[Paper Review] Pomeron dominance in deeply virtual Compton scattering and the femto holographic image of the proton

D. Müller|ArXiv.org|Apr 30, 2006

Particle physics theoretical and experimental studies14 citations

TL;DR

This paper proposes that soft pomeron dominance in deeply virtual Compton scattering (DVCS) at high energy enables extraction of generalized parton distributions (GPDs) from HERA data, revealing a 3D femto-holographic image of quark and gluon distributions inside the proton. Using double logarithmic approximation and Mellin-Barnes integrals, the study derives transverse spatial distributions showing partons extend beyond the proton's charge radius, with mean squared distances ~40–50% larger than the 0.6 fm charge radius, consistent with experimental t-slopes.

ABSTRACT

The dominance of the soft pomeron in soft high energy scattering and the evolution to the deeply virtual regime, predicted by perturbation theory, allow us to reveal generalized parton distributions from H1 and ZEUS measurements of deeply virtual Compton scattering. These distributions encode a holographic image of the proton, which will be presented.

Motivation & Objective

• To extract generalized parton distributions (GPDs) from HERA measurements of deeply virtual Compton scattering (DVCS) using soft pomeron dominance.
• To reconstruct a 3D femto-holographic image of quark and gluon distributions inside the proton at small longitudinal momentum fraction x.
• To connect non-perturbative soft pomeron input with perturbative QCD evolution in the double logarithmic approximation.
• To explain the observed energy and virtuality dependence of DVCS cross sections via pomeron exchange and anomalous dimension poles.
• To test the consistency of the model with experimental t-slope data from hard vector meson electroproduction and DVCS.

Proposed method

• Utilizes soft pomeron dominance in Regge phenomenology, with trajectory αP(t) = 1.08 + 0.25t, to model non-perturbative input at low scales.
• Applies double logarithmic approximation to resum dominant logarithmic terms in the evolution equations for parton densities.
• Employs Mellin-Barnes integrals to express GPDs in terms of initial conditions with pomeron poles at spin n=1.
• Derives approximate analytic forms for GPDs HΣ and HG at leading order, incorporating scale evolution via αs(Q²)/αs(Q₀) exponentiation.
• Performs Fourier transform of GPDs to obtain transverse spatial distributions ρ(x, b, Q²) in impact parameter space.
• Uses exponential and multipole form factor ansätze to model t-dependence and extract mean squared transverse distances ⟨b²⟩.

Experimental results

Research questions

• RQ1 How does soft pomeron dominance in high-energy scattering enable extraction of generalized parton distributions from DVCS data?
• RQ2 What is the spatial transverse distribution of gluons and sea quarks inside the proton at small x, as reconstructed from GPDs?
• RQ3 To what extent does the double logarithmic approximation reproduce the observed energy and virtuality dependence of DVCS amplitudes?
• RQ4 How do the mean squared transverse distances ⟨b²⟩ of partons compare to the proton's charge radius, and what explains their increase?
• RQ5 Can the t-slope of DVCS cross sections be consistently explained by the interplay of soft pomeron input and perturbative evolution?

Key findings

• The mean squared transverse distance ⟨b²⟩ for partons is found to be 40–50% larger than the proton's charge radius of 0.6 fm, indicating extended spatial distributions.
• The t-slope of the DVCS amplitude, B(W, Q²), follows a logarithmic scaling behavior consistent with experimental observations in hard vector meson electroproduction.
• The double logarithmic approximation successfully reproduces the energy and virtuality dependence of the cross section, with deviations from leading-order predictions reduced by radiative corrections.
• The gluon GPD H^G(x, η=0, t) is significantly broader than the sea quark GPD H^Σ, with the latter being much smaller in magnitude.
• The multipole ansatz leads to a longer tail in the transverse distribution compared to the exponential form, increasing the average ⟨b²⟩ by up to 30%.
• The model's predictions are consistent with HERA data when normalized with a single non-perturbative parameter, validating the soft pomeron input and perturbative evolution framework.