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Universality of multi-particle production in QCD at high energies

Fabio Dominguez, Cyrille Marquet, Anna M. Stasto, Bo-Wen Xiao

TL;DR

The paper analyzes the color structure of multi-particle production in high-energy pA-type collisions within the CGC framework. It shows that leading contributions, to all orders in α_s and in the large-N_c limit (except for large rapidity gaps), arise exclusively from dipole and quadrupole Wilson-line correlators, with higher-point objects like sextupoles suppressed by 1/N_c^2. The authors illustrate the result with explicit cases (SIDIS, single hadron production, di-jet production) and provide an inductive proof that adding more final-state particles preserves the dipole/quadrupole description. This leads to a potential universal small-x k_t factorization based on two fundamental correlators, greatly simplifying the treatment of multi-particle final states in dilute-dense collisions.

Abstract

By studying the color structure of multi-particle production processes in p+A-type (dilute-dense) collisions, we find that higher-point functions beyond typical dipoles and quadrupoles, e.g., sextupoles, octupoles, etc., naturally appear in the cross sections, but are explicitly suppressed in the large-N_c limit. We evaluate the sextupole in the McLerran-Venugopalan model and find that, in general, its analytical form cannot be written as combination of dipoles and quadrupoles. Within the Color Glass Condensate framework, we present a proof that in the large-N_c limit, all multi-particle production processes in the collision of a dilute system off a dense can, up to all orders in α_s, be described in terms of only dipoles and quadrupoles.

Universality of multi-particle production in QCD at high energies

TL;DR

The paper analyzes the color structure of multi-particle production in high-energy pA-type collisions within the CGC framework. It shows that leading contributions, to all orders in α_s and in the large-N_c limit (except for large rapidity gaps), arise exclusively from dipole and quadrupole Wilson-line correlators, with higher-point objects like sextupoles suppressed by 1/N_c^2. The authors illustrate the result with explicit cases (SIDIS, single hadron production, di-jet production) and provide an inductive proof that adding more final-state particles preserves the dipole/quadrupole description. This leads to a potential universal small-x k_t factorization based on two fundamental correlators, greatly simplifying the treatment of multi-particle final states in dilute-dense collisions.

Abstract

By studying the color structure of multi-particle production processes in p+A-type (dilute-dense) collisions, we find that higher-point functions beyond typical dipoles and quadrupoles, e.g., sextupoles, octupoles, etc., naturally appear in the cross sections, but are explicitly suppressed in the large-N_c limit. We evaluate the sextupole in the McLerran-Venugopalan model and find that, in general, its analytical form cannot be written as combination of dipoles and quadrupoles. Within the Color Glass Condensate framework, we present a proof that in the large-N_c limit, all multi-particle production processes in the collision of a dilute system off a dense can, up to all orders in α_s, be described in terms of only dipoles and quadrupoles.

Paper Structure

This paper contains 13 sections, 19 equations, 16 figures.

Table of Contents

  1. Introduction
  2. General considerations
  3. Known cases: one and two particles in the final state
  4. SIDIS
  5. Single hadron production in $pA$
  6. Di-jet production in DIS
  7. Di-jet production in $pA$
  8. Three particles in the final state
  9. Proof of the general case
  10. Leading order
  11. Higher order $\alpha_s$ corrections
  12. Conclusion
  13. Large-$N_c$ evaluation of correlators in the McLerran-Venugopalan model

Figures (16)

  • Figure 1: Diagram contributing to the process $q\to qgg$. The dotted line represents the multiple scattering with the target.
  • Figure 2: Diagrams with the amplitude and conjugate amplitude for the process $q\to qg$
  • Figure 3: Alternative representation for the $q\to qg$.
  • Figure 4: Graphical representation of the Fierz identity.
  • Figure 5: Graphical representation of the two amplitudes to be used along the paper.
  • ...and 11 more figures