Anomalous cross section for photon-photon scattering in gauge theories

We consider the deep inelastic structure functions of the photon in an asymptotically free gauge theory. In contrast to the case of a hadronic target, we find that the shortdistance analysis determines the shape and magnitude and not merely the Q 2 dependence of the structure functions. The structure functions of the free quark theory are renormalized by finite, calculable factors. For example, at x = 0.1, we find that F 2 will, at large Q 2, exceed the free quark result by a factor 1.751, while for x = 0.5, F 2 is suppressed asymptotically, relative to the free quark theory, by a factor 0.964, and at x = 0.8, by a factor 0.611.