Rare Λ_cto p ell^+ell^- decay in the relativistic quark model

The relativistic quark model based on the quasipotential approach with the QCD-motivate potential is employed for the calculation of the form factors of the $\Lambda_c\to p$ rare weak transitions. Their momentum dependence is explicitly determined without additional assumptions and extrapolations in the whole kinematical range of the momentum transfer squared $q^2$. The differential $\Lambda_c\to p l^+l^-$ decay branching fractions and angular distributions are calculated on the basis of these form factors. Both the perturbative and effective Wilson coefficients, which include contributions of vector meson resonances, are used. The calculated branching fraction of the $\Lambda_c\to p \mu^+\mu^-$ rare decay is well consistent with the experimental upper limit very recently set by the LHCb Collaboration.