Prospects of discovering new physics in rare charm decays

The LHCb bounds on the branching ratio of rare decay $D^0 \to \mu^+ \mu^-$ and the constraints on the branching ratio of $D^+ \to \pi^+ \mu^+ \mu^-$ in the nonresonant regions enable us to improve constraints on new physics contributions. Using the effective Lagrangian approach we determine sizes of the Wilson coefficients allowed by the existing LHCb bounds on rare charm decays. Then we discuss contributions to rare charm meson decay observables in several models of new physics: a model with an additional spin-1 weak triplet, leptoquark models, Two Higgs doublets model of type III, and a $Z'$ model. Here we complement the discussion by $D^0 - \bar D^0$ oscillations data. Among considered models, only leptoquarks can significantly modify Wilson coefficients. Assuming that the differential decay width for $D^+ \to \pi^+ \mu^+ \mu^-$ receives NP contribution, while the differential decay width for $D^+ \to \pi^+ e^+ e^-$ is Standard Model-like, we find that lepton flavor universality can be violated and might be observed at high dilepton invariant mass.