Physical Anomalous Dimensions at Small $x$

TL;DR

This work investigates uncertainties in the QCD analysis of the proton structure function $F_2(x,Q^2)$ at small $x$, focusing on the role and ambiguities of the unphysical gluon density. It develops a framework of physical anomalous dimensions, kernels relating physical observables like $F_2$ and $F_L$, which are scheme-invariant and calculable in perturbation theory, to disentangle perturbative from non-perturbative effects. The paper analyzes fixed-order and resummed (BFKL-based) approaches, discusses factorization-scheme transformations (notably the SDIS scheme), and extends the formalism to heavy-flavour structure functions, highlighting how small-$x$ resummation enters both gluon- and quark-driven channels. The proposed observables-based methodology aims to provide more reliable perturbative predictions and guide phenomenology in small-$x$ QCD.

Abstract

I present a theoretical discussion of the uncertainties related to the QCD analysis of the proton structure function $F_2(x,Q^2)$ at small $x$. The role played by the `unphysical' gluon density is pointed out. It is shown how the study of more observables can reduce the theoretical uncertainty and, in particular, an alternative method of analysis, based on the introduction of physical anomalous dimensions, is suggested.