Low- and high-mass components of the photon distribution functions

The structure of the general solution of the inhomogeneous evolution equations allows the separation of a photon structure function into perturbative (``anomalous") and non-perturbative contributions. The former part is fully calculable, and can be identified with the high-mass contributions to the dispersion integral in the photon mass. Properly normalized ``state" distributions can be defined, where the \gamma\to\qqbar splitting probability is factored out. These state distributions are shown to be useful in the description of the hadronic event properties, and necessary for a proper eikonalization of jet cross sections. Convenient parametrizations are provided both for the state and for the full anomalous parton distributions. The non-perturbative parts of the parton distribution functions of the photon are identified with the low-mass contributions to the dispersion integral. Their normalizations, as well as the value of the scale Q_0 at which the perturbative parts vanish, are fixed by approximating the low-mass contributions by a discrete, finite sum of vector mesons. The shapes of these hadronic distributions are fitted to the available data on F_2^\gamma(x,Q^2). Parametrizations are provided for Q_0=0.6\,GeV and Q_0=2\,GeV, both in the DIS and the \overline{\mathrm{MS}} factorization schemes. The full parametrizations are extended towards virtual photons. Finally, the often-used ``FKP-plus-TPC/2\gamma" solution for F_2^\gamma(x,Q^2) is commented upon.