Use of a running coupling in the NLO calculation of forward hadron production
B. Ducloué (Institut de Physique Théorique, Université Paris-Saclay, CNRS, CEA, F-91191 Gif-sur-Yvette, France, Department of Physics, 40014 University of Jyväskylä, Finland and Helsinki Institute of Physics, 00014 University of Helsinki, Finland); E. Iancu (Institut de Physique Théorique, Université Paris-Saclay, CNRS, CEA, F-91191 Gif-sur-Yvette, France); T. Lappi (Department of Physics, 40014 University of Jyväskylä, Finland and Helsinki Institute of Physics, 00014 University of Helsinki, Finland); A. H. Mueller (Department of Physics, Columbia University, New York, New York 10027, USA); G. Soyez (Institut de Physique Théorique, Université Paris-Saclay, CNRS, CEA, F-91191 Gif-sur-Yvette, France); et al - Show all 7 authors
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 unreasonably 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 1 to 2 orders of magnitude from those obtained with a prescription in momentum space. We show that this discrepancy is an artifact 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.
