Possibility To Study Photon Scattering By Proton In The Reaction e+p -> e+p+gamma

TL;DR

This work proposes using the reaction $ep\rightarrow ep\gamma$ in kinematics with small transverse momentum transfer to extract the proton Compton scattering cross section and, from it, proton polarizabilities $\alpha_p$ and $\beta_p$. The approach relies on a high-luminosity internal-jet target at a storage ring (NEP) to enable full kinematic reconstruction from exclusive $\gamma$ and recoil-proton final states, enabling discrimination from Bethe-Heitler bremsstrahlung and detailed mapping of $\gamma p$ scattering. Cross-section estimates indicate signal rates of order $\sim 10^3$ events/hour for plausible run conditions, with background suppression achievable by selecting low $Q^2$ and appropriate photon angles. The analysis emphasizes the need for refined theoretical models beyond the equivalent-photon approximation to accurately extract polarizabilities, but foresees a practical path to high-precision determinations of the proton’s elastic structure and the $\,\gamma p\,$-scattering amplitude. Overall, the paper outlines a viable experimental program to probe nucleon structure through high-statistics measurements of $\gamma p$ scattering via $ep$ bremsstrahlung processes at a next-generation storage-ring facility.

Abstract

A theoretical possibility to determine the proton Compton scattering cross section from the reaction $ep\rightarrow epγ$ is studied in the kinematics with a small transversal momentum transfer in the electron leg. With the exception of the region of forward photon directions and extreme photon energies close to the maximum ones or zero, registration of the particles $γ$ and $p$ in the final state can enable one to distinguish the sub-process of the Compton scattering from the electron bremsstrahlung background and, owing to complete kinematical reconstruction of each individual event, measure in detail energy and angular dependence of the $γp$-scattering cross section. The count rate expected with a storage ring like NEP having luminosity $L \approx 2 \cdot 10^{35}$ cm$^{-2}\cdot$ sec$^{-1}$ as projected is $\approx 10^3$ events/hour. Such measurements might help to determine proton polarizabilities with high statistical accuracy.

Figures (31)

• Figure 1: Mechanisms of the reaction $ep \rightarrow ep\gamma$: a) subprocess of photon scattering by proton; b) electron large angle bremsstrahlung.
• Figure 2: $Q$-dependence of the proton Compton scattering contribution (15) (curve a) and electron bremsstrahlung (19) (curve b) at $E$= 200 MeV, $\nu$ = 100 MeV, $\theta_\gamma \,=\, 90^o$. Dot curves present the results in the scalar model for photon radiation by electron (curve $c$) and proton (curve $d$).
• Figure 3: Cross sections for the reaction $ep \rightarrow ep\gamma$ at cut-off $Q_{max}$ = 10 MeV (solid lines) and $Q_{max}$ = 20 MeV (dashed lines). Labels $a$) and $b$) refer to the diagrams contributions (see Fig. \ref{['fig-1']}), (15) and (19), respectively, $E$= 200 MeV. Dot curves present the cross sections in the scalar model with cut-off $Q_{max}$ = 10 MeV for photon radiation by electron (curve $c$) and proton (curve $d$).
• Figure 4: Diagrams for Compton scattering in the scalar model.
• Figure :