Power corrections and renormalons in Drell-Yan production

TL;DR

The paper reassesses power corrections in Drell-Yan production by examining infrared renormalons within a full soft-gluon resummation framework. Using both double-logarithmic and all-order Wilson-line approaches, the authors show that leading $1/Q$ renormalon ambiguities cancel once soft emissions at all angles are included, pushing non-perturbative effects to order $\Lambda_{\rm QCD}^2/(Q^2(1-z)^2)$. The analysis identifies the leading non-perturbative sensitivity with $u=1$ in the Borel plane, corresponding to $\mathcal{O}(N^2\Lambda_{\rm QCD}^2/Q^2)$, and demonstrates that these corrections factor through initial boundary conditions in the Wilson-line evolution. The work draws connections to hadronic event shapes and discusses potential universality and phenomenological consequences for resummed cross sections across processes. Overall, perturbative QCD with proper soft-gluon treatment remains reliable in the perturbative domain, with residual power corrections appearing at the $1/Q^2$ level.

Abstract

The resummed Drell-Yan cross section in the double-logarithmic approximation suffers from infrared renormalons. Their presence was interpreted as an indication for non-perturbative corrections of order $\lqcd/(Q(1-z))$. We find that, once soft gluon emission is accurately taken into account, the leading renormalon divergence in the resummed cross section is cancelled by higher-order perturbative contributions in the exponent of the resummed cross section. From this evidence, `higher twist' corrections to the hard cross section in Drell-Yan production should therefore intervene only at order $\lqcd^2/((Q^2 (1-z)^2)$ in the entire perturbative domain $Q (1-z) > \lqcd$. We compare this result with hadronic event shape variables, comment on the potential universality of non-perturbative corrections to resummed cross sections, and on possible implications for phenomenology.

Figures (3)

• Figure 1: $\alpha_s^4$-contribution to the partonic Drell-Yan cross section. $\gamma^\star$ represents a photon with invariant mass $Q^2$ that splits into a lepton pair.
• Figure 2: (a) Cut diagrams with fermion loops. (b) Non-vanishing contribution with no cut fermion loop. The crosses denote counterterm insertions.
• Figure 3: Diagram for the cusp anomalous dimension. The double lines denote a Wilson line with cusp (alternatively, they can be interpreted as eikonal propagators).