Polarizability of non-interacting 2D Dirac electrons has a 1/ √ qv − ω singularity at the boundary of electron-hole excitations. The screening of this singularity by long-range electron-electron interactions is usually treated within the random phase approximation. The latter is exact only in the limit of N → ∞, where N is the "color" degeneracy. We find that the ladder-type vertex corrections become crucial close to the threshold as the ratio of the n-th order ladder term to the same order RPA contribution is ln n |qv − ω|/N n . We perform analytical summation of the infinite series of ladder diagrams which describe excitonic effect. Beyond the threshold, qv > ω, the real part of the polarization operator is found to be positive leading to the appearance of a strong and narrow plasmon resonance.PACS numbers: 73.23. -b, 72.30.+q Introduction. Many properties of interacting twodimensional electrons with linear Dirac spectrum ǫ = ±vp, found in graphene monolayers, differ sharply from those with the parabolic spectrum present in conventional semiconductor heterostructures [1,2]. Vanishing density of states at the Dirac point and less effective screening of Coulomb interaction lead to electronic properties of graphene being qualitatively different.One of the distinct signatures of non-interacting 2D electrons in graphene, caused by the absence of spectrum curvature, is a divergent behavior of the polarization operator (charge susceptibility) at the threshold for the excitation of electron-hole pairs [3,4,5,6,7], Π (0) (ω, q) = −N q 2 /16 q 2 v 2 − ω 2 , where N is the degree of degeneracy (in graphene N = 4 in the absence of magnetic field). The effects of electron-electron interaction on the polarization operator are customarily accounted for by the random phase approximation (RPA) [5,8,9,10], which sums the infinite series of electron loops,

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