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Angular and long range rapidity correlations in particle production at high energy

Alex Kovner, Michael Lublinsky

TL;DR

The paper addresses the origin of ridge-type long-range rapidity and angular correlations observed in high-energy pp, pPb, and AA collisions. It develops a high-density QCD/Color Glass Condensate framework linking initial-state wave functions, gluon saturation, and early-time dynamics, and compares Gaussian versus non-Gaussian treatments and different evolution schemes (BK/JIMWLK, KLWMIJ). It finds that correlations arise naturally from boost-invariant gluon fields and the domain structure set by the saturation scale, but that leading 1/Nc and Gaussian approximations can miss important contributions, making Pomeron loops essential for quantitative predictions; the dipole-model and double Pomeron exchange perspectives illustrate different mechanisms and energy dependences. The work highlights the need to go beyond simple approximations to capture fluctuations and loops, guiding future theoretical efforts to provide robust, first-principles descriptions of ridge phenomena in high-energy hadronic collisions.

Abstract

We discuss the general mechanism leading to long-range rapidity and angular correlations produced in high energy collisions (the "ridge"). This effect naturally appears in the high energy QCD and is strongly sensitive to physics of the gluon saturation. We comment on various recent practical realizations of the main idea, paying special attention to $N_c$ counting and stress the relevance of Pomeron loops.

Angular and long range rapidity correlations in particle production at high energy

TL;DR

The paper addresses the origin of ridge-type long-range rapidity and angular correlations observed in high-energy pp, pPb, and AA collisions. It develops a high-density QCD/Color Glass Condensate framework linking initial-state wave functions, gluon saturation, and early-time dynamics, and compares Gaussian versus non-Gaussian treatments and different evolution schemes (BK/JIMWLK, KLWMIJ). It finds that correlations arise naturally from boost-invariant gluon fields and the domain structure set by the saturation scale, but that leading 1/Nc and Gaussian approximations can miss important contributions, making Pomeron loops essential for quantitative predictions; the dipole-model and double Pomeron exchange perspectives illustrate different mechanisms and energy dependences. The work highlights the need to go beyond simple approximations to capture fluctuations and loops, guiding future theoretical efforts to provide robust, first-principles descriptions of ridge phenomena in high-energy hadronic collisions.

Abstract

We discuss the general mechanism leading to long-range rapidity and angular correlations produced in high energy collisions (the "ridge"). This effect naturally appears in the high energy QCD and is strongly sensitive to physics of the gluon saturation. We comment on various recent practical realizations of the main idea, paying special attention to counting and stress the relevance of Pomeron loops.

Paper Structure

This paper contains 15 sections, 77 equations, 9 figures.

Table of Contents

  1. Introduction
  2. Experimental data on di-hadron correlations
  3. The "Ridge" in heavy ion collisions.
  4. Angular correlations in $pp$ @CMS
  5. Ridge in $pPb$ @CMS
  6. Correlations from Theory
  7. General considerations
  8. A little more hands on.
  9. Correlations with Gaussian averaging - the large $N_c$ conundrum.
  10. The dipole model at large $N_c$.
  11. Double Pomeron exchange model
  12. Disappearance of correlations at $Q=0$.
  13. The $Q\ne 0$ contribution.
  14. Conclusions
  15. Derivation of single and double inclusive production probabilities

Figures (9)

  • Figure 1: Soft ridge from STAR The centrality dependence.
  • Figure 2: Hard ridge from PHOBOS
  • Figure 3: Soft ridge from ALICE
  • Figure 4: Di-hadron correlations from CMS Left: minimal bias data; Right: high multiplicity data.
  • Figure 5: Multiplicity dependence of the ridge in $pPb$.
  • ...and 4 more figures