  We reexamine the effect of long-range Coulomb interactions on the
quasiparticle velocity in graphene. Using a nonperturbative functional
renormalization group approach with partial bosonization in the forward
scattering channel and momentum transfer cutoff scheme, we calculate the
quasiparticle velocity, $v (k)$, and the quasiparticle residue, $Z$, with
frequency-dependent polarization. One of our most striking results is that $v (
k ) \propto \ln [ C_k (\alpha) / k ]$ where the momentum- and
interaction-dependent cutoff scale $C_k (\alpha) $ vanishes logarithmically for
$k \rightarrow 0$. Here $k$ is measured with respect to one of the charge
neutrality (Dirac) points and $\alpha=2.2$ is the strength of dimensionless
bare interaction. Moreover, we also demonstrate that the so-obtained
multilogarithmic singularity is reconcilable with the perturbative expansion of
$v (k)$ in powers of the bare interaction.
