Measuring the QCD Gell Mann-Low $\Psi$-function

Abstract

We present a general method for extracting the Gell Mann-Low logarithmic derivative of an effective charge of an observable directly from data as a mean for empirically verifying the universal terms of the QCD $\beta$-function. Our method avoids the biases implicit in fitting to QCD-motivated forms as well as the interpolation errors introduced by constructing derivatives from discrete data. We also derive relations between moments of effective charges as new tests of perturbative QCD.