Effect of Scheme Transformations on a Beta Function with Vanishing One-Loop Term

Abstract

It is commonly stated that because terms in the beta function of a theory at the level of $\ell \ge 3$ loops and higher are scheme-dependent, it is possible to define scheme transformations that can be used to remove these terms, at least in the vicinity of zero coupling. We prove that this is not, in general, possible in the situation where a beta function is not identically zero but has a vanishing one-loop term.

6 pages, latex

References in corpus (16)

• The five-loop beta function of Yang-Mills theory with fermions
• Eliminating the Renormalization Scale Ambiguity for Top-Pair Production Using the Principle of Maximum Conformality
• An Analysis of Scheme Transformations in the Vicinity of an Infrared Fixed Point
• Scheme-Independent Series Expansions at an Infrared Zero of the Beta Function in Asymptotically Free Gauge Theories
• Scheme Transformations in the Vicinity of an Infrared Fixed Point
• Scheme-Independent Calculation of ${\gamma }_{\bar{\psi }\psi ,IR}$ for an SU(3) Gauge Theory
• Conformal Behavior at Four Loops and Scheme (In)Dependence
• Generalized Scheme Transformations for the Elimination of Higher-Loop Terms in the Beta Function of a Gauge Theory
• Derivation of the exact expression for the D function in N=1 SQCD
• New Scheme Transformations and Application to Study Scheme Dependence of an Infrared Zero of the Beta Function in Gauge Theories
• Banks-Zaks fixed point analysis in momentum subtraction schemes
• Infrared Fixed Point Physics in $\mathrm{SO}(N_c)$ and $\mathrm{Sp}(N_c)$ Gauge Theories
• Physics of the Non-Abelian Coulomb Phase: Insights from Padé Approximants
• On the Question of an Ultraviolet Zero of the Beta Function of the $\lambda ({\vec{\varphi }}^2{)}_4^2$ Theory
• Renormalization-Group Behavior of ${\varphi }^3$ Theories in $d=6$ Dimensions
• Study of the Question of an Ultraviolet Zero in the Six-Loop Beta Function of the O($N$) $\lambda |\vec{\varphi }{|}^4$ Theory