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

## TL;DR

This paper investigates ambiguities in the BLM/PMC scale-setting procedure in perturbative QCD, demonstrating their significant impact on predictions for top-antitop production cross-sections at hadron colliders.

## Contribution

It identifies three key ambiguities in the BLM/PMC method and assesses their numerical effects on QCD predictions for top-quark pair production.

## Key findings

- Ambiguity in the highest-order PMC scale choice affects cross-section predictions.
- Definitions of other PMC scales also significantly influence results.
- Numerical impact of ambiguities is comparable to conventional scale-setting uncertainties.

## Abstract

In any calculation in perturbative Quantum Chromodynamics (QCD) a choice needs to be made for the unphysical renormalisation 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 $t\bar{t}$ 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.