${\mathrm{\Lambda }}_c\to N$ form factors from lattice QCD and phenomenology of ${\mathrm{\Lambda }}_c\to n{\mathrm{\ell }}^{+}{\nu }_{\mathrm{\ell }}$ and ${\mathrm{\Lambda }}_c\to p{\mu }^{+}{\mu }^{-}$ decays

A lattice QCD determination of the ${\mathrm{\Lambda }}_c\to N$ 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 $a\approx 0.11:{\rm fm},:0.085:{\rm fm}$andpionmassesintherange$230:{\rm MeV} \lesssim m_\pi \lesssim 350$ MeV. The form factors are extrapolated to the continuum limit and the physical pion mass using modified $z$ expansions. The rates of the charged-current decays ${\mathrm{\Lambda }}_c\to n{e}^{+}{\nu }_e$ and $\Lambda_c \to n, \mu^+ \nu_\mu$arepredictedtobe$\left( 0.405 \pm 0.016_{,\rm stat} \pm 0.020_{,\rm syst} \right)|V_{cd}|^2 :{\rm ps}^{-1}$and$\left( 0.396 \pm 0.016_{,\rm stat} \pm 0.020_{,\rm syst} \right)|V_{cd}|^2 :{\rm ps}^{-1}$, respectively. The phenomenology of the rare charm decay $\Lambda_c \to p, \mu^+ \mu^-$ is also studied. The differential branching fraction, the fraction of longitudinally polarized dimuons, and the forward-backward asymmetry are calculated in the Standard Model and in an illustrative new-physics scenario.