The Photon Structure Function at Small-x

It is shown that recent small–x measurements of the photon structure function F γ 2 (x,Q) by the LEP–OPAL collaboration are consistent with parameter–free QCD predictions at all presently accessible values of Q. Recently the OPAL collaboration [1] at the CERN–LEP collider has extended the measurements of the photon structure function F γ 2 (x,Q ) into the small–x region down to x ≃ 10, probing lower values of x than ever before. The observed rise of F γ 2 towards low values of x, x < 0.1, is in agreement with general QCD renormalization group (RG) improved expectations. It has, however, been noted that the rising small–x data at lower scales Q ≃ 2 − 4 GeV lie above the original QCD expectations anticipated almost a decade ago [2, 3]. It is the purpose of the present note to demonstrate that more recent and updated parameter–free QCD predictions [4] for F γ 2 (x,Q) are in general also consistent with the OPAL small–x measurements at all presently accessible values of Q. Before presenting our results it is instructive to recapitulate briefly the main differences between the original GRVγ [2] approach to the photonic parton distributions and the more recent parameter–free predictions of GRS [4]. In the latter approach a coherent superposition of vector mesons has been employed, which maximally enhances the u–quark contributions to F γ 2 , for determining the hadronic parton input f γ had (x,Q20) at a GRV–like [5] input scale Q 0 ≡ μ LO = 0.26 GeV and Q 0 ≡ μ NLO = 0.40 GeV for calculating the (anti)quark and gluon distributions f(x,Q) of a real photon in leading order (LO) and next–to–LO (NLO) of QCD. Furthermore, in order to remove the ambiguity of the hadronic light quark sea and gluon input distributions of the photon (being related to the ones of the pion, fπ(x,Q20), via vector meson dominance), inherent to the older GRVγ [2] and SaS [3] parametrizations, predictions [6] for q̄ (x,Q) and g(x,Q) have been used by GRS [4] which follow from constituent quark model constraints [7]. These latter constraints allow to express q̄ π and g entirely in terms of the experimentally known pionic valence density and the rather well known quark–sea and gluon distributions of the nucleon [6], using most recent updated valence–like input parton densities of the nucleon. Since more recent DIS small–x measurements at HERA imply somewhat less steep sea and gluon distributions of the proton [5], the structure functions of the photon will therefore