V. Summary and Conclusions

We have discussed here a simple model for the associated production of heavy new flavors in photon-hadron and hadron-hadron collisions. Our fundamental assumption is that the subprocesses of lowest order in the QCD perturbation series dominate the production of heavy quarks. For real and virtual photoproduction this fixes the internal mechanism to be while for hadron-hadron collisions we consider a mixture of and .

The major unknown quantity in the calculations is the shape of , the distribution of vector gluons in a nucleon. We calculate with a range of shapes for this function discussed earlier in the context of QCD gluon contributions to large- production. With this range for the input gluon distributions, the internal process is found quickly to dominate over in the hadroproduction of heavy flavors at high energy. This result contradicts the hypothesis of Fritzsch (24) and of Halzen (35) that processes always dominate. Our results tend to support the original idea of Ellis and Einhorn (36) that the production of heavy flavors offers an opportunity to estimate empirically the shape of the gluon distribution. However, we find that the precision to which measurements of charm production (or the production of flavors heavier than charm) can really be said to determine the gluon distribution is limited because of unknown effects attributable to higher-order corrections not included in our calculation. These effects may be important.

However, it should be within the capability of experiments to test soon the basic idea that gluons participate in the production of heavy quarks. Vector gluons have often been assigned an ambiguous role in parton-model calculations. For example, in the constituent-interchange model for large- production, gluon exchange is used to determine the shape of quark distributions, but gluons are not considered in that model to be constituents themselves. (37) In our approach, the difference in the cross section for at depending on whether or not we include the mechanism or not is about a factor of 50. It is difficult to envision a mechanism not involving initial gluons which could contribute this much cross section. Similarly, it is hard to imagine a fundamental process for photoproduction of heavy quarks which does not involve gluons and which is consistent with experimental constraints.

We have not included here a discussion of the cross section for the production of heavy quarks bound together in the same hadron, production, production, production, etc. These processes are conceptually more difficult since we have to deal with both the production and confinement of heavy quarks. There are several models which are roughly consistent with our approach here which make different predictions for these processes. (38) Since there are available good data on production in different beams and there will probably be more information on production soon, this is a potentially rewarding area in which to generalize the calculations presented here.

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