  Optical pump-terahertz probe differential transmission measurements of
as-prepared single layer graphene (AG)(unintentionally hole doped with Fermi
energy $E_F$ at $\sim$180 meV), nitrogen doping compensated graphene (NDG) with
$E_F$ $\sim$10 meV and thermally annealed doped graphene (TAG) are examined
quantitatively to understand the opposite signs of photo-induced dynamic
terahertz conductivity $\Delta\sigma$. It is negative for AG and TAG but
positive for NDG. We show that the recently proposed mechanism of multiple
generations of secondary hot carriers due to Coulomb interaction of
photoexcited carriers with the existing carriers together with the intraband
scattering can explain the change of photoinduced conductivity sign and its
magnitude. We give a quantitative estimate of $\Delta\sigma$ in terms of
controlling parameters - the Fermi energy $E_F$ and momentum relaxation time
$\tau$. Further, the cooling of photoexcited carriers is analyzed using
super-collision model which involves defect mediated collision of the hot
carriers with the acoustic phonons, thus giving an estimate of the deformation
potential.
