Extrapolation of Spin-Dependent Cross Sections to the Real Photon Point at Jefferson Lab

Understanding the spin structure of the nucleon remains a central challenge in QCD, as quarks and gluons contribute to nucleon spin in a non-trivial way. A key approach to studying this structure is through spin-dependent observables at the real photon point (Q² = 0), which provide the foundation for testing sum rules such as the Gerasimov–Drell–Hearn (GDH) relation. Since direct real photon data are limited, we analyze polarized electron scattering data from Jefferson Lab and extrapolate to Q² = 0 in order to recover the real photon limit. Specifically, we extrapolate the transverse–transverse cross section (σ_TT) for the proton, deuteron, and neutron from EG4 expierment, and both σ_TT and σ_LT (transverse–longitudinal) for polarized ³He from E97-110 expierment. Our method uses both linear and quadratic fits of A₁F₁, g₁, and g₂ at fixed W values to determine cross sections at the real photon point. Proton results are consistent with existing photon data, while deuteron and neutron results show an enhanced Δ(1232) resonance. For ³He, σ_TT exhibits a strong Δ(1232) peak and σ_LT is consistent with zero, as expected. This extrapolation technique can also be applied to improve neutron extractions from ³He. With these neutrons, together with the results presented here, future spin sum rule analyses can be compared across different data sources.