  We discuss leptogenesis in a model with heavy right-handed Majorana neutrinos
propagating in a constant but otherwise generic CPT-violating axial time-like
background (which could be motivated by string theory considerations). At
temperatures much higher than the temperature of the electroweak phase
transition we solve analytically but approximately (using Pade approximants)
the corresponding Boltzmann equations, which describe lepton asymmetry
generation due to the tree-level decays of the heavy neutrinos into standard
model leptons. These leptons are effectively massless at such temperatures. The
current work completes in a rigorous way a preliminary treatment of the same
system, by some of the present authors. In this earlier work, lepton asymmetry
was crudely estimated considering the decay of a right-handed neutrino at rest.
Our present analysis includes thermal momentum modes for the heavy neutrino and
this leads to a total lepton asymmetry which is bigger by a factor of two as
compared to the previous estimate. Nevertheless, our current and preliminary
results for the freezeout are found to be in agreement (within a 12.5%
uncertainty). Our analysis depends on a novel use of Pade approximants to solve
the Boltzmann equations and may be more widely useful in cosmology.
