Detailed QCD analysis of the photon structure function

The effects of nonasymptotic terms in the photon structure function ${F}_{2}^{\ensuremath{\gamma}}(x,{Q}^{2})$ predicted by QCD are studied directly in $x$ space in leading and subleading order. The full (regular) solution including the hadronic nonasymptotic (${{Q}_{0}}^{2}$-dependent input) terms is shown to be free from the unphysical singularities of the asymptotic solution and is furthermore positive definite for suitable chosen boundary conditions (at ${Q}^{2}={{Q}_{0}}^{2}$) and in the physically relevant $x$ region ($W\ensuremath{\gtrsim}2$ GeV). The implications of the nonasymptotic solution and of their perturbatively uncalculable boundary conditions for the determination of $\ensuremath{\Lambda}$ and for the predictive power of purely perturbative QCD in the determination of ${F}_{2}^{\ensuremath{\gamma}}(x,{Q}^{2})$ are critically analyzed. Furthermore, taking carefully into account charm production, detailed predictions are given for present and future (unfolded) data. Similarly to the case of deepinelastic lepton-nucleon scattering, the (nonperturbative) photonic input parton distributions at ${Q}^{2}={{Q}_{0}}^{2}$ are different for leading- and higher-order calculations. This implies that the differences between leading- and higher-order predictions for ${F}_{2}^{\ensuremath{\gamma}}(x,{Q}^{2})$ are too small to be distinguished by present experiments. The only clean test of QCD, independent of the hadronic input, can be achieved by observing an increase of ${F}_{2}^{\ensuremath{\gamma}}(x,{Q}^{2})$ with $\mathrm{ln}{Q}^{2}$ for fixed values of $x$.