Abstract
We introduce a general expression which enables the parton distribution, unintegrated over the parton transverse momentum, to be obtained from the conventional parton densities. We use the formalism to study the effects of the transverse momentum $q_t$ of the incoming partonic system on the calculation of the transverse momentum spectra of prompt photons produced in high energy pp and $p\bar{p}$ collisions. For the purposes of illustration, we use the double logarithm approximation. For large $q_t$ we calculate the effect directly from the perturbative formalism, whereas for small $q_t$ we bound the effect using two extreme hypotheses. In both $q_t$ domains we find that the shapes of the prompt photon spectra are not significantly modified, although the cross sections are enhanced.
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