Renormalization Scheme Dependence and the Renormalization Group Beta Function

Abstract

The renormalization that relates a coupling "a" associated with a distinct renormalization group beta function in a given theory is considered. Dimensional regularization and mass independent renormalization schemes are used in this discussion. It is shown how the renormalization $a^{\ast }=a+x_2{a}^2$ is related to a change in the mass scale $\mu$ that is induced by renormalization. It is argued that the infrared fixed point is to be a determined in a renormalization scheme in which the series expansion for a physical quantity $R$ terminates.

16 pages, 1 figure, minor typos fixed and additional comments made; accepted at Physical Review D

References in corpus (7)

• Five-Loop Running of the QCD coupling constant
• Hadronic Z- and tau-Decays in Order alpha_s^4
• The QCD Running Coupling
• Generalization of the Brodsky-Lepage-Mackenzie optimization within the $\{\beta \}$-expansion and the Principle of Maximal Conformality
• Generalized Scheme Transformations for the Elimination of Higher-Loop Terms in the Beta Function of a Gauge Theory
• New Scheme Transformations and Application to Study Scheme Dependence of an Infrared Zero of the Beta Function in Gauge Theories
• The effective exponent gamma(Q) and the slope of the beta function

Cited by in corpus (5)

• Comparing optimized renormalization schemes for QCD observables
• Multiple Couplings and Renormalization Scheme Ambiguities
• Achieving effective renormalization scale and scheme independence via the Principle of Observable Effective Matching
• Renormalization Scheme Dependence of $\beta$-Functions In Lorentz-Violating Quantum Field Theory
• Renormalisation