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Has HERA reached a new QCD regime?

E. Gotsman, E. Levin, M. Lublinsky, U. Maor, E. Naftali, K. Tuchin

TL;DR

The paper argues that HERA data indicate a transition into high-density QCD dynamics, proposing a dipole-based saturation framework that matches short-distance pQCD with long-distance Regge/VDM behavior via a two-scale picture. It presents a Glauber–Mueller eikonal model with a calculable saturation scale Q_s(x), incorporates DGLAP evolution for small-distance physics, and demonstrates how shadowing corrections moderate gluon growth while preserving key DIS diffractive observables. While the model reproduces many HERA results and offers testable THERA predictions, it also acknowledges that soft-hard matching approaches can mimic some signatures, underscoring the need for additional observables (e.g., F2 slope, J/ψ energy dependence, γγ^* processes) to distinguish mechanisms. The work outlines concrete future measurements and theoretical links (initial conditions for nonlinear evolution) that will clarify whether gluon saturation truly defines a new QCD regime at high parton densities.

Abstract

These notes are a summary of our efforts to answer the question in the title. Our answer is in the affirmative as: (i) HERA data indicate a large value of the gluon structure function; (ii) no contradictions with the asymptotic predictions of high density QCD have been observed; and (iii) the numerical estimates of our model give a natural description of the size of deviation from the routine DGLAP explanation. We discuss the alternative approaches and possible new experiments.

Has HERA reached a new QCD regime?

TL;DR

The paper argues that HERA data indicate a transition into high-density QCD dynamics, proposing a dipole-based saturation framework that matches short-distance pQCD with long-distance Regge/VDM behavior via a two-scale picture. It presents a Glauber–Mueller eikonal model with a calculable saturation scale Q_s(x), incorporates DGLAP evolution for small-distance physics, and demonstrates how shadowing corrections moderate gluon growth while preserving key DIS diffractive observables. While the model reproduces many HERA results and offers testable THERA predictions, it also acknowledges that soft-hard matching approaches can mimic some signatures, underscoring the need for additional observables (e.g., F2 slope, J/ψ energy dependence, γγ^* processes) to distinguish mechanisms. The work outlines concrete future measurements and theoretical links (initial conditions for nonlinear evolution) that will clarify whether gluon saturation truly defines a new QCD regime at high parton densities.

Abstract

These notes are a summary of our efforts to answer the question in the title. Our answer is in the affirmative as: (i) HERA data indicate a large value of the gluon structure function; (ii) no contradictions with the asymptotic predictions of high density QCD have been observed; and (iii) the numerical estimates of our model give a natural description of the size of deviation from the routine DGLAP explanation. We discuss the alternative approaches and possible new experiments.

Paper Structure

This paper contains 29 sections, 25 equations, 20 figures, 2 tables.

Table of Contents

  1. Problems:
  2. Main idea:
  3. Scales in DIS:
  4. Theoretical status of high parton density QCD:
  5. Model:
  6. Advantages of the model:
  7. Disadvantages of the model:
  8. Asymptotic predictions:
  9. Phenomenological parameters of the model:
  10. $\mathbf{ R^2}$ - size of the target.
  11. $\mathbf{ Q^2_0 = 1/r^2_{sep}}$ - separation parameter.
  12. Solution of the DGLAP evolution equations.
  13. Our model versus HERA data:
  14. $\mathbf{\sigma_{tot}(\gamma^* + p )}$ at low $\mathbf{x}$ and $\mathbf{Q^2}$.
  15. $\mathbf{F_2}$.
  16. ...and 14 more sections

Figures (20)

  • Figure 1: The packing factor for the gluon from HERA experimental data.
  • Figure 2: The parton distribution in the transverse plane. The curve shows the saturation scale $Q_s(x;A)$
  • Figure 3: The pictorial form of the non-linear evolution equation in the hdQCD kinematic region.
  • Figure 4: The $r_{\perp}$ dependence of $\sigma^{dipole}_{tot}$ (Fig. 4-a) and $\sigma^{dipole}_{diff}$ (Fig.4-b).
  • Figure 7: Figs.7-a - 7-b show the effective shrinkage of the diffraction peak in our model for $F_2$ and $xG$
  • ...and 15 more figures