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

In any calculation in perturbative quantum chromodynamics (QCD) a choice needs to be made for the unphysical renormalization scale, mu(R). The Brodsky-Lepage-Mackenzie/principle of maximum conformality (BLM/PMC) scale-setting procedure is one proposed method for selecting this scale. In this work we identify three ambiguities in the BLM/PMC procedure itself. Their numerical impact is studied using the example of the total cross section for t (t) over bar production through next-to-next-to-leading order in QCD. One ambiguity 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 the cross 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 the definitions of the other PMC scales and is similarly found to have a large impact on the cross section.