mu^-$, $\Lambda_c \to p\,\mu^+\mu^-$, and $D^0 \to \pi^+\pi^-\,\mu^+\mu^-$ decays, and work out constraints on new physics Wilson coefficients $\mathcal{C}_{7,9,10}^{(\prime)}$. While results are consistent with the standard model, we find sizeable room for new physics that can be cleanly signaled with null test observables, not probed with searches in other sectors such as kaon and $b$-decays. The decay $D^0 \to \pi^+\pi^-\,\mu^+\mu^-$ requires better understanding of hadronic contributions to be competitive in the current fit. Progress can be achieved by precision study of the double differential decay rate in the dipion and dimuon masses, together with improved theory modelling and $D \to \pi \pi$ transition form factors. On the other hand, the 4-body decay is an important contributor to the future global analysis due to its angular distributions that probe complementary combinations of Wilson coefficients, and as a QCD laboratory. The decay $\Lambda_c \to p\,\ell^+\ell^-$ is the rising star due to the simplicity of a 3-body decay with available form factors from lattice QCD, sensitivity to both 4-fermion and electromagnetic dipole couplings and its null test forward-backward asymmetry.