Direct vs . resolved photon : an exercise in factorization

Direct and resolved photon interactions are shown to be intimately related through the factorization mechanism. It is argued that in theoretically consistent analysis of jet production in γp and ep collisions the LO resolved γ contribution must be considered together with the NLO direct γ component. Recent data from HERA therefore do not provide a direct evidence for the former component, but should rather be interpreted as a manifestation of the O(α 2 α 2 s) term in ep interactions. In recent months an increasing flow of fresh data from HERA at DESY has brought several interesting new results on the structure of photon. Among them, the interpretation [1, 2] of data on two-jet events an as evidence for the resolved γ contribution to γp interactions has attracted considerable attention. I consider this interpretation as premature. Due to close relation between direct and resolved γ components, based on the general factoriza-tion arguments, there is in fact no principal difference between these two contributions. I shall argue that in theoretically consistent treatment of γp interactions, the usual resolved γ component should always be considered simultaneously with the NLO direct one, which, in fact, leads to kinematically very similar final state configurations. For the case of quarks inside the photon, the separation of γp interactions into " direct " and " resolved " components is theoretically ambiguous and doesn't allow a unique interpretation of observed jet correlations as an evidence for the " resolved " photon. Let me start with an important comment on the photon structure functions. To the order O(αα s) the evolution equations for quark (of flavour i and charge e i), gluon and photon distribution functions inside the real photon read dD γ/γ (x, M) d ln M = 0, D γ/γ (x, M) = δ(1 − x) (1) dD g/γ (x, M) d ln M = α s π 2n f j=1 1 x dy y D q j /γ (y, M)P (0) g/q x y + α s π 1 x dy y D g/γ (y, M)P (0) g/g x y (2) dD q i /γ (x, M) d ln M = α π k i (x) + α s π 1 x dy y D q i /γ (y, M)P (0) q/q x y + α s π 1 x dy y D g/γ (y, M)P (0) q/g x y (3)