  We theoretically study the many-body effects of electron electron interaction
on the single particle spectral function of doped bilayer graphene. Using
random phase approximation, we calculate the real and imaginary part of the
self-energy and hence the spectral function. The spectral function near the
Fermi surface shows the usual quasiparticle peak, establishing doped bilayer
graphene, in contrast to the unstable neutral system, to be a Fermi liquid.
Away from the Fermi surface, an additional broad plasmaron peak is visible in
the spectral function. From the low energy behaviour of the self-energy we
calculate the quasiparticle residue and the effective mass of the
quasiparticles as a function of carrier density. We present results for both
the on-shell and the off-shell approximation for the quasiparticle
renormalization.
