  A longstanding question in QCD is the origin of the mass gap in the
Yang-Mills sector of QCD, i.e., QCD without quarks. In Landau gauge QCD this
mass gap, and hence confinement, is encoded in a mass gap of the gluon
propagator, which is found both in lattice simulations and with functional
approaches. While functional methods are well suited to unravel the mechanism
behind the generation of the mass gap, a fully satisfactory answer has not yet
been found. In this work we solve the coupled Dyson-Schwinger equations for the
ghost propagator, gluon propagator and three-gluon vertex. We corroborate the
findings of earlier works, namely that the mass gap generation is tied to the
longitudinal projection of the gluon self-energy, which acts as an effective
mass term in the equations. Because an explicit mass term is in conflict with
gauge invariance, this leaves two possible scenarios: If it is viewed as an
artifact, only the scaling solution survives; if it is dynamical, gauge
invariance can only be preserved if there are longitudinal massless poles in
either of the vertices. We find that there is indeed a massless pole in the
ghost-gluon vertex, however in our approximation with the assumption of
complete infrared dominance of the ghost this pole is only present for the
scaling solution. We also put forward a possible mechanism that may reconcile
the scaling solution, with an infrared dominance of the ghost, with the
decoupling solutions based on longitudinal poles in the three-gluon vertex as
seen in the PT-BFM scheme.
