Systematic all-orders method to eliminate renormalization-scale and scheme ambiguities in perturbative QCD

Area of Science:

• High Energy Physics
• Quantum Field Theory
• Particle Physics

Background:

• Perturbative Quantum Chromodynamics (QCD) predictions often suffer from renormalization scheme and scale ambiguities.
• These ambiguities introduce systematic errors and complicate theoretical calculations.
• Understanding the behavior of the running coupling is crucial for accurate predictions.

Purpose of the Study:

• To introduce a generalized renormalization scheme to address ambiguities in perturbative QCD.
• To systematically determine the argument of the running coupling.
• To automate the calculation of perturbative coefficients and expose patterns in nonconformal terms.

Main Methods:

• Generalization of conventional renormalization schemes within dimensional regularization.
• Systematic determination of the running coupling argument order by order.
• Identification of patterns in nonconformal beta functions and degeneracy in perturbative coefficients.

Main Results:

• The proposed method illuminates renormalization scheme and scale ambiguities.
• It reveals a general pattern of nonconformal {\beta(i)} terms and special degeneracy in perturbative coefficients.
• The method allows for systematic and automatable determination of the running coupling argument.

Conclusions:

• The new method satisfies renormalization group principles.
• It eliminates an unnecessary source of systematic error in perturbative QCD predictions.
• This approach offers a more robust and precise way to handle renormalization in high-energy physics.