Analysis of a Zero of a Beta Function Using All-Orders Summation of Diagrams

Abstract

Conventionally, one calculates a zero in a beta function by computing this function to a given loop order and solving for the zero. Here we discuss a different method which is applicable in theories where one can perform a partial diagrammatic summation to infinite-loop order. We show that this method, compared with the conventional method, yields much better agreement with exact results in the case of an asymptotically free gauge theory with $\mathcal{N}=1$ supersymmetry. Applications to other field theories are also discussed.

5 pages, latex

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• Scheme-Independent Series Expansions at an Infrared Zero of the Beta Function in Asymptotically Free Gauge Theories
• Scheme-Independent Calculation of ${\gamma }_{\bar{\psi }\psi ,IR}$ for an SU(3) Gauge Theory
• Infrared Fixed Point Physics in $\mathrm{SO}(N_c)$ and $\mathrm{Sp}(N_c)$ Gauge Theories
• Scheme-Independent Calculations of Physical Quantities in an $\mathcal{N}=1$ Supersymmetric Gauge Theory
• An Integral Formalism for the Construction of Scheme Transformations in Quantum Field Theory
• A Comparative Study of Criticality Conditions for Anomalous Dimensions using Exact Results in an $\mathcal{N}=1$ Supersymmetric Gauge Theory