Renormalization group invariance and optimal QCD renormalization scale-setting: a key issues review

Area of Science:

• High Energy Physics
• Quantum Field Theory
• Particle Physics

Background:

• Renormalization group invariance (RGI) is crucial for valid physical predictions in quantum field theory.
• Perturbative quantum chromodynamics (pQCD) calculations often struggle with scheme dependence and convergence.
• Previous work introduced scale-setting approaches for RGI in pQCD.

Purpose of the Study:

• To provide an in-depth comparison of two RGI-based scale-setting methods: PMC and PMS.
• To analyze the performance of PMC and PMS for physical observables R(e+e-) and [Formula: see text] at four-loop order in pQCD.
• To evaluate the convergence properties and scale dependence of predictions from each method.

Main Methods:

• The Principle of Maximum Conformality (PMC) absorbs β-function terms into the running coupling's scale.
• The Principle of Minimum Sensitivity (PMS) determines the optimal renormalization scale by minimizing the observable's slope.
• Analysis of R(e+e-) and [Formula: see text] observables up to four-loop order in pQCD.

Main Results:

• Both PMC and PMS show small scale dependence at four-loop order, agreeing with conventional methods.
• PMC demonstrates superior pQCD series convergence by eliminating renormalon terms, unlike PMS.
• PMC predictions exhibit highly suppressed residual scale dependence, even at low orders.

Conclusions:

• The PMC provides a rigorous foundation for high-precision pQCD predictions by ensuring RGI.
• PMC effectively eliminates systematic errors associated with arbitrary scale choices.
• PMC is broadly applicable to various high-energy hadronic processes, including multi-scale problems.