Abstract
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.
Highlights
Particle production in proton-proton or proton-nucleus collisions at forward rapidities and semihard transverse momenta of a few GeV represents an important source of information about the small-x part of the nuclear wave function, where gluon occupation numbers are high and nonlinear effects like gluon saturation and multiple scattering are expected to be important
We have continued our work on the next-to-leading order (NLO) corrections to the single inclusive particle production at forward rapidities in high energy proton-nucleus collisions
Our main focus was on the choice of the scale for the running of the QCD coupling. This coupling appears in two distinct places in the calculation: the high-energy evolution of the dipole S matrix, as described by the (NLO) BK equation and the NLO impact factor
Summary
Particle production in proton-proton or proton-nucleus collisions at forward rapidities and semihard transverse momenta of a few GeV represents an important source of information about the small-x part of the nuclear wave function, where gluon occupation numbers are high and nonlinear effects like gluon saturation and multiple scattering are expected to be important. The final results for the cross section need not be exactly the same in this scheme and the “canonical” one (which uses a momentum-space RC prescription in the impact factor), yet, they were expected to lie close to each other, because the Fourier transform roughly identifies momenta with the inverse of coordinates It came as a real surprise (and as a bad news for the reliability of the NLO formalism as a whole) when it turned out that the numerical results are dramatically different within these two schemes: the NLO corrections obtained in the new scheme have the opposite sign as compared to those in the “canonical” scheme, and they are tremendously larger—by 1 to 2 orders of magnitude, depending upon the final transverse momentum [1]. We present in Appendix A the usual RC prescriptions used in relation with the BK equation together with a physical discussion
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