Elastic scattering of a quark from a color field: longitudinal momentum exchange

Abstract

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 of freedom in CGC are Wilson lines which enter in the effective quark (and gluon) propagators and re-sum 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 $p_t$) 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 pQCD 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 $F_2$ and $F_L$ at all $x$ and thus generalize the dipole model of DIS. We outline 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 $p_t$ 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 $p_t$ physics.

arXiv comment22 pages, 14 figures

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• Quark jets scattering from a gluon field: from saturation to high $p_t$
• Rapidity loss, spin and angular asymmetries in scattering of a quark from color field of a proton (nucleus)
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• Single Inclusive Hadron Production in DIS at Small $x$: Next to Leading Order Corrections
• Ultrarelativistic quark-nucleus scattering in a light-front Hamiltonian approach
• Gluon-mediated inclusive Deep Inelastic Scattering from Regge to Bjorken kinematics
• Multiparticle production in proton-nucleus collisions beyond eikonal accuracy
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• Color Glass Condensate meets High Twist Expansion
• Parton model contributions as next-to-eikonal corrections to the dipole factorization of DIS and SIDIS at low $x_{Bj}$
• Forward quark jet-nucleus scattering in a light-front Hamiltonian approach