We consider hadron production in deep inelastic scattering of electrons on photons. 1. (i)Exploiting the leading order QCD corrections due to gluon bremsstrahlung we find that the photon structure functions rapidly approach their asymptotic form which can be calculated in QCD. 2. (ii)Replacing QCD by a theory with a fixed quark-gluon coupling constant (scalar or abelian gluons) gives dramatic changes: for Bjorken x away from 0, the asymptotic form of the structure function is scale-invariant, with a shape quite unlike the QCD shape, and the structure function diverges for x = 0. 3. (iii)The pointlike component of the photon gives final state jets emerging at large angles to the axis of the real + virtual photon, in contrast to the hadronic component of the photon.
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In this paper we expand our earlier work \[4\]o n a number of points. We continue to exploit the zeroth-order Born approximation \[5\]( fig. la) and also lowest-order QCD via the Altarelli-Parisi equation (fig. lb). This is adequate for our purposes here. (Higher-order QCD corrections to the structure functions themselves have been extensively studied elsewhere \[6\].) * Work supported in part by the Department of Energy under contract DE-AC03-76SF00515. * Present address: Dept. of Theoretical Physics, University of Lund, S61vegatan 14A, S-22362 Lund, Sweden.. § Kade Fellow, on leave from Technische Hochschule Aachen.