[Paper Review] Small-x Deep Inelastic Scattering via the Pomeron in AdS

Richard C. Brower, Marko Djurić+2 more|arXiv (Cornell University)|Apr 2, 2012

Black Holes and Theoretical Physics3 citations

TL;DR

This paper applies the AdS/CFT correspondence with the Pomeron exchange in a hard-wall deformed AdS space to model small-x deep inelastic scattering (DIS) at strong coupling, achieving excellent agreement with HERA data (χ²/d.o.f. = 1.04). It demonstrates that incorporating confinement effects via the hard-wall model significantly improves the fit over pure Pomeron exchange, highlighting the importance of confinement over saturation at LHC energies.

ABSTRACT

We examine the process of Deep Inelastic Scattering (DIS) in the small-x limit, where Pomeron exchange dominates. Using the AdS/CFT correspondence, we study Pomeron exchange in the dual string theory in AdS space, which allows us to study DIS at strong coupling. Two possibilities are examined, a purely conformal model, and a model with a hard-wall cutoff introduced to take into account the effects of confinement. Comparing our calculations with HERA DIS data, we find a very good agreement not only at large $Q^2$ dominated by conformal symmetry, but due to our strong coupling approach which allows us to go beyond traditional pQCD methods, at small $Q^2$ as well, taking into account all available HERA small x data.

Motivation & Objective

• To model small-x deep inelastic scattering (DIS) at strong coupling using the AdS/CFT correspondence.
• To incorporate confinement effects into the Pomeron exchange framework via the hard-wall model in AdS space.
• To test whether the inclusion of confinement improves agreement with HERA experimental data on the structure function F₂(x,Q²).
• To explore the relative importance of saturation and confinement effects in high-energy scattering processes.
• To extend the applicability of the AdS Pomeron framework to exclusive processes like deeply virtual Compton scattering (DVCS).

Proposed method

• Use the BPST Pomeron exchange kernel derived from the SL(2,C) Schrödinger equation in AdS₃, with a hard-wall cutoff at z = z₀ to model confinement.
• Apply the eikonal approximation to compute the imaginary part of the scattering amplitude using the hard-wall Pomeron wave function.
• Construct an approximate ansatz for the eikonal amplitude that includes both short- and long-distance behavior, with a cutoff at b = z₀.
• Fit the model parameters (ρ, g₀², z₀, Q′) to HERA data on F₂(x,Q²) using a phenomenological normalization and momentum-space wave functions.
• Use the optical theorem to relate the total cross section to the imaginary part of the forward amplitude, ensuring consistency with unitarity.
• Extend the framework to exclusive processes like DVCS by modifying the photon wave functions and evaluating the full amplitude beyond the eikonal approximation.

Experimental results

Research questions

• RQ1 Can the AdS/CFT correspondence with a hard-wall deformed AdS space accurately describe small-x DIS data from HERA?
• RQ2 How do confinement effects, introduced via a hard-wall cutoff at z₀, influence the Pomeron exchange and the resulting F₂(x,Q²) structure function?
• RQ3 What is the relative importance of confinement versus saturation effects in high-energy scattering, particularly at LHC energies?
• RQ4 Can the AdS Pomeron framework be extended to exclusive processes like deeply virtual Compton scattering (DVCS) with good agreement to data?
• RQ5 Does the hard-wall Pomeron model interpolate between soft and hard Pomeron behaviors across different Q² scales?

Key findings

• The model achieves a very good fit to HERA DIS data with χ²/d.o.f. = 1.04, indicating high predictive power with minimal phenomenological parameters.
• The fitted hard-wall cutoff scale is z₀ = 6.04 ± 0.15 GeV⁻¹, consistent with the QCD confinement scale ΛQCD ~ 1/z₀.
• The effective Pomeron intercept αP = 1 + εeff varies with Q², showing a smooth interpolation between soft and hard Pomeron behaviors, as confirmed by the data.
• Confinement effects become dominant over saturation effects at LHC energies, as shown in the relative importance analysis in Figure 4.
• Preliminary results suggest the AdS Pomeron framework can also describe exclusive processes like DVCS, with good agreement to experimental data across different Q² values.
• The normalization constant C(τ,z,z′) is fixed by requiring consistency with the t=0 limit, ensuring unitarity and correct normalization of the amplitude.