On the use of a running coupling in the NLO calculation of forward hadron production

TL;DR

This paper investigates the large dependence on the running coupling prescription in NLO calculations of forward hadron production, identifying the cause and proposing a new coordinate-space method to improve predictive reliability.

Contribution

The authors reveal the origin of the prescription dependence and introduce a new coordinate-space approach that aligns with momentum-space results, enhancing calculation consistency.

Findings

Discrepancy arises from interplay between asymptotic freedom and Fourier transform.

Coordinate-space running coupling can mimic hard scattering, causing spurious results.

New prescription in coordinate space resolves the large dependence issue.

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.