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 andtotheeffectivenuclearstresstensor. Suchcorrections leadtoa modifiedtwo-photonexchangeamplitude inelectron–nucleusscatteringandgeneratemeasurableeffectsinspin-dependentobservables. Theformalismismotivatedbyphase–memory–extendedeffectiveoperatorparametrizationsbutisimplementedpurelyatthelevelofeffectivegeometryandscatteringamplitudes, withoutintroducingnewdegreesoffreedom.Buildingonestablishedresultsforprotonpressuredistributionsandnuclearresponsefunctions,wederivequantitativepredictionsforthe magnitudeandkinematicdependenceof theasymmetry. Thesepredictionsare falsifiable andcanbetestedinfutureprecisionmeasurementsatfacilitiessuchasMAMIandMESA.