Abstract
In high energy proton-nucleus collisions, the single- and double-inclusive soft gluon productions at the leading order have been calculated and phenomenologically studied in various approaches for many years. These studies do not take into account the saturation and multiple rescatterings in the field of the proton. The first saturation correction to these leading order results (the terms that are enhanced by the combination {alpha}_s^2{mu}^2 , where μ2 is the proton’s color charge squared per unit transverse area) has not been completely derived despite recent attempts using a diagrammatic approach. This paper is the first in a series of papers towards analytically completing the first saturation correction to physical observables in high energy proton-nucleus collisions. Our approach is to analytically solve the classical Yang-Mills equations in the dilute-dense regime using the Color Glass Condensate effective theory and compute physical observables constructed from classical gluon fields. In the current paper, the Yang-Mills equations are solved perturbatively in the field of the dilute object (the proton). Next-to-leading order and next-to-next-to-leading order analytic solutions are explicitly constructed. A systematic way to obtain all higher order analytic solutions is outlined.
Highlights
The two decades worth of experimental measurements at RHIC and, the LHC have provided many unexpected results, including strong evidence for the formation of a strongly coupled plasma of quarks and gluons in heavy-ion collisions at high energy
Our approach is to analytically solve the classical Yang-Mills equations in the dilute-dense regime using the Color Glass Condensate effective theory and compute physical observables constructed from classical gluon fields
This plasma demonstrated properties of a nearly perfect fluid; this fact facilitated a theoretical description of the collision dynamics in the framework of hydrodynamics starting just about 1 fm/c after the heavy ion impact
Summary
The two decades worth of experimental measurements at RHIC and, the LHC have provided many unexpected results, including strong evidence for the formation of a strongly coupled plasma of quarks and gluons in heavy-ion collisions at high energy. Beyond the leading order result, the first saturation corrections in the projectile to single- and double-inclusive gluons production were partially calculated in refs. It should be mentioned that the classical Yang-Mills equations can be and were solved numerically This approach was used for calculating the single- and double-inclusive gluon productions to all orders in both projectile and target color charge densities [44,45,46]. These calculations rely on truncating the final state interactions at proper finite time.
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