  We address and solve a puzzle raised by a recent calculation [1] of the
cross-section for particle production in proton-nucleus collisions to
next-to-leading order: the numerical results show an un- reasonably large
dependence upon the choice of a prescription for the QCD running coupling,
which spoils the predictive power of the calculation. Specifically, the results
obtained with a prescription formulated in the transverse coordinate space
differ by one to two orders of magnitude from those obtained with a
prescription in momentum space. We show that this discrepancy is an artefact of
the interplay between the asymptotic freedom of QCD and the Fourier transform
from coordinate space to momentum space. When used in coordinate space, the
running coupling can act as a fictitious potential which mimics hard scattering
and thus introduces a spurious contribution to the cross-section. We identify a
new coordinate-space prescription which avoids this problem and leads to
results consistent with those obtained with the momentum-space prescription.
