  We address the puzzling weak-coupling perturbative behavior of graphene
interaction effects as manifested experimentally, in spite of the effective
fine structure constant being large, by calculating the effect of Coulomb
interactions on the quasiparticle properties to next-to-leading order in the
random phase approximation (RPA). The focus of our work is graphene suspended
in vacuum, where electron-electron interactions are strong and the system is
manifestly in a nonperturbative regime. We report results for the quasiparticle
residue and the Fermi velocity renormalization at low carrier density. The
smallness of the next-to-leading order corrections that we obtain demonstrates
that the RPA theory converges rapidly and thus, in contrast to the usual
perturbative expansion in the bare coupling constant, constitutes a
quantitatively predictive theory of graphene many-body physics for any coupling
strength.
