Updated flexible global parametrization of generalized parton distributions from elastic and deep inelastic inclusive scattering data

TL;DR

This work delivers UVA2, an updated, physically constrained parametrization of GPDs H and E across quark, antiquark, and gluon sectors, anchored by deep inelastic scattering data, nucleon elastic form factors, and lattice QCD moments. Built on a reggeized spectator framework, UVA2 provides analytic expressions in the kinematic variables $X$, $\zeta$, and $t$ at a common initial scale $Q_0^2=0.58\ \,\mathrm{GeV^2}$, and implements LO PQCD evolution to predict Compton form factors for DVCS and related processes across fixed-target to EIC kinematics. The framework enforces symmetry constraints, polynomiality via Mellin moments, and linking constraints from lattice results to stabilize the otherwise ill-posed GPD extraction, enabling robust predictions of CFFs and 3D partonic structure with quantified uncertainties. The model is public, integrates seamlessly with DVCS phenomenology, and sets the stage for future upgrades to NLO evolution, higher-twist effects, and comprehensive uncertainty analyses, including potential extraction of the gluon GPD from DVCS data at high $Q^2$.

Abstract

An updated flexible parametrization of the generalized parton distributions in the quark, antiquark and gluon sectors is presented using constraints from high precision electron nucleon deep inelastic scattering data, as well as from the $u$, $d$ quark and gluonic contributions to the nucleon electromagnetic elastic form factors. The latter include recently updated lattice QCD moment calculations. The generalized parton distributions in the vector sector are $H$ and $E$. We rigorously constrain the partonic components, $H_{u_v}$, $H_{d_v}$, $H_{\bar{u}}$, $H_{\bar{d}}$, $H_{\bar{s}}$ and $H_{g}$, and the analogous quantities for $E$, with proper uncertainty quantification. These distributions obey leading order perturbative QCD evolution equations in $α_S$. Parametric forms at the initial scale, $Q_o^2 = 0.58$ $\mathrm{GeV}^2$, for both quarks and gluon distributions are presented as a function of the relevant kinematic variables, namely, the parton momentum fraction, $x$, the skewness, $ξ$, and the invariant, $t$. We also present the Compton form factors entering the deeply virtual Compton scattering process in the kinematic regimes for both fixed target and electron-ion collider settings.

Figures (26)

• Figure 1: Schematic representation of a deeply virtual exclusive scattering graph within a QCD factorized scenario, from the reaction $e p \rightarrow e' p'M$, where $M$ can be either a meson or a photon.
• Figure 2: Coefficients of the Compton form factors, $C^+$ (left) and $C^-$ (right). The figure displays the symmetries around $x=0$, displayed in Eq.\ref{['eq:CFFpm']}.
• Figure 3: Left: Integrand, $H_q^+(x,\xi,t) C^+$, in Eq.\ref{['eq:ReH']} compared to the coefficient $C^-$ which shows a similar symmetry; Right: GPD $H^+_u$ used to evaluate the integrand in Eq.(\ref{['eq:ReH']}) shown on the l.h.s..
• Figure 4: Contributions to the kernel of the CFF illustrating the role of the singular term, $1/(x-\xi)$, and the non singular term, $1/(x+\xi)$ in the integration, Eq.\ref{['eq:CFFasymm']}, for $\xi=0.25$. The coefficient $C^-$ is shown because it has the same symmetry as $C^+H^+$.
• Figure 5: Contributions to the real CFF calculated according to Eq.(\ref{['eq:ReH_Gaussian']}) for the $u$-quark, plotted vs. $\zeta$, at the kinematics point, $Q^2 = 4$ GeV$^2$, $t=-0.5$ GeV$^2$. The allowed maximum value of $\zeta=x_{Bj}$ at this kinematic point is $\zeta_{max}=0.51$, which is where the curves subside. The curve denoted "log" corresponds to ${\bf (1)}$ in the text, while"singular" and "non-singular" correspond to terms ${\bf (2)}$ and ${\bf (3)}$, respectively.