[Paper Review] Non-Perturbative High-Energy QCD

Arthur Hebecker|ArXiv.org|Nov 8, 2001

Quantum Chromodynamics and Particle Interactions2 references3 citations

TL;DR

This paper reviews non-perturbative high-energy QCD, focusing on the asymptotic rise of hadronic cross sections and the theoretical challenges in understanding them beyond perturbation theory. It examines small-x deep inelastic scattering at HERA, diffraction, and Regge theory, concluding that despite progress in BFKL and saturation models, a first-principles understanding remains elusive, with future precision data from THERA expected to provide critical insights.

ABSTRACT

It is the aim of this talk to review our understanding of the high-energy limit of QCD, focussing, in particular, on recent theoretical developments. After a brief introduction, I will recall why the true high-energy limit of QCD scattering processes is genuinly non-perturbative and why it has so far not been possible to apply lattice methods to this type of physics. Given the experimental fact of slowly rising hadronic cross sections, we are thus faced with a fundamental problem comparable to that of confinement but without the promise of the lattice. During the last years, the experimental side of this field has largely been driven by the HERA accelerator, which has, naturally, also influenced recent theoretical work in high-energy QCD. I will therefore devote the second part of the talk to small-x deep inelastic scattering, in particular the physics of diffraction, and attempt to describe its impact on the wider field of non-perturbative high-energy QCD.

Motivation & Objective

• To understand the non-perturbative high-energy limit of QCD, where standard perturbative and lattice methods fail.
• To analyze the origin of the slowly rising total hadronic cross sections observed experimentally at high center-of-mass energies.
• To explore the role of small-x deep inelastic scattering and diffraction in probing the energy evolution of the proton's color field.
• To assess the viability of theoretical frameworks such as Regge theory, BFKL evolution, and saturation models in describing high-energy scattering.
• To identify open theoretical challenges and future experimental directions, particularly from HERA and THERA, for resolving the high-energy asymptotics of QCD.

Proposed method

• Analyzes the Froissart bound and unitarity constraints to establish theoretical limits on cross-section growth.
• Applies Regge theory to describe high-energy scattering via $ t $-channel reggeon exchange, with amplitudes scaling as $ (s/s_0)^{\alpha(t)} $.
• Uses the dipole picture in high-energy QCD, where the $ \gamma^* $-proton amplitude is expressed as a convolution over dipole cross sections.
• Employs the BFKL equation and nonlinear saturation models (e.g., GLAP, BK) to describe the energy evolution of parton densities at small $ x $.
• Utilizes the stochastic vacuum model to describe soft $ t $-channel exchanges in diffractive processes.
• Evaluates the role of the odderon ($ C=P=-1 $) in diffractive scattering and its experimental constraints from HERA data.

Experimental results

Research questions

• RQ1 Why do hadronic cross sections rise slowly with energy, and what is the underlying field-theoretic mechanism for this asymptotic behavior?
• RQ2 How can the Froissart bound be realized in a dynamical QCD framework, and what role does confinement play in this regime?
• RQ3 To what extent can the dipole picture and BFKL evolution describe the energy dependence of small-x structure functions in deep inelastic scattering?
• RQ4 What is the experimental status of the odderon, and can diffractive processes with tagged leading protons provide a clean probe of its existence?
• RQ5 Can future high-luminosity HERA and THERA experiments resolve the transverse structure of the proton at high energies through diffractive measurements?

Key findings

• The total hadronic cross section rises asymptotically as $ s^{\delta} $ with $ \delta \approx 0.07 $, and the data are currently indistinguishable from $ \ln s $ or $ \ln^2 s $ behavior.
• The Froissart bound limits cross-section growth to $ \ln^2 s $, but no field-theoretic mechanism has been identified to saturate this bound in QCD.
• Regge theory provides a framework for high-energy amplitudes via $ (s/s_0)^{\alpha(t)} $ scaling, but the underlying QCD dynamics remain non-perturbative.
• The dipole model successfully describes HERA data on structure functions, with small dipoles showing faster energy growth consistent with perturbative BFKL evolution.
• HERA data show no evidence for odderon exchange, suggesting its suppression may be due to the proton's quark-diquark structure, though this remains unconfirmed.
• Tagged leading proton measurements offer a clean probe of the proton's color field and could resolve the transverse structure of the proton at high energy.