Elastic scattering of a quark from a color field: longitudinal momentum exchange
Résumé
Perturbative QCD in the small Bjorken-x limit can be formulated as an effective theory known as the color glass condensate (CGC) formalism. The CGC formalism takes into account the dynamics of large gluon densities at small x and has been successfully applied to deep inelastic scattering (DIS) and particle production in high-energy hadronic and nuclear collisions in the small-x kinematic region. The effective degrees of freedom in CGC are Wilson lines which enter in the effective quark (and gluon) propagators and resum multiple soft scatterings from the small-x gluon field of the target. It is however known that the CGC effective theory breaks down when one probes the moderately large-x (high-pt) kinematics where collinear factorization and DGLAP evolution of parton distribution functions should be the right framework. Here we propose a general framework which may allow one to eventually unify the two approaches and to calculate perturbative QCD cross sections in both small and large Bjorken-x regions. We take the first step towards this goal by deriving an expression for the quark propagator in a background field which includes scatterings from both small- and large-x modes of the gluon field of the target. We describe how this quark propagator can be used to calculate QCD structure functions F2 and FL at all x and thus generalize the dipole model of DIS. We outline that this approach can also be used to extend the so-called hybrid approach to particle production in the forward rapidity region of high-energy hadronic and nuclear collisions to all x and pt regions and speculate on how one may apply the same techniques to extend the McLerran-Venugopalan effective action used in high-energy heavy-ion collisions to include high-pt physics.
Mots clés
energy: high
quark: propagator
energy: hadronic
quantum chromodynamics: perturbation theory
parton: distribution function
model: deep inelastic scattering
heavy ion: energy
gluon: density
factorization: collinear
heavy ion: scattering
model: dipole
color glass condensate
kinematics
Bjorken
nucleus
longitudinal momentum
structure function
elastic scattering
background field
effective action
DGLAP equation
Wilson loop
rapidity
hybrid
color