Optimal Renormalization-Group Improvement of R(s) via the Method of Characteristics

Abstract

We discuss the application of the method of characteristics to the renormalization-group equation for the perturbative QCD series within the electron-positron annihilation cross-section. We demonstrate how one such renormalization-group improvement of this series is equivalent to a closed-form summation of the first four towers of renormalization-group accessible logarithms to all orders of perturbation theory.

References in corpus (7)

• Closed-Form Summation of RG-Accessible Logarithmic Contributions to Semileptonic B-Decays and Other Perturbative Processes
• Optimal Renormalization-Group Improvement of the Perturbative Series for the e^+ e^- -Annihilation Cross-Section
• Complete Renormalization Group Improvement- Avoiding Scale Dependence in QCD Predictions
• Renormalization group improvement of the effective potential in massive ${\varphi }^4$ theory
• Renormalization-Group Improvement of Effective Actions Beyond Summation of Leading Logarithms
• Renormalization Group Summation and the Free Energy of Hot QCD
• Vanishing of the Bare Coupling in Four Dimensions

Cited by in corpus (7)

• The massive analytic invariant charge in QCD
• Optimal Renormalization-Group Improvement of Two Radiatively-Broken Gauge Theories
• Renormalization Group and Conformal Symmetry Breaking in the Chern-Simons Theory Coupled to Matter
• The Effective Potential in the Massive ${\varphi }_4^4$ Model
• Summation of Higher Order Effects using the Renormalization Group Equation
• The renormalization group improved effective potential in massless models
• On the Standard Approach to Renormalization Group Improvement