On the determination of the proton electromagnetic form factors from the DVCS measurements

TL;DR

The paper proposes extracting the proton electromagnetic form factors from exclusive photon leptoproduction data in BH-dominated kinematics, leveraging the direct sensitivity of the Bethe-Heitler amplitude to $F_{1}(t)$ and $F_{2}(t)$. By fitting BH-dominated CLAS data with dipole and $P$-pole parametrizations and, in one case, fixing $F_{2}(t)$ to a known form, the authors obtain constraints on $F_{1}(t)$ and $F_{2}(t)$ and propagate these to the Sachs form factors $G_{E}(t)$ and $G_{M}(t)$, with notable deviations from elastic-scattering fits such as YAHL18, especially for $G_{E}(t)$. The resulting proton radii indicate a smaller charge radius $r_E$ than the PDG elastic values, with the closest agreement to PRad when $F_{2}(t)$ is fixed; the magnetic radius $r_M$ remains broadly consistent with PDG. The work provides a cohesive framework for integrating EP and elastic scattering data to achieve a unified, precise determination of nucleon electromagnetic form factors and offers new insights into the proton radius puzzle.

Abstract

We present a detailed analysis of the proton electromagnetic form factors (FFs) using exclusive photon leptoproduction (EP) data in kinematic regions where the Bethe-Heitler (BH) contribution dominates the deeply virtual Compton scattering (DVCS) cross section. By exploiting the strong sensitivity of the BH amplitude to the Dirac and Pauli FFs, we determine $F_{1}(t)$, $F_{2}(t)$ and the corresponding Sachs FFs from several fitting scenarios based on dipole and $ P $-pole parametrizations, and evaluate the charge and magnetic radii of the proton. We show that EP measurements in the range $ 0.11 < |t| < 0.45 $ GeV$ ^2 $ provide meaningful constraints on $F_{1}(t)$, while offering limited sensitivity to $F_{2}(t)$. Our results systematically favor smaller charge radius values compared with those from traditional elastic electron-proton scattering measurements, consistent with recent high-precision PRad measurements. This study demonstrates that EP measurements, especially when covering smaller values of $|t|$, can serve as a complementary and powerful tool for determining the proton electromagnetic structure and may offer additional insight into the long-standing charge-radius puzzle. The methodology developed here establishes a framework for future combined analyses of EP and elastic electron-proton scattering data which enables a unified determination of the nucleon FFs.

Figures (8)

• Figure 1: EP process shown in terms of laboratory-frame kinematic variables. Figure taken from Ref. Belitsky:2001ns.
• Figure 2: Diagrammatic representation of DVCS and BH processes. In DVCS (left), the real photon is emitted by the struck quark inside the proton, whereas in BH it is emitted from the lepton line, either after (center) or before (right) scattering off the proton. Figure taken from Ref. Adams:2024pxw.
• Figure 3: The ratio of the BH, DVCS, and $\mathcal{I}$ (denoted as INT) contributions to the four-fold EP cross section of Eq. (\ref{['Eq4']}) (denoted as XS), shown separately as functions of $\phi$. The results are calculated using the Gepard package Kumericki:2006xxKumericki:2007saKumericki:2009uqCuic:2023mki with the KM15 Kumericki:2015lhb model at fixed kinematics $Q^2 = 1~\text{GeV}^2$ and $t = -0.1~\text{GeV}^2$, for different values of $x_B$.
• Figure 4: Comparison of the Dirac form factor $F_{1}(t)$ extracted from the five analyses performed in this work with the YAHL18 parametrization Ye:2017gyb. For clarity, only the uncertainty band of Fit 5 is shown, corresponding to the analysis with the largest number of data points.
• Figure 5: Same as Fig. \ref{['fig:F1']}, but for the Pauli form factor $F_{2}(t)$.