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A lattice QCD determination of the $\Lambda_c \to N$ vector, axial vector,and tensor form factors is reported. The calculation was performed with $2+1$flavors of domain wall fermions at lattice spacings of $a\approx 0.11\:{\rmfm},\:0.085\:{\rm fm}$ and pion masses in the range $230\:{\rm MeV} \lesssimm_\pi \lesssim 350$ MeV. The form factors are extrapolated to the continuumlimit and the physical pion mass using modified $z$ expansions. The rates ofthe charged-current decays $\Lambda_c \to n\, e^+ \nu_e$ and $\Lambda_c \to n\,\mu^+ \nu_\mu$ are predicted to be $\left( 0.405 \pm 0.016_{\,\rm stat} \pm0.020_{\,\rm syst} \right)|V_{cd}|^2 \:{\rm ps}^{-1}$ and $\left( 0.396 \pm0.016_{\,\rm stat} \pm 0.020_{\,\rm syst} \right)|V_{cd}|^2 \:{\rm ps}^{-1}$,respectively. The phenomenology of the rare charm decay $\Lambda_c \to p\,\mu^+ \mu^-$ is also studied. The differential branching fraction, the fractionof longitudinally polarized dimuons, and the forward-backward asymmetry arecalculated in the Standard Model and in an illustrative new-physics scenario.

$\Lambda_c \to N$ form factors from lattice QCD and phenomenology of $\Lambda_c \to n \ell^+ \nu_\ell$ and $\Lambda_c \to p \mu^+ \mu^-$ decays