Abstract
In the QCD FESR, Eq. 1.13, the integral around the circle of radius \(|s_0|\) can be performed in two ways, named Fixed Order Perturbation Theory (FOPT), and Contour Improved Perturbation Theory (CIPT). In FOPT the strong coupling is frozen on the circle, i.e. at \(s = |s_0|\), and the renormalization group (RG) improvement, \((\mu ^2 = q^2)\), in all logarithms is performed after integration.
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