Abstract
We continue our studies of possible generalization of the Color Glass Condensate (CGC) effective theory of high energy QCD to include the high $p_t$ (or equivalently large $x$) QCD dynamics as proposed in [JJM-elastic]. Here we consider scattering of a quark from both the small and large $x$ gluon degrees of freedom in a proton or nucleus target and derive the full scattering amplitude by including the interactions between the small and large $x$ gluons of the target. We thus generalize the standard eikonal approximation for parton scattering which can now be deflected by a large angle (and therefore have large $p_t$) and also lose a significant fraction of its longitudinal momentum (unlike the eikonal approximation). The corresponding production cross section can thus serve as the starting point toward derivation of a general evolution equation that would contain DGLAP evolution equation at large $Q^2$ and the JIMWLK evolution equation at small $x$. This amplitude can also be used to construct the quark Feynman propagator which is the first ingredient needed to generalize the Color Glass Condensate (CGC) effective theory of high energy QCD to include the high $p_t$ dynamics. We outline how it can be used to compute observables in the large $x$ (high $p_t$) kinematic region where the standard Color Glass Condensate formalism breaks down.
Highlights
Twist expansion and the collinear factorization approach [1] to particle production in QCD is a powerful and extremely useful formalism for particle production in high energy hadronic/nuclear collisions at high pt
The color glass condensate (CGC) formalism is an effective field theory approach to QCD at high energies which relies on the fact that at high energy a hadron or nucleus wave function contains many gluons, referred to as gluon saturation [3,4], and is a dense many-body system which is most efficiently described via semiclassical methods [5]
We have derived the amplitude for scattering of a high energy quark on the gluon field of a proton or nucleus target including both small and large x gluon modes of the target
Summary
Twist expansion and the collinear factorization approach [1] to particle production in QCD is a powerful and extremely useful formalism for particle production in high energy hadronic/nuclear collisions at high pt. This infinite Wilson line resums multiple scatterings of a high energy quark (moving along the positive z axis) on a soft background color field to all orders in the soft field 1⁄2igSatan. [9], we went beyond eikonal approximation by including scattering from a large x gluon field denoted AμðxÞ, which, unlike the soft field S−, carries large longitudinal momentum and can cause a large deflection of the projectile quark. We managed to resum all the multiple scatterings of the projectile quark from the soft field and one scattering from the large x (sometimes referred to as the hard field, where “hard” refers to a large longitudinal momentum) Z VAPðzt; xþÞ ≡ Pexp ig xþ dzþS−a ðzt; zþÞta ; ð8Þ where anti-path-ordering (AP) in the amplitude means fields with the largest argument appear to the left
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