  A theoretical investigation of the possible existence of the chiral polaron
formation in graphene is reported. We present an analytical method to calculate
the ground-state of the electron-phonon system within the framework of the
Lee-Low and Pines theory. On the basis of our model, the influence of
electron-optical phonon interaction onto the graphene electronic spectrum is
examined. In this paper, we only considered doubly degenerate optical phonon
modes of E_2g symmetry near the zone center Gamma. We show analytically that
the energy dispersions of both valance and conduction bands of the pristine
graphene differ significantly than those obtained through the standard electron
self energy calculations due to the electron-phonon interactions. Furthermore,
we prove that the degenerate band structure of the graphene promote the chiral
polaron formation.
