How Protons Shatter Colored Glass

TL;DR

This work develops a analytic description of gluon production in high-energy, asymmetric collisions within the Color Glass Condensate framework, focusing on a proton–nucleus system where the proton's saturation momentum is much less than that of the nucleus. By solving the Yang-Mills equations with a weak/strong-field separation and incorporating RG evolution of the CGC density, it derives a compact expression for the gluon spectrum $\frac{dN}{d^2k_\perp dy}$ that interpolates between perturbative and saturated regimes. The results reveal distinct transverse-momentum scalings: $\sim 1/k_\perp^4$ at high $k_\perp$ and $\sim 1/k_\perp^2$ between the two saturation scales, with clear $A$-scaling laws and a direct link between the rapidity slope of $dN/dy$ and the RG evolution of the CGC charge density. The findings provide experimental handles to probe CGC dynamics and RG evolution at RHIC and LHC, and are readily generalizable to other rapidities and asymmetric collisions.

Abstract

We consider the implications of the Color Glass Condensate for the central region of p+A collisions. We compute the k_t distribution of radiated gluons and their rapidity distribution dN/dy analytically, both in the perturbative regime and in the region between the two saturation momenta. We find an analytic expression for the number of produced gluons which is valid when the saturation momentum of the proton is much less than that of the nucleus. We discuss the scaling of the produced multiplicity with A. We show that the slope of the rapidity density dN/dy provides an experimental measure for the renormalization-group evolution of the color charge density of the Color Glass Condensate (CGC). We also argue that these results are easily generalized to collisions of nuclei of different A at central rapidity, or with the same A but at a rapidity far from the central region.

Figures (3)

• Figure 1: The solutions of the Yang-Mills equations in the various parts of the light-cone. The charge distributions propagate along the $x^-$, $x^+$ axes. In the space-like regions behind the charge distributions the fields are just gauge transformations of vacuum fields, rotated by the respective charge densities of the sources. In the forward light-cone, the field at time $\rightarrow\infty$ is given by gauge rotated plane wave solutions $\beta$ and $\beta^i$.
• Figure 2: Schematic $k_\perp$ distribution for particles produced in high-energy $p+A$ collisions (or, more generally, for particles produced in $A_1+A_2$ collisions at rapidity $y$ such that $\chi_1(y)\ll\chi_2(y)$). In the perturbative regime, ${\rm d} N/{\rm d} k_\perp^2{\rm d} y\sim1/k_\perp^4$. Inbetween the saturation scales for the two sources, ${\rm d} N/{\rm d} k_\perp^2{\rm d} y\sim1/k_\perp^2$.
• Figure 3: Schematic rapidity distribution for particles produced in high-energy $p+A$ collisions (or, more generally, for particles produced in $A_1+A_2$ collisions at $A_1\ll A_2$). The upper curve refers to the perturbative regime, the lower curve refers to $k_\perp$ between the saturation scales for the two sources.