Systematic description of hadron's response to non-local QCD probes: Froissart-Gribov projections in analysis of deeply virtual Compton scattering

TL;DR

The paper develops Froissart-Gribov projections for DVCS to map a hadron’s response to cross-channel spin-$J$ probes, extending the formalism to spin-$1/2$ targets. It connects FG projections with GPDs through the dual parametrization and Abel tomography, and derives explicit FG projections for both spinless and spin-$1/2$ cases, including electric and magnetic combinations; it also establishes sum rules linking FG projections to Mellin moments of GPDs and forward-like functions. The authors apply the method to GK, MMS, and KM15 GPD models, comparing with model-independent DVCS CFF extractions, and show that FG projections are observable and discriminative, though currently limited by data precision and missing higher forward-like contributions. The work provides a bridge to lattice QCD via Mellin moments, suggests broad DVCS phenomenology applications, and outlines future directions including mass corrections, non-diagonal processes, and resonance spectroscopy through spin-$J$ probes.

Abstract

We revisit the application of the Froissart-Gribov (FG) projections in the analysis of amplitudes for the Deeply Virtual Compton Scattering (DVCS), providing essential information on generalized parton distributions (GPDs). The pivotal role of these projections in a systematic description of a hadron's response to the string-like QCD probes characterised by different values of angular momentum $J$ is emphasised. For the first time, we establish a relationship between the FG projections and GPDs for spin-$\frac{1}{2}$ targets, and we investigate these quantities in various GPD models. Finally, we provide the first numerical estimates for the FG projections based on the DVCS amplitudes directly extracted from experimental data. We argue the method of the FG projections deserves a broad application in the DVCS phenomenology.

Figures (6)

• Figure 1: A non-local QCD quark probe provides a tower of local operators of spin-$J$ with invariant momentum transfer $\Delta^2=(p'-p)^2$ exciting the target nucleon.
• Figure 2: First weight functions $2(2J+1) \left(\frac{Q_J(1/x)}{x^2}-\delta_{J0} \frac{1}{x} \right)$ entering definition of the $F_J(t)$ projections.
• Figure 3: First weight functions $2 \frac{ 2J+1}{ J(J+1)} \frac{(-1)}{x} \sqrt{\frac{1}{x^2}-1} \, {\cal Q}_J^1(1/x )$ entering the definition of the $F^{(M)}_J(t)$ projections (\ref{['FG_projection_Magnetic']}).
• Figure 4: $F_{J}^{(E),\mathrm{DVCS}}$ for $J=0,2,4$ at $Q^2 = 2\,\mathrm{GeV}^2$ as a function of $t$. First row: results obtained with the GK (solid black), MMS (dashed red) and KM (dotted blue) models. Thin lines denote estimates obtained with only GPD $H$. Second row: as before, with addition of results obtained with the CFFs coming from global analysis of the DVCS data Moutarde:2019tqa (light turquoise bands, corresponding to $68\%$ confidence level). Dark inner bands are for results obtained with only the CFF $\mathcal{H}$.
• Figure 5: $F_{J}^{(M),\mathrm{DVCS}}$ for $J=2,4,6$ at $Q^2 = 2\,\mathrm{GeV}^2$ as a function of $t$. For further description see the caption of Fig. \ref{['fig:modelsDVCSE']}