Photon structure function as calculated using perturbative quantum chromodynamics

The calculation of the moments of the photon structure function using perturbative quantum chromodynamics is briefly reviewed and extended with special emphasis being placed on the large magnitude of the next-to-leading-order corrections with respect to the leading-logarithm calculation. In addition, the moments are inverted in order to study the detailed $Q^2$ dependence of the structure function. It is found that even for large values of $x$ the structure function is not positive definite when the next-to-leading-order corrections are included, indicating the unreliability of the calculation. This result is insensitive to the scheme used to define the coupling constant ${\overline{g}}^2$. A brief discussion of a vector-dominance estimate of possible background terms is also included.