  We review how vertex constraints inherited from the thermal ground state
strongly reduce the integration support of loop four-momenta associated with
massive quasi-particles in bubble diagrams constituting corrections to the free
thermal quasi-particle pressure. In spite of the observed increasingly
suppressing effect when increasing 2-particle-irreducible (2PI) loop order, a
quantitative analysis enables us to disprove the conjecture voiced in
hep-th/0609033 that the loop expansion would terminate at a finite order. This
reveals the necessity to investigate exact expressions of (at least some)
higher-loop order diagrams. Explicit calculation shows that although the
behaviour of the 2PI three-loop contribution at low temperatures displays
hierarchical suppression compared to lower loop-orders, its high-temperature
expression instead dominates all lower orders. However, an all-loop-order
resummation of a class of 2PI bubble diagrams is shown to yield an analytic
continuation of the low-temperature hierarchy to all temperatures in the
deconfining phase.
