Nonperturbative Corrections in Resummed Cross Sections

TL;DR

The authors investigate nonperturbative corrections in resummed QCD cross sections and show that infrared renormalons induce power-suppressed ambiguities that can be absorbed into vacuum matrix elements of nonlocal operators defined along Wilson lines. By analyzing Drell–Yan momentum space, jet cross sections, and inclusive lepton-pair production, they identify leading power corrections: a $b^2\Lambda^2$ term in the Sudakov exponent, a $y_0\Lambda/\delta$ shift in jet observables, and a $1/Q$ term in inclusive DY, each associated with distinct nonlocal operator structures. They provide an operator/Effective Field Theory interpretation using eikonal quark descriptions and derive explicit expressions for the corresponding nonperturbative matrix elements ($S_2$, $A_{2\rm J}$, $A_{\rm DY}$). The work suggests a small set of universal nonperturbative parameters that encode the leading power corrections across high-energy cross sections and aligns with Collins–Soper parameterizations, offering a principled framework to quantify nonperturbative effects in resummed QCD processes.

Abstract

We show that the resummation of large perturbative corrections in QCD leads to ambiguities in high energy cross sections that are suppressed by powers of large momentum scales. These ambiguities are caused by infrared renormalons, which are a general feature of resummed hard-scattering functions in perturbative QCD, even though these functions are infrared safe order-by-order in perturbation theory. As in the case of the operator product expansion, the contributions of infrared renormalons to coefficient functions may be absorbed into the definition of higher-dimensional operators, which induce nonperturbative corrections that are power-suppressed at high energies. The strength of the suppression is determined by the location of the dominant infrared renormalon, which may be identified explicitly in the resummed series. In contrast to the operator product expansion, however, the relevant operators in factorized hadron-hadron scattering and jet cross sections are generally nonlocal in QCD, although they may be expressed as local operators in an effective theory for eikonalized quarks. In this context, we verify and interpret the presence of $1/Q$ corrections to the inclusive Drell-Yan cross section with $Q$ the pair mass. In a similar manner, we find $\exp(-b^2\ln Q)$ corrections in the impact parameter space of the transverse momentum distributions of the Drell-Yan process and $e^+e^-$ annihilation. We also show that the dominant nonperturbative corrections to cone-based jet cross sections behave as $1/(Qδ)$, with $δ$ the opening angle of the jet and $Q$ the center of mass energy.