  Thermal leptogenesis, in the framework of the standard model with three
additional heavy Majorana neutrinos, provides an attractive scenario to explain
the observed baryon asymmetry in the universe. It is based on the
out-of-equilibrium decay of Majorana neutrinos in a thermal bath of standard
model particles, which in a fully quantum field theoretical formalism is
obtained by solving Kadanoff-Baym equations. So far, the leading two-loop
contributions from leptons and Higgs particles are included, but not yet gauge
corrections. These enter at three-loop level but, in certain kinematical
regimes, require a resummation to infinite loop order for a result to leading
order in the gauge coupling. In this work, we apply such a resummation to the
calculation of the lepton number density. The full result for the simplest
"vanilla leptogenesis" scenario is by $\mathcal{O}(1)$ increased compared to
that of quantum Boltzmann equations, and for the first time permits an estimate
of all theoretical uncertainties. This step completes the quantum theory of
leptogenesis and forms the basis for quantitative evaluations, as well as
extensions to other scenarios.
