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Deep inelastic scattering at strong coupling from gauge/string duality : the saturation line

Y. Hatta, E. Iancu, A. H. Mueller

TL;DR

This work investigates deep inelastic scattering at strong coupling using gauge/string duality, focusing on unitarity corrections and the saturation line in the high-energy, small-$x$ regime. The authors show that unitarization proceeds via two distinct mechanisms: at relatively low photon virtuality $Q^2$, single Pomeron exchange dominates, while at higher $Q^2$ multiple graviton exchanges take over, making diffractive processes the main contributor to the DIS cross-section. They map a two-branch saturation line in the $\tau$-$\rho$ plane, with a crossover at $(\rho_c,\tau_c)$, and find that beyond this crossover, diffraction saturates the energy-momentum sum rule. The results support a partonic interpretation at strong coupling where all partons have transverse momenta below the saturation scale $Q_s(\tau)$ and occupancy of order one, providing a unified picture bridging weak and strong coupling insights and highlighting the central role of diffractive dynamics in the strong-coupling regime.

Abstract

For gauge theories which admit a dual string description, we analyze deep inelastic scattering at strong 't Hooft coupling and high energy, in the vicinity of the unitarity limit. We discuss the onset of unitarity corrections and determine the saturation line which separates weak scattering from strong scattering in the parameter space of rapidity and photon virtuality. We discover that the approach towards unitarity proceeds through two different mechanisms, depending upon the photon virtuality Q^2 : single Pomeron exchange at relatively low Q^2 and, respectively, multiple graviton exchanges at higher Q^2. This implies that the total cross-section at high energy and large Q^2 is dominated by diffractive processes. This is furthermore suggestive of a partonic description where all the partons have transverse momenta below the saturation momentum and occupation numbers of order one.

Deep inelastic scattering at strong coupling from gauge/string duality : the saturation line

TL;DR

This work investigates deep inelastic scattering at strong coupling using gauge/string duality, focusing on unitarity corrections and the saturation line in the high-energy, small- regime. The authors show that unitarization proceeds via two distinct mechanisms: at relatively low photon virtuality , single Pomeron exchange dominates, while at higher multiple graviton exchanges take over, making diffractive processes the main contributor to the DIS cross-section. They map a two-branch saturation line in the - plane, with a crossover at , and find that beyond this crossover, diffraction saturates the energy-momentum sum rule. The results support a partonic interpretation at strong coupling where all partons have transverse momenta below the saturation scale and occupancy of order one, providing a unified picture bridging weak and strong coupling insights and highlighting the central role of diffractive dynamics in the strong-coupling regime.

Abstract

For gauge theories which admit a dual string description, we analyze deep inelastic scattering at strong 't Hooft coupling and high energy, in the vicinity of the unitarity limit. We discuss the onset of unitarity corrections and determine the saturation line which separates weak scattering from strong scattering in the parameter space of rapidity and photon virtuality. We discover that the approach towards unitarity proceeds through two different mechanisms, depending upon the photon virtuality Q^2 : single Pomeron exchange at relatively low Q^2 and, respectively, multiple graviton exchanges at higher Q^2. This implies that the total cross-section at high energy and large Q^2 is dominated by diffractive processes. This is furthermore suggestive of a partonic description where all the partons have transverse momenta below the saturation momentum and occupation numbers of order one.

Paper Structure

This paper contains 11 sections, 110 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Saturation momentum and geometric scaling in perturbative QCD
  3. DIS at strong coupling
  4. The setup
  5. Limit of the single Pomeron approximation : A lesson from a sum rule
  6. Mapping the high--energy 'phase diagram'
  7. Anomalous dimension of twist--two operators in ${\mathcal{N}=4}$ SYM
  8. The Pomeron propagator
  9. Saturation line from multiple graviton exchanges
  10. Physical discussion: Towards a partonic picture at strong coupling
  11. On the breakdown of the eikonal approximation at ultrahigh energies

Figures (3)

  • Figure 1: A 'phase diagram' for the high energy evolution in pQCD in the presence of unitarity corrections and gluon saturation. (We recall that $\bar{\alpha}_s\equiv\alpha_sN_c/\pi$.)
  • Figure 2: The analytic structure of the integrand in Eq. (4.24) in the complex $j$ plane, together with various contours used when evaluating the integral.
  • Figure 3: Proposed 'phase diagram' for DIS at high energy and strong coupling when $\,\ln N_c^2 \gg \sqrt{\lambda}$. The continuous, thick, line represents the saturation line. The other boundaries are explained in the text.