  The Coulomb interaction between massless Dirac fermions may induce dynamical
chiral symmetry breaking by forming excitonic pairs in clean graphene, leading
to semimetal-insulator transition. If the Dirac fermions have zero bare mass,
an exact continuous chiral symmetry is dynamically broken and thus there are
massless Goldstone excitons. If the Dirac fermions have a small bare mass, an
approximate continuous chiral symmetry is dynamically broken and the resultant
Goldstone type excitons become massive, which is analogous to what happens in
QCD. In this paper, after solving Dyson-Schwinger gap equation in the presence
of a small bare fermion mass, we found a remarkable reduction of the critical
Coulomb interaction strength for excitonic pair formation and a strong
enhancement of dynamical fermion mass. We then calculate the masses of
Goldstone type excitons using the SVZ sum rule method and operator product
expansion technique developed in QCD and find that the exciton masses are much
larger than bare fermion mass but smaller than dynamical fermion mass gap. We
also study the spin susceptibilities and estimate the masses of non-Goldstone
type excitons using the same tools.
