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

Rare $\Lambda_c\to p \ell^+\ell^-$ decay in the relativistic quark model