Abstract
We present a method to systematically include the corrections to the eikonal approximation that are associated with the finite width of the target. The retarded gluon propagator in background field is calculated at next-to-next-to-eikonal (NNE) accuracy by using this method. The corrections to the strict eikonal limit of the gluon propagator are found to be Wilson lines decorated by gradients of the background field of the target. The result is then applied to single inclusive gluon production and to single transverse spin asymmetry for a polarized target in pA collisions.
Highlights
The high energy limit of the dilute-dense scattering processes adopts two key approximations within the Color Glass Condensate (CGC, see [1] and references therein) effective theory
We have presented a systematic expansion of the retarded gluon propagator in a background field
The corrections associated with the finite width of the target were calculated at next-to-next-to-eikonal accuracy
Summary
The high energy limit of the dilute-dense scattering processes adopts two key approximations within the Color Glass Condensate (CGC, see [1] and references therein) effective theory. The other one is referred to as eikonal approximation, in which the constituents of the projectile just experience color rotation upon scattering with the target, picking a Wilson line at a given transverse point but integrated along the light-cone direction of propagation of the projectile, for which the target appears as infinitely Lorentz contracted. Corrections suppressed by inverse powers of the energy of the collision are systematically neglected within the eikonal limit. We study such power suppressed corrections to the CGC, namely next-to-eikonal contributions due to finite width of the target [2, 3]. A similar analysis in the context of soft gluon resummation for hard scattering amplitudes is performed in [4, 5]
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