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Baryon Stopping and the Valence Quark Distribution at Small x

Kazunori Itakura, Yuri V. Kovchegov, Larry McLerran, Derek Teaney

TL;DR

This work connects baryon stopping in heavy-ion collisions to the small-$x$ evolution of valence quarks within the Color Glass Condensate. By extending Mueller's dipole framework to reggeon exchange, it derives a nonlinear evolution equation for valence-quark distributions that includes saturation effects and solves it in linear and nonlinear regimes. The analysis yields an evolved valence distribution with an anomalous dimension and a Regge-like intercept that can describe BRAHMS net-proton data within uncertainties, thereby providing a perturbative handle on baryon transport at small x. Overall, the paper links high-density QCD dynamics to observable baryon stopping, offering a coherent picture of valence-quark evolution in saturated nuclear matter.

Abstract

We argue that the amount of baryon stopping observed in the central rapidity region of heavy ion collisions at RHIC is proportional to the nuclear valence quark distributions at small x. By generalizing Mueller's dipole model to describe Reggeons we construct a non-linear evolution equation for the valence quark distributions at small x in the leading double-logarithmic approximation. The equation includes the effects of gluon saturation in it. The solution of the evolution equation gives a valence quark distribution function $dn_{val}/dy \sim e^{-(0.4\div0.5) y}$. We show that this y-dependence as well as the predictions of Regge theory are consistent with the net-proton rapidity distribution reported by BRAHMS.

Baryon Stopping and the Valence Quark Distribution at Small x

TL;DR

This work connects baryon stopping in heavy-ion collisions to the small- evolution of valence quarks within the Color Glass Condensate. By extending Mueller's dipole framework to reggeon exchange, it derives a nonlinear evolution equation for valence-quark distributions that includes saturation effects and solves it in linear and nonlinear regimes. The analysis yields an evolved valence distribution with an anomalous dimension and a Regge-like intercept that can describe BRAHMS net-proton data within uncertainties, thereby providing a perturbative handle on baryon transport at small x. Overall, the paper links high-density QCD dynamics to observable baryon stopping, offering a coherent picture of valence-quark evolution in saturated nuclear matter.

Abstract

We argue that the amount of baryon stopping observed in the central rapidity region of heavy ion collisions at RHIC is proportional to the nuclear valence quark distributions at small x. By generalizing Mueller's dipole model to describe Reggeons we construct a non-linear evolution equation for the valence quark distributions at small x in the leading double-logarithmic approximation. The equation includes the effects of gluon saturation in it. The solution of the evolution equation gives a valence quark distribution function . We show that this y-dependence as well as the predictions of Regge theory are consistent with the net-proton rapidity distribution reported by BRAHMS.

Paper Structure

This paper contains 10 sections, 118 equations, 10 figures.

Table of Contents

  1. Introduction
  2. Valence Quark Distribution in the Semi-Classical Approximation
  3. Including nonlinear evolution in the double logarithmic approximation
  4. Solution of the linear DLA equation
  5. Solution of the Full Nonlinear Equation with a Simple Model for $N$
  6. Relation to RHIC data on baryon stopping
  7. Conclusions
  8. The Light Cone Wave Function
  9. Initial Conditions for Quantum Evolution
  10. Solution of the model non-linear evolution equation

Figures (10)

  • Figure 1: The various phases of high density QCD. (For specific numerical estimates see LL). In the Color Glass Condensate the gluon density is large. In the Color Quantum Fluid phase, the density is low, but correlation functions are power law behaved with anomalous dimensions. In the parton gas phase, the density is described by the ordinary evolution equations of DGLAP or BFKL equation.
  • Figure 2: The ladder diagrams for the evolution of baryon number.
  • Figure 3: The ladder diagrams for the evolution of baryon number including the possibility of interaction with the Color Glass Condensate.
  • Figure 4: The phase space distribution of valence quarks and gluons as a function of $p_T$ at fixed $x$.
  • Figure 5: Soft valence quark wave function of a nucleon.
  • ...and 5 more figures