When semantics turns to substance: reformulating QCD analysis of F_2^{\gamma}(x,Q^2)}

TL;DR

This paper revisits the QCD analysis of the photon structure function F_2^{ ext{γ}}(x,Q^2), emphasizing the importance of proper definitions and complete calculations, revealing significant differences from conventional approaches.

Contribution

It provides a revised framework for LO and NLO QCD analyses of F_2^{ ext{γ}}, highlighting missing elements in previous methods and clarifying the role of QED effects.

Findings

Conventional LO and NLO analyses are incomplete and differ significantly from the complete versions.

Complete NLO analysis requires two uncalculated quantities, while LO analysis can be performed with four known quantities.

Arguments supporting the conventional approach are flawed and support the revised framework.

Abstract

QCD analysis of F_2^{\gamma}(x,Q^2) is revisited. It is emphasized that the presence of the inhomogeneous term in the evolution equations for quark distribution functions of the photon implies important difference in the way factorization mechanism works in photon-hadron and photon-photon collisions as compared to the hadronic ones. Moreover, a careful definitions of the very concepts of the ``leading order'' and ``next-to-leading order'' QCD analysis of F_2^{\gamma} are needed in order to separate genuine QCD effects from those of pure QED origin. After presenting such definitions, I show that all existing allegedly LO, as well as NLO analyses of F_2^{\gamma}(x,Q^2) are incomplete. The source of this incompleteness of the conventional approach is traced back to the lack of clear identification of QCD effects and to the misinterpretation of the behaviour of q^{\gamma}(x,M) as a function of \alpha_s(M). Complete LO and NLO QCD analyses of F_2^{\gamma}(x,Q^2) are shown to differ substantially from the conventional ones. Whereas complete NLO analysis requires the knowledge of two so far uncalculated quantities, a complete LO one is currently possible, but compared to the conventional formulation requires the inclusion of four known, but in the existing LO analyses unused quantities. The arguments recently advanced in favour of the conventional approach are analyzed and shown to contain a serious flaw. If corrected, they actually lends support to my claim.