QCD instantons and high-energy diffractive scattering

Abstract

We pursue the intriguing possibility that larger-size instantons build up diffractive scattering, with the marked instanton-size scale 〈ρ〉≈0.5 fm being reflected in the conspicuous “geometrization” of soft QCD. As an explicit step in this direction, the known instanton-induced cross sections in deep-inelastic scattering (DIS) are transformed into the familiar colour dipole picture, which represents an intuitive framework for investigating the transition from hard to soft physics in DIS at small xBj. The simplest instanton (I) process without final-state gluons is studied first. With the help of lattice results, the qq̄-dipole size r is carefully increased towards hadronic dimensions. Unlike perturbative QCD, one now observes a competition between two crucial length scales: the dipole size r and the size ρ of the background instanton that is sharply localized around 〈ρ〉≈0.5 fm. For r≳〈ρ〉, the dipole cross section indeed saturates towards a geometrical limit, proportional to the area π〈ρ〉2, subtended by the instanton. In case of final-state gluons, lattice data are crucially used to support the emerging picture and to assert the range of validity of the underlying IĪ-valley approach. As function of an appropriate energy variable, the resulting dipole cross section turns out to be sharply peaked at the sphaleron mass in the soft regime. The general geometrical features remain like in the case without gluons.