New Scheme Transformations and Application to Study Scheme Dependence of an Infrared Zero of the Beta Function in Gauge Theories

Abstract

We present two new one-parameter families of scheme transformations and apply these to study the scheme dependence of the infrared zero in the beta function of an asymptotically free non-Abelian gauge theory up to four-loop order. Our results provide a further quantitative measure of this scheme dependence, showing that for moderate values of the gauge coupling and the parameter specifying the scheme transformation, this dependence is relatively mild. We also remark on a generalized multi-parameter family of rational scheme transformations.

arXiv comment13 pages, latex

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• Six dimensional QCD at two loops
• Banks-Zaks fixed point analysis in momentum subtraction schemes
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• $A_k\bar{F}$ Chiral Gauge Theories
• Scheme-Independent Calculations of Anomalous Dimensions of Baryon Operators in Conformal Field Theories
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• Renormalization Scheme Dependence in a QCD Cross Section
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• Study of the Ultraviolet Behavior of an O($N$) $|\vec{\varphi }{|}^6$ Theory in $d=3$ Dimensions
• Search for an Ultraviolet Zero in the Seven-Loop Beta Function of the $\lambda {\varphi }_4^4$ Theory
• A Comparative Study of Criticality Conditions for Anomalous Dimensions using Exact Results in an $\mathcal{N}=1$ Supersymmetric Gauge Theory