  Contrary to the common lore based on naive dimensional analysis, the seesaw
scale for neutrino masses can be naturally in the TeV range, with small
parameters coming from radiative corrections. We present one such class of
type-I seesaw models, based on the left-right gauge group $SU(2)_L\times
SU(2)_R\times U(1)_{B-L}$ realized at the TeV scale, which fits the observed
neutrino oscillation parameters as well as other low energy constraints. We
discuss how the small parameters of this scenario can arise naturally from one
loop effects. The neutrino fits in this model use quasi-degenerate heavy
Majorana neutrinos, as also required to explain the matter-antimatter asymmetry
in our Universe via resonant leptogenesis mechanism. We discuss the constraints
implied by the dynamics of this mechanism on the mass of the right-handed gauge
boson in this class of models with enhanced neutrino Yukawa couplings compared
to the canonical seesaw model and find a lower bound of $m_{W_R}\geq 9.9$ TeV
for successful leptogenesis assuming maximal CP asymmetry for each flavor. We
also present a model with explicit neutrino mass fit, where the lower bound
goes up to 13.1 TeV due to less than maximal primordial CP asymmetry predicted
by the model.
