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The Principle of Maximum Conformality (PMC) offers superior renormalization group invariance (RGI) for quantum field theory predictions compared to the Principle of Minimum Sensitivity (PMS). PMC ensures scheme and scale independence, improving perturbative QCD convergence and reducing systematic errors.

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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.