Problems in the resummation of soft-gluon effects in the transverse-momentum distributions of massive vector bosons in hadronic collisions
S. Frixione, P. Nason, G. Ridolfi
TL;DR
The paper analyzes soft-gluon resummation for transverse-momentum distributions of massive vector bosons in hadronic collisions, focusing on the Drell–Yan regime. It contrasts impact-parameter (b-space) and $q_T$-space resummations, showing factorial growth from the small-$b$ region in the former and geometrical singularities in the latter that limit applicability. Explicit NLL expressions are derived: in a simple model a closed-form form factor emerges involving Gamma functions, while the realistic case uses a Mellin transform to include PDF evolution and reveals Landau-pole–driven non-analyticities. The work argues that the factorial growth is an artefact of the formulation rather than a renormalon, and discusses the implications for nonperturbative treatments and practical phenomenology of $q_T$ distributions.
Abstract
We consider the resummation of soft-gluon emission in the transverse-momentum distribution of vector mesons in hadronic collisions. We find that the resummed expression in the impact-parameter formulation has an expansion in $\as$ with factorially growing terms with oscillating signs. These diverging terms arise from the small impact-parameter region of integration, and are of a subleading nature. We also obtain a closed expression for the next-to-leading logarithm resummation in $\qt$-space, and we study its analytic structure. We find in this case that, although no factorially growing terms are present, there are geometrical singularities that severely restrict the range of applicability of the resummation formula.