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

TL;DR

This paper introduces a direct data-driven method to extract the QCD Gell Mann-Low $eta$-function, enabling empirical verification of its universal terms without fitting biases or interpolation errors.

Contribution

It presents a novel approach for measuring the Gell Mann-Low $eta$-function directly from data, avoiding traditional fitting and interpolation issues.

Findings

Method successfully extracts the $eta$-function from experimental data.

Derived relations between moments of effective charges as new QCD tests.

Provides a framework for empirical validation of perturbative QCD predictions.

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.