Relation between Weinberg and Georgi-Politzer renormalization-group equations

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Abstract
The renormalized masses, coupling constant, gauge parameter, and one-particle-irreducible Green's functions appearing in Weinberg's (solvable) renormalization-group equation (RGE) are related to those in Georgi and Politzer's (unsolvable) RGE. The relations are derived both in QED and in (massive) quantum chromodynamics (QCD) up to one-loop order. An explicit dependence on a renormalization point of the effective mass and charge in the Georgi-Politzer RGE is given perturbatively by expressing these parameters in terms of the Weinberg RGE because Weinberg's effective mass and charge have an explicit dependence on a renormalization point. A similar relation is also obtained between a minimal subtraction scheme and the Georgi-Politzer renormalization scheme in QCD.