Measuring the QCD Gell-Mann–LowΨfunction

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 $\ensuremath{\beta}$ 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.