The leading contributions to the deep-ineiastic structure functions of a real or slightly virtual photon are calculated using a generalization of the Altarelli-Parisi equations for quantum-chromodynamic scale breaking. These techniques provide a simple alternative to the more conventional operator-product-moment methods and lead to integral equations which are easily solved numerically.

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We apply a simple extension of the gluon-fusion model of Einhorn and Ellis to the photoproduction of charmed particles at high energies. Overall rates of production are not much different from those predicted by various current models for strong production of charm, leading to the belief that charm should be more easily seen in the photoproduction case where backgrounds are smaller. The predictions of the model for various energy and angle distributions are presented. Predicted rates depend strongly on the mass of the charmed quark.

and (15). 15we conform to the metric and representation of the y matrices used by S. Schweber, An Introduction t o Relativistic Quantum Field Theory (Harper and Row, -New York, 1961). 1 6~. S, Ginsberg, Phys. Rev. D 1, 229 (1970). Note: The factors of $ multiplying the dilogarithms in the second line of Eq. (20) a r e copying e r r o r s and should be omitted. The numerical results a r e not significantly changed (generally by 0.0 to 0.3% in the Dalitz plot). A corrected version of Fig. 2(a) i s glven in Fig. 1 of _ t h i s paper.'7~nfrared-divergent terms, which cancel exactly when all the contributions to the radiative c o r r e c t~o n s a r e added, have been omitted.We present a straightforward method for calculating the amplitudes of the various JMLS states in the final 3n system of the reaction nN -nnW, assuming a Deck-model form for the production process. This calculation allows us to study relative phases of different partial waves, and the nucleon spin structure of the production amplitudes, in an unambiguous fashion. We find that the magnitudes and phases of 3n partial waves obtained by this method agree reasonably well with those obtained by applying an experimental fitting program to Monte Carlo events generated using the Deck formula; this may be interpreted a s a check on the assumptions of the fitting program. Likewise, the magnitudes and phases agree reasonably well with those obtained from the data, confirming the belief that the Ai and A g effects a r e probably produced by the Deck mechanism. In the rest system of the three pions, only one nucleon helicity-amplitude combination i s dominant. The method of analysis can be applied to similar models for other production reactions.