Nonperturbative Corrections in Resummed Cross Sections

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.