Effective Geometric Corrections in Electron–Nucleus Scattering: Implications for the Lead Beam-Normal Single-Spin Asymmetry

We investigate a geometric interpretation of anomalies observed in electron scattering off heavy nuclei, focusing on the long-standing puzzle of the beam-normal single-spin asymmetry in 208Pb. We introduce a minimal effective parametrization in which small phase- and memory-like modulations of temporal evolution induce direction-dependent corrections to lepton propagators and to the effective nuclear stress tensor. These corrections lead to a modified two-photon exchange amplitude in electron–nucleus scattering and generate measurable effects in spin-dependent observables. The formalism is implemented strictly at the level of effective geometry and scattering amplitudes, without introducing new physical degrees of freedom or violating standard QED principles. Building on established results for proton pressure distributions and nuclear response functions, we embed the geometric correction into a consistent nuclear structure model and derive quantitative predictions for the magnitude and kinematic dependence of the beam-normal asymmetry. The resulting effects are perturbative, constrained by existing bounds from lighter nuclei and electron–proton scattering, yet potentially enhanced in heavy targets due to strong nuclear gradients. Our predictions are falsifiable and can be tested in future precision measurements at facilities such as MAMI and MESA.