High energy pA collisions in the color glass condensate approach I. Gluon production and the Cronin effect

TL;DR

This work develops a covariant-gauge, classical-field CGC framework to compute gluon production in high-energy pA collisions, solving the Yang–Mills equations to first order in the dilute proton source and to all orders in the dense nuclear source. It establishes k_⊥-factorization for gluon production in terms of Wilson-line correlators and demonstrates the exact equivalence with other gauges, notably the Fock–Schwinger gauge results of Dumitru and McLerran. The Cronin effect is analyzed in both the plain MV model and with quantum evolution, showing that naive x-dependence enhances the effect at forward rapidities while proper JIMWLK evolution can suppress it, highlighting distinct regimes where independent multiple scatterings or small-x evolution dominate. The results provide a coherent picture of gluon production and Cronin physics across rapidities and energies, with implications for RHIC and LHC phenomenology and a foundation for the companion quark-production study.

Abstract

We study gluon production in high energy proton-nucleus collisions in the semi-classical framework of the Color Glass Condensate. We develop a general formalism to compute gluon fields in covariant gauge to lowest order in the classical field of the proton and to all orders in the classical field of the nucleus. The use of the covariant gauge makes the diagrammatic interpretation of the solution more transparnt. k_t-factorization holds to this order for gluon production -- Our results for the gluon distribution are equivalent to the prior diagrammatic analysis of Kovchegov and Mueller. We also show that these results are equivalent to the computation of gluon production by Dumitru and McLerran in the Fock-Schwinger gauge. We demonstrate how the Cronin effect arises in this approach, and examine its behavior in the two extreme limits of a) no small-x quantum evolution, and b) fully saturated quantum evolution. In both cases, the formalism reduces to Glauber's formalism of multiple scatterings. We comment on the possible implications of this study for the interpretation of the recent results on Deuteron-Gold collisions at the Relativistic Heavy Ion Collider (RHIC).

Figures (12)

• Figure 1: The three gluon vertex $\Gamma^{\sigma\rho+}_{bac}(q,p,k)$ and the four gluon vertex $\Gamma^{\sigma\rho++}_{bacd}(q,p,k_1,k_2)$ that can be inserted on the gluon propagator.
• Figure 2: Diagrammatic representation of the field $A_{(0,1)}^-$. A solid boldface line represents one power of $\rho_{_{A}}$, and a dashed boldface line represents one power of $\rho_p$.
• Figure 3: Diagrammatic representation of the current $J_{(1,\infty)}^+$ and of the fields $A_{(1,\infty)}^+$ and $A_{(1,\infty)}^i$. The circled vertex is the vertex $\Gamma^{i-+}$ where the transition $A_{(1,\infty)}^+\to A_{(1,\infty)}^i$ takes place.
• Figure 4: Contributions to $A_{(1,\infty)}^-$ by a direct transition $A_{(1,\infty)}^+\to A_{(1,\infty)}^-$. Left: via the 3-point vertex; the boxed vertex is the vertex $\Gamma^{--+}$. Right: via the 4-point vertex; the dotted boxed vertex is the vertex $\Gamma^{--++}$.
• Figure 5: Contributions to $A_{(1,\infty)}^-$ by a transition $A_{(1,\infty)}^+\to A_{(1,\infty)}^i\to A_{(1,\infty)}^-$. The triangular vertex is the vertex $\Gamma^{-i+}$.