Systematic Analysis of Scaling Properties in Deep Inelastic Scattering

TL;DR

This paper systematically analyzes various proposed scaling laws in deep inelastic scattering at small x using the Quality Factor method, comparing their validity against experimental data from HERA and making predictions for other processes.

Contribution

It introduces a comprehensive analysis of different QCD-inspired scaling variables in deep inelastic scattering, evaluating their phenomenological validity with the QF method and experimental data.

Findings

Fixed coupling and running coupling scalings fit data well.

Diffusive scaling is disfavored by the data.

Adjusting initial conditions improves the running coupling II scaling.

Abstract

Using the ``Quality Factor'' (QF) method, we analyse the scaling properties of deep-inelastic processes at HERA and fixed target experiments for x<0.01. We look for scaling formulae of the form sigma(tau), where tau(log Q^2, Y) is a scaling variable suggested by the asymptotic properties of QCD evolution equations with rapidity Y. We consider four cases: ``Fixed Coupling'', corresponding to the original geometric scaling proposal and motivated by the asymptotic properties of the Balitsky-Kovchegov (BK) equation with fixed QCD coupling constant, two versions ``Running Coupling I,II'' of the scaling suggested by the BK equation with running coupling, and ``Diffusive Scaling'' suggested by the QCD evolution equation with Pomeron loops. The Quality Factors, quantifying the phenomenological validity of the candidate scaling variables, are fitted on the total and DVCS cross-section data from HERA and predictions are made for the elastic vector-meson and for the diffractive cross-sections at fixed small x_pom or beta. The first three scaling formulae have comparably good QF while the fourth one is disfavored. Adjusting initial conditions gives a significant improvement of the ``Running Coupling II'' scaling.