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The Cucchieri-Mendes bounds for the gluon propagator are discussed for thefour dimensional pure gauge SU(3) theory. Assuming a pure power law dependenceon the inverse of the lattice volume, the lattice data gives a vanishing zeromomentum gluon propagator in the infinite volume limit. Our investigation showsthat this result is robust against variations of the lattice volumes andcorrections to the power law. Moreover, it is consistent with theGribov-Zwanziger horizon condition and contradicts the SU(2) analysis, whichassumed the same type of dependence on the inverse of the volume. Our analysisconsiders also more general ansatze that, although not conclusive, open thepossibility of having $D(0) \ne 0$ in the infinite volume limit. A solution tothis puzzle requires further investigations.

Does The Lattice Zero Momentum Gluon Propagator for Pure Gauge SU(3) Yang-Mills Theory Vanish in the Infinite Volume Limit?