Non-perturbative high-energy QCD

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.

Reflective Scattering From Unitarity Saturation

“…As it was noted in Introduction, the operator S is defined in the Hilbert space spanned over vectors corresponding to the observable physical particles and the unitarity is formulated in terms of the physical particles. The attempts to construct S-matrix in perturbative QCD [9] have difficulties related to the problem of confinement [8,10] and the problem of the undefined scale dependence entering S-matrix through α s [11]. Moreover, as it was shown in [12], the color fields can be represented by harmonic oscillators (gluons) only in the limit when the strong interaction coupling constant tends to zero, i.e.…”

Froissart bound from gluon saturation

“…Here, however, we are mostly interested in points b ⊥ which are not so far away from the black disk, since we would like to study how the latter expands by incorporating points from the grey area. In this regime, i.e., for b > R(τ, Q 2 ) but such that 4 Strictly speaking, there is no geometric scaling in this regime, but for power counting purposes one can assume that…”

“…The adequacy of perturbation theory even for such a limited purpose -the study of the quantum evolution of the cross-section with s -is still non-trivial [4], and has been in fact disputed in recent papers [9]. It is first of all clear that ordinary perturbation theory, in the form of the BFKL equation [10] -which resums the dominant radiative corrections at high energy, but neglects the non-linear effects associated with high parton densities -, fails to describe the asymptotic behaviour at high energy: The BFKL equation predicts a power-law growth for the total cross section: σ ∼ s ωᾱs , with ω = 4 ln 2 andᾱ s = α s N c /π, which clearly violates the Froissart bound.…”

Remarks on the high-energy behavior of string scattering amplitudes in warped spacetimes

“…This might be a hint on a non-perturbative nature of the high-energy scattering in the Regge limit. Other indications are reviewed in [19].…”