Factorization scheme analysis of $F_2^{\gamma}(x,Q^2)$ and parton distributions functions of the photon

Abstract

Factorization scheme analysis of $F_2^{\gamma}(x,Q^2)$ in the next-to-leading order QCD is revisited. It is emphasized that the presence of the inhomogeneous term in the evolution equations for quark distribution functions of the photon implies subtle but important difference in the way factorization mechanism works in photon-hadron and photon-photon collisions as compared to the hadronic ones. It is argued that none of the existing NLO analyses of $F_2^{\gamma}(x,Q^2)$ takes this difference properly into account. The source of the ensuing incompleteness is traced back to the misinterpretation of the behaviour of $q^{\gamma}(x,M)$ as a function of $\alpha_s(M)$. Parton model interpretation of the so called ``constant terms'' in the LO photonic coefficient function $C_{\gamma}^{(0)}(x)$ is given and smooth transition between the properties of virtual and real photon analyzed. Finally phenomenological consequences of this analysis are discussed.