[Paper Review] The AdS Graviton/Pomeron Description of Deep Inelastic Scattering at Small x

Richard C. Brower, Marko Djurić+2 more|arXiv (Cornell University)|Jun 28, 2011

Black Holes and Theoretical Physics3 citations

TL;DR

This paper proposes a holographic description of deep inelastic scattering at small x using the AdS/CFT correspondence, where the Pomeron is identified as a Reggeized graviton in AdS₅. By incorporating confinement via a hardwall model and using an eikonalized AdS₃ representation, the model achieves a precise fit to HERA DIS data, with a best-fit Pomeron intercept of j₀ ≈ 1.22 and χ² = 1.04, demonstrating strong agreement with experimental data across a wide Q² range.

ABSTRACT

In the holographic or AdS/CFT dual to QCD, the Pomeron is identified with a Reggeized Graviton in $AdS_5$. We emphasize the importance of confinement, which in this context corresponds to a deformation of $AdS_5$ geometry in the IR. The holographic Pomeron provides a very good fit to the combined data from HERA for Deep Inelastic Scattering at small $x$, lending new confidence to this AdS dual approach to high energy diffractive scattering.

Motivation & Objective

• To develop a unified description of soft and hard diffractive scattering in QCD using the AdS/CFT correspondence.
• To incorporate confinement effects into the holographic Pomeron model via a hardwall deformation of AdS₅ geometry.
• To explain the Q² dependence of the effective Pomeron intercept observed in HERA data through diffusion in AdS₃.
• To test the viability of the strong-coupling BPST graviton/Pomeron as a phenomenological model for high-energy diffractive processes.
• To lay the foundation for predicting double diffractive Higgs production at the LHC using the same AdS-based framework.

Proposed method

• Model the Pomeron as a Reggeized graviton in AdS₅ space, with the bare intercept j₀ = 1.22 derived from the BPST model.
• Use the holographic optical theorem to relate the DIS cross section to the Pomeron exchange amplitude in impact parameter space (b⊥, z).
• Implement confinement via a hardwall cutoff at z = z_cut, modifying the wave functions and introducing confining images in the eikonal approximation.
• Apply the eikonal representation in transverse AdS₃ space, with the Pomeron kernel satisfying a Schrödinger-like equation involving Lorentz boost generators.
• Derive the structure function F₂(x, Q²) using a delta-function approximation for the wave functions, leading to a diffusion-like form in log z.
• Fit the resulting expression to HERA data from H1 and ZEUS, comparing conformal, hardwall, and eikonalized hardwall models.

Experimental results

Research questions

• RQ1 Can the AdS/CFT correspondence provide a unified description of soft and hard diffractive scattering in QCD at high energy?
• RQ2 How does the inclusion of confinement via a hardwall model affect the description of the effective Pomeron intercept in DIS at small x?
• RQ3 To what extent can the Q² dependence of the effective Pomeron intercept be explained by diffusion in AdS₃ space?
• RQ4 Does the holographic Pomeron model with a strong-coupling graviton description reproduce HERA DIS data better than perturbative QCD approaches?
• RQ5 Can the eikonalized hardwall model restore unitarity while maintaining a good fit to data, and what is its predictive power for LHC diffractive processes?

Key findings

• The hardwall eikonal model achieves the best fit to HERA DIS data, with a reduced chi-squared value of χ² = 1.04.
• The effective Pomeron intercept shows a Q² dependence consistent with diffusion in log z, as predicted by the AdS₃ eikonal model.
• The conformal model fails to describe data at low Q² (< 2–3 GeV²), while the hardwall model significantly improves the fit in this regime.
• The transition scale Q_c²(x) from conformal to confinement behavior increases with 1/x, occurring before saturation effects become dominant.
• The model exhibits asymptotic growth as s^{j₀} with j₀ ≈ 1.22, indicating a need for eikonalization to restore unitarity at very high energies.
• The holographic framework successfully describes the dominance of gluon dynamics at small x, supporting the large N_c approximation.