How to perform QCD analysis of DIS in Analytic Perturbation Theory

TL;DR

This paper applies Fractional Analytic Perturbation Theory to analyze the nonsinglet nucleon structure function in deep inelastic scattering, comparing it with standard perturbative QCD across a wide range of momentum transfers.

Contribution

It introduces the use of FAPT in QCD analysis of DIS structure functions and demonstrates its effectiveness over a broad Q^2 range compared to standard methods.

Findings

FAPT provides a consistent description of $F_2(x,Q^2)$ at low and high Q^2.

The approach remains valid down to $Q^2 \,\sim\, 0.3$ GeV^2.

Comparison shows advantages of FAPT over standard perturbation theory.

Abstract

We apply (Fractional) Analytic Perturbation Theory (FAPT) to the QCD analysis of the nonsinglet nucleon structure function $F_2(x,Q^2)$ in deep inelastic scattering up to the next leading order and compare the results with ones obtained within the standard perturbation QCD. Based on a popular parameterization of the corresponding parton distribution we perform the analysis within the Jacobi Polynomial formalism and under the control of the numerical inverse Mellin transform. To reveal the main features of the FAPT two-loop approach, we consider a wide range of momentum transfer from high $Q^2\sim 100 {\rm GeV}^2$ to low $Q^2\sim 0.3 {\rm GeV}^2$ where the approach still works.