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In any calculation in perturbative Quantum Chromodynamics (QCD) a choiceneeds to be made for the unphysical renormalisation scale, $\mu_R$. TheBrodsky-Lepage-Mackenzie/Principle of Maximum Conformality (BLM/PMC)scale-setting procedure is one proposed method for selecting this scale. Inthis work we identify three ambiguities in the BLM/PMC procedure itself. Theirnumerical impact is studied using the example of the total cross-section for$t\bar{t}$ production through Next-to-Next-to-Leading Order in QCD. Oneambiguity is the arbitrary choice of the value of the highest-order PMC scale.The numerical impact of this choice on the BLM/PMC prediction for thecross-section is found to be comparable to the impact of the choice of $\mu_R$in the conventional scale-setting approach. Another ambiguity relates to thedefinitions of the other PMC scales and is similarly found to have a largeimpact on the cross-section.

Ambiguities of the principle of maximum conformality procedure for hadron collider processes