We investigate the discrepancy that exists at low-xT​=2pT​/s​ between
the next--to--leading order QCD calculations of prompt photon production and
the measured cross section. The central values of the measured cross section
are of order 100\% larger than QCD predictions in this region. It has been
suggested that the bremsstrahlung contribution may account for this
discrepancy. The quark fragmentation function Dγ/q​(z) has not been
measured and an exactly known asymptotic form is normally used in calculations.
We examine the effect of much larger fragmentation functions on the QCD
predictions. After illustrating the effect of the large fragmentation functions
in some detail for recent CDF data at s​=1.8~TeV, we perform a χ2
fit to 8 prompt photon data sets ranging in CMS energy from 24~GeV to 1.8~TeV.
While a large fragmentation function normalization may prove to play an
important role in resolving the discrepancy, the present theoretical and
experimental uncertainties prevent any definite normalization value from being
determined.Comment: 14 pages, LBL-33122 and UCB-PTH-92/38. 13 figures available by email,
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